Engineering Basics Page 93 of 93

Basics

Basic Information as SI-system, Unit converters, Physical constants...

Acceleration of Gravity and Newtons Second Law

Acceleration of gravity and Newtons Second Law - SI and Imperial units.

Acceleration of gravity is one of the most used physical constants - most known from

Newton's Second Law

F = m g (1)

where

F = force

m = mass

g = acceleration of gravity

The force caused by gravity - g - is called weight. Note! Mass - m - is a property.

The acceleration of gravity can be observed by measuring the change velocity of a free falling object:

g = dv / dt (2)

where

dv = change in velocity

dt = change in time

If we drop an object we will observe that it will accelerate to a speed of 9,81 m/s or 32,174 ft/s in one second.

Acceleration of Gravity in SI Units

g = 9.81 m/s2

Acceleration of Gravity in Imperial Units

g = 32.174 ft/s2

Velocity and Distance Traveled of a Free Falling Object

The velocity of a free falling object can be expressed as:

v = g t (3)

where

v = velocity

The distance traveled by a free falling object can be expressed as:

s = 1/2 g t2 (4)

where

s = distance traveled by the object

The velocity and distance traveled by a free falling object:

Time (s)

Velocity

Distance

m/s

ft/s

m

ft

1

9.8

32.2

4.9

16.1

2

19.6

64.3

19.6

64.3

3

29.4

96.5

44.1

144.8

4

39.2

128.7

78.5

257.4

5

49.1

160.9

122.6

402.2

6

58.9

193.0

176.6

579.1

7

68.7

225.2

240.3

788.3

8

78.5

257.4

313.9

1,029.6

9

88.3

289.6

397.3

1,303.0

10

98.1

321.7

490.5

1,608.7

Note! The velocity is achieved without any aero-dynamical resistance (vacuum). Obviously the air resistance will be significant for increasing velocities.

Air Properties

Air properties - temperature, density, specific heat, thermal conductivity, expansion coefficient, kinematic viscosity and Prandtl number for temperatures between -150oC and 400oC.

Common properties for air can be taken from the table below:

Temperature
-
t -
(
oC)

Density
-
ρ -
(kg/m
3)

Specific heat capacity
-
cp -
(kJ/kg.K)

Thermal conductivity
-
l -
(W/m.K)

Kinematic viscosity
ν x 10-6
(m
2/s)

Expansion coefficient
b x 10-3
(1/K)

Prandtl's number
Pr

-150

2.793

1.026

0.0116

3.08

8.21

0.76

-100

1.980

1.009

0.0160

5.95

5.82

0.74

-50

1.534

1.005

0.0204

9.55

4.51

0.725

0

1.293

1.005

0.0243

13.30

3.67

0.715

20

1.205

1.005

0.0257

15.11

3.43

0.713

40

1.127

1.005

0.0271

16.97

3.20

0.711

60

1.067

1.009

0.0285

18.90

3.00

0.709

80

1.000

1.009

0.0299

20.94

2.83

0.708

100

0.946

1.009

0.0314

23.06

2.68

0.703

120

0.898

1.013

0.0328

25.23

2.55

0.70

140

0.854

1.013

0.0343

27.55

2.43

0.695

160

0.815

1.017

0.0358

29.85

2.32

0.69

180

0.779

1.022

0.0372

32.29

2.21

0.69

200

0.746

1.026

0.0386

34.63

2.11

0.685

250

0.675

1.034

0.0421

41.17

1.91

0.68

300

0.616

1.047

0.0454

47.85

1.75

0.68

350

0.566

1.055

0.0485

55.05

1.61

0.68

400

0.524

1.068

0.0515

62.53

1.49

0.68

More about Air Composition!

Air Composition

Dry air is a mechanical mixture of nitrogen, oxygen, carbon dioxide and more

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Air is a mixture of gases, 78% nitrogen and 21% oxygen with traces of water vapor, carbon dioxide, argon, and various other components. We usually model air as a uniform (no variation or fluctuation) gas with properties that are averaged from all the individual components.

Gas

Ratio compared to Dry Air (%)

Molecular Mass
-
M -
(kg/kmol)

Chemical Symbol

Boiling Point
(
oC)

By volume

By weight

Oxygen

20.95

23.20

32.00

O2

-196

Nitrogen

78.09

75.47

28.02

N2

-183

Carbon Dioxide

0.03

0.046

44.01

CO2

-78.5

Hydrogen

0.00005

~ 0

2.02

H2

-252.87

Argon

0.933

1.28

39.94

Ar

-186

Neon

0.0018

0.0012

20.18

Ne

-246

Helium

0.0005

0.00007

4.00

He

-269

Krypton

0.0001

0.0003

83.8

Kr

-153.4

Xenon

9 10-6

0.00004

131.29

Xe

-108.1

The water or vapor content in air varies. The maximum moisture carrying capacity of air depends primarily on the temperature.

The composition of air is unchanged until the height of approximately 10.000 m.

The average air temperature diminishes at the rate of about 0.6
oC for each 100 m vertical height

"One Standard Atmosphere" is defined as the pressure equivalent to that exerted by a 760 mm column of mercury at 0oC sea level and at standard gravity (32.174 ft/sec2).

Common Pressure Units frequently used as alternative to "one Atmosphere"

British Imperial System

Principal system of units

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These units form the basis for the Imperial system formerly used in Commonwealth countries and U.S. customary system used in the US.

The basic difference between dimensional systems is not in the units employed but in the primary dimensions.

Note that the use of four, three, two or even one(!) primary quantities is a human choice and not basic nature.

Imperial Primary Quantities

Primary Quantity

Dimensions

Common Units

Force

F

pound-force

Mass

M

ounce, pound, slug, ton

Length

L

inch, foot, yard
rod, chain, furlong, mile

Time

T

second, minute
hour, day

Imperial Secondary Quantities

Some common imperial secondary quantities:

Primary Quantity

Dimensions

Common Units

Acceleration

L / T2

foot per second squared

Area

L2

square foot, square yard
acre, square mile

Density

M / L3

pounds per cubic foot

Frequency

1/T

cycle per second

Impulse

F T

pound-force second

Momentum

ML / T

pound foot per second

Power

LF / T

foot pound-force per second
horsepower

Pressure

F / L2

pound-force per square inch

Velocity

L / T

foot per second
mile per hour, knot

Volume

L3

pint, quart, gallon
cubic foot, cubic yard

Work

L F

foot pound-force

Unit Converter with the most Common Units

Common converting units for Acceleration, Area, Density, Energy, Energy per unit mass, Force, Heat flow rate, Heat flux, Heat generation per unit volume and many more

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Acceleration

foot/second2, meter/second2, gal, galileo, inch/second2

Area

acre, are, barn, sq.ft., sq.in., foot2, hectare, inch2, mile2, section, meter2, township, yard2, hectares

Density

kg/cubic meter, gram/centimeter3, lmb/cubic inch, lbm/cubic foot, slug/cubic foot, kilogram/cubic meter, lbm/gallon (US liq)

Energy

British Thermal Unit (Btu), calorie, joule, kilojoule, electron volt, erg, foot lbf, foot poundal, kilocalorie, kilowatt hour, watt hour,

Energy per unit mass

Flow - see Volume flow

Force

dyne, kilogram force (kgf), kilopound force, kip, lbf (pound force), ounce force (avoirdupois), poundal, newton

Heat flow rate

Heat flux

Heat generation per unit volume

Heat generation per unit mass

Heat transfer coefficient

Length

feet, meters, centimeters, kilometers, miles, furlongs, yards, micrometers, inches,angstrom, cubit, fathom, foot, hand, league, light year, micron, mil, nautical mile, rod,

Mass, weight

pounds, kilograms, grams, ounces, grains, tons (long), tons (short), tons (metric), carat, grain, ounce mass, pound mass (lbm), slug, tonne

Mass flow rate

Moment of Inertia

Power

horsepower, kilowatt, watt,btu/second, calorie/second, foot lbf/second, kilocalorie/second

Power per unit area

Pressure

atmosphere, centimeters of mercury, foot of water, bar, barye, centimeter of water, dyne/centimeter2, inch of mercury, inch of water, kgf/centimeter2, kgf/meter2, lbf/foot2, lbf/inch2 (psi), millibar, millimeter of mercury, pascal, torr, newton/meter2

Rotation

revolutions,

Specific energy

Specific heat capacity

Specific Volume

Temperature

celsius, rankine, kelvin, centigrade, fahrenheit,

Thermal conductivity

Thermal diffusivity

Thermal resistance

Time

year, month, day, hour, minute, second, millisecond

Torque, Moment

foot-pound torque, newton-meter

Velocity, speed

foot/second, inch/second, meter/second, kilometer/hour, knot, mile/hour,nautical mile per hour

Viscosity dynamic

Viscosity kinematic

Volume

barrel, gallon, cubic centimeter (cm3), cubic feet (foot3), cubic inch (inch3), cubic meter (meter3), cubic yard (yard3), quarts, liters, acre foot, board foot, bushel, cord, cup, dram, fluid ounce, peck, pint, quart, tablespoon, teaspoon,

Volume flow

Weight see Mass

Conversion Chart inch to mm

Convert fractional and/or decimal inches to metric mm or vice versa

The table below can be used to convert between fractional and /or decimal inches and metric millimeters.

Inches

Metric

Fractional

Decimal

mm

.

0.0039

0.1000

.

0.0079

0.2000

.

0.0118

0.3000

1/64

0.0156

0.3969

.

0.0157

0.4000

.

0.0197

0.5000

.

0.0236

0.6000

.

0.0276

0.7000

1/32

0.0313

0.7938

.

0.0315

0.8000

.

0.0354

0.9000

.

0.0394

1.0000

.

0.0433

1.1000

3/64

0.0469

1.1906

.

0.0472

1.2000

.

0.0512

1.3000

.

0.0551

1.4000

.

0.0591

1.5000

1/16

0.0625

1.5875

.

0.0630

1.6000

.

0.0669

1.7000

.

0.0709

1.8000

.

0.0748

1.9000

5/64

0.0781

1.9844

.

0.0787

2.0000

.

0.0827

2.1000

.

0.0866

2.2000

.

0.0906

2.3000

3/32

0.0938

2.3813

.

0.0945

2.4000

.

0.0984

2.5000

7/64

0.1094

2.7781

.

0.1181

3.0000

1/8

0.1250

3.1750

.

0.1378

3.5000

9/64

0.1406

3.5719

5/32

0.1563

3.9688

.

0.1575

4.0000

11/64

0.1719

4.3656

.

0.1772

4.5000

3/16

0.1875

4.7625

.

0.1969

5.0000

13/64

0.2031

5.1594

.

0.2165

5.5000

7/32

0.2188

5.5563

15/64

0.2344

5.9531

.

0.2362

6.0000

1/4

0.2500

6.3500

.

0.2559

6.5000

17/64

0.2656

6.7469

.

0.2756

7.0000

9/32

0.2813

7.1438

.

0.2953

7.5000

19/64

0.2969

7.5406

5/16

0.3125

7.9375

.

0.3150

8.0000

21/64

0.3281

8.3344

.

0.3346

8.5000

11/32

0.3438

8.7313

.

0.3543

9.0000

23/64

0.3594

9.1281

.

0.3740

9.5000

3/8

0.3750

9.5250

25/64

0.3906

9.9219

.

0.3937

10.0000

13/32

0.4063

10.3188

.

0.4134

10.5000

27/64

0.4219

10.7156

.

0.4331

11.0000

7/16

0.4375

11.1125

.

0.4528

11.5000

29/64

0.4531

11.5094

15/32

0.4688

11.9063

.

0.4724

12.0000

31/64

0.4844

12.3031

.

0.4921

12.5000

1/2

0.5000

12.7000

.

0.5118

13.0000

33/64

0.5156

13.0969

17/32

0.5313

13.4938

.

0.5315

13.5000

35/64

0.5469

13.8906

.

0.5512

14.0000

9/16

0.5625

14.2875

.

0.5709

14.5000

37/64

0.5781

14.6844

.

0.5906

15.0000

19/32

0.5938

15.0813

39/64

0.6094

15.4781

.

0.6102

15.5000

5/8

0.6250

15.8750

.

0.6299

16.0000

41/64

0.6406

16.2719

.

0.6496

16.5000

21/32

0.6563

16.6688

.

0.6693

17.0000

43/64

0.6719

17.0656

11/16

0.6875

17.4625

.

0.6890

17.5000

45/64

0.7031

17.8594

.

0.7087

18.0000

23/32

0.7188

18.2563

.

0.7283

18.5000

47/64

0.7344

18.6531

.

0.7480

19.0000

3/4

0.7500

19.0500

49/64

0.7656

19.4469

.

0.7677

19.5000

25/32

0.7813

19.8438

.

0.7874

20.0000

51/64

0.7969

20.2406

.

0.8071

20.5000

13/16

0.8125

20.6375

.

0.8268

21.0000

53/64

0.8281

21.0344

27/32

0.8438

21.4313

.

0.8465

21.5000

55/64

0.8594

21.8281

.

0.8661

22.0000

7/8

0.8750

22.2250

.

.8858

22.5000

57/64

.89063

22.6219

.

.9055

23.0000

29/32

.90625

23.0188

59/64

.92188

23.4156

.

.9252

23.5000

15/16

.93750

23.8125

.

.9449

24.0000

61/64

.95313

24.2094

.

.9646

24.5000

31/32

.96875

24.6063

.

.9843

25.0000

63/64

.98438

25.0031

1

1.000

25.40

.

1.0039

25.5000

.

1.0236

26.0000

.

1.0433

26.5000

.

1.0630

27.0000

.

1.0827

27.5000

.

1.1024

28.0000

.

1.1220

28.5000

.

1.1417

29.0000

.

1.1614

29.5000

.

1.1811

30.0000

.

1.2205

31.0000

1 1/4

1.2500

31.7500

.

1.2598

32.0000

.

1.2992

33.0000

.

1.3386

34.0000

.

1.3780

35.0000

.

1.4173

36.0000

.

1.4567

37.0000

.

1.4961

38.0000

1 1/2

1.5000

38.1000

.

1.5354

39.0000

.

1.5748

40.0000

.

1.6142

41.0000

.

1.6535

42.0000

.

1.6929

43.0000

.

1.7323

44.0000

1 3/4

1.7500

44.4500

.

1.7717

45.0000

.

1.8110

46.0000

.

1.8504

47.0000

.

1.8898

48.0000

.

1.9291

49.0000

.

1.9685

50.0000

2

2.0000

50.8000

.

2.0079

51.0000

.

2.0472

52.0000

.

2.0866

53.0000

.

2.1260

54.0000

.

2.1654

55.0000

.

2.2047

56.0000

.

2.2441

57.0000

2 1/4

2.2500

57.1500

.

2.2835

58.0000

.

2.3228

59.0000

.

2.3622

60.0000

.

2.4016

61.0000

.

2.4409

62.0000

.

2.4803

63.0000

2 1/2

2.5000

63.5000

.

2.5197

64.0000

.

2.5591

65.0000

.

2.5984

66.0000

.

2.6378

67.0000

.

2.6772

68.0000

.

2.7165

69.0000

2 3/4

2.7500

69.8500

.

2.7559

70.0000

.

2.7953

71.0000

.

2.8346

72.0000

.

2.8740

73.0000

.

2.9134

74.0000

.

2.9528

75.0000

.

2.9921

76.0000

3

3.0000

76.2000

.

3.0315

77.0000

.

3.0709

78.0000

.

3.1102

79.0000

.

3.1496

80.0000

.

3.1890

81.0000

.

3.2283

82.0000

.

3.2677

83.0000

.

3.3071

84.0000

.

3.3465

85.0000

.

3.3858

86.0000

.

3.4252

87.0000

.

3.4646

88.0000

3 1/2

3.5000

88.9000

.

3.5039

89.0000

.

3.5433

90.0000

.

3.5827

91.0000

.

3.6220

92.0000

.

3.6614

93.0000

.

3.7008

94.0000

.

3.7402

95.0000

.

3.7795

96.0000

.

3.8189

97.0000

.

3.8583

98.0000

.

3.8976

99.0000

.

3.9370

100.0000

4

4.0000

101.6000

.

4.3307

110.0000

4 1/2

4.5000

114.3000

.

4.7244

120.0000

5

5.0000

127.0000

.

5.1181

130.0000

.

5.5118

140.0000

.

5.9055

150.0000

6

6.0000

152.4000

.

6.2992

160.0000

.

6.6929

170.0000

.

7.0866

180.0000

.

7.4803

190.0000

.

7.8740

200.0000

8

8.0000

203.2000

.

9.8425

250.0000

10

10.0000

254.0000

20

20.0000

508.0000

30

30.0000

762.0000

40

40.0000

1016.000

60

60.0000

1524.000

80

80.0000

2032.000

100

100.0000

2540.000



Density, Specific Weight and Specific Gravity

An introduction and definition of density, specific weight and specific gravity - formulas with examples

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Density

Density is defined as an objects mass per unit volume. Mass is a property.

The density can be expressed as

ρ = m / V = 1 / vg (1)

where

ρ = density (kg/m3)

m = mass (kg)

V = volume (m3)

vg = specific volume (m3/kg)

The SI units for density are kg/m3. The imperial (BG) units are lb/ft3 (slugs/ft3). While people often use pounds per cubic foot as a measure of density in the U.S., pounds are really a measure of force, not mass. Slugs are the correct measure of mass. You can multiply slugs by 32.2 for a rough value in pounds.

The higher the density, the tighter the particles are packed inside the substance. Density is a physical
property constant at a given temperature and density can help to identify a substance.

Example - Use the Density to Identify the Material:

An unknown liquid substance has a mass of 18.5 g and occupies a volume of 23.4 ml. (milliliter).

The density can be calculated as

ρ = [18.5 (g) / 1000 (g/kg)] / [23.4 (ml) / 1000 (ml/l) 1000 (l/m3) ]

    = 18.5 10-3 (kg) / 23.4 10-6 (m3)

    = 790 kg/m3

If we look up densities of some common substances, we can find that ethyl alcohol, or ethanol, has a density of 790 kg/m3. Our unknown liquid may likely be ethyl alcohol!

Example - Use Density to Calculate the Mass of a Volume

The density of titanium is 4507 kg/m3 . Calculate the mass of 0.17 m3 titanium!

m = 0.17 (m3) 4507 (kg/m3)

    = 766.2 kg

Specific Weight

Specific Weight is defined as weight per unit volume. Weight is a force.

Specific Weight can be expressed as

γ = ρ g (2)

where

γ = specific weight (kN/m3)

g = acceleration of gravity (m/s2)

The SI-units of specific weight are kN/m3. The imperial units are lb/ft3. The local acceleration g is under normal conditions 9.807 m/s2 in SI-units and 32.174 ft/s2 in imperial units.

Example - Specific Weight Water

Specific weight for water at 60 oF is 62.4 lb/ft3 in imperial units and 9.80 kN/m3 in SI-units.

Example - Specific Weight Some other Materials

Product

Specific Weight - γ

Imperial Units
(lb/ft
3)

SI Units
(kN/m
3)

Ethyl Alcohol

49.3

7.74

Gasoline

42.5

6.67

Glycerin

78.6

12.4

Mercury

847

133

SAE 20 Oil

57

8.95

Seawater

64

10.1

Water

62.4

9.80

Specific Gravity

The Specific Gravity - SG - is a dimensionless unit defined as the ratio of density of the material to the density of water at a specified temperature. Specific Gravity can be expressed as

SG = = ρ / ρH2O (3)

where

SG = specific gravity

ρ = density of fluid or substance (kg/m3)

ρH2O = density of water (kg/m3)

It is common to use the density of water at 4 oC (39oF) as reference - at this point the density of water is at the highest.

Since Specific Weight is dimensionless it has the same value in the metric SI system as in the imperial English system (BG). At the reference point the Specific Gravity has same numerically value as density.

Example - Specific Gravity

If the density of iron is 7850 kg/m3, 7.85 grams per cubic centimeter (cm3), 7.85 kilograms per liter, or 7.85 metric tons per cubic meter - the specific gravity of iron is:

SG = 7850 kg/m3/ 1000 kg/m3

    = 7.85

(the density of water is 1000 kg/m3)

Equilibrium

Mechanical, thermal, electrostatic, phase and chemical equilibrium

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Systems have reached equilibrium when there is no change in the macroscopic state of the systems. Equilibrium of some common systems are described below. Note that the properties describing the state of a system depends on the boundary of the system.

Mechanical Equilibrium

Mechanical systems have reached equilibrium when there is no movement between the systems.

Thermal Equilibrium

Thermodynamic systems have reached equilibrium when there is no heat transfer between the systems. To reach this state of equilibrium the systems must have the same temperature.

Electrostatic Equilibrium

Electrostatic systems have reached equilibrium when there is no net charge flow between the systems.

Phase Equilibrium

Material substance systems have reached equilibrium when there is no net phase transformation, like melting, between the systems.

Chemical Equilibrium

Chemical systems have reached equilibrium when there is no net chemical reaction between the system

Flow Units Converter

Convert between common used volume flow units like gpm, liter/sec, cfm, m3/h and more - online flow unit converter

Flow Units Converting Table

The tables below can used to convert between some common used flow units:

multiply by

Convert to

US gpd

US gpm

cfm

IMP gpd

IMP gpm

Convert from

m3/s

22800000

15852

2119

19000000

13200

m3/min

380000

264.2

35.32

316667

220

m3/h

6333.3

4.403

0.589

5277.8

3.67

liter/sec

22800

15.852

2.119

19000

13.20

liter/min

380

0.2642

0.0353

316.7

0.22

liter/h

6.33

0.0044

0.00059

5.28

0.0037

US gpd

1

0.000695

0.000093

0.833

0.000579

US gpm

1438.3

1

0.1367

1198.6

0.833

cfm

10760.3

7.48

1

8966.9

6.23

Imp gpd

1.2

0.00083

0.00011

1

0.00069

Imp gpm

1727.3

1.2

0.161

1439.4

1

 

multiply by

Convert to

m3/s

m3/min

m3/h

liter/sec

liter/min

liter/h

Convert from

m3/s

1

60

3600

1000

60000

3600000

m3/min

0.0167

1

60

16.67

1000

60000

m3/h

0.000278

0.0167

1

0.278

16.67

1000

liter/sec

0.001

0.06

3.6

1

60

3600

liter/min

0.0000167

0.001

0.06

0.0167

1

60

liter/h

2.7 10-7

0.000017

0.001

0.00028

0.0167

1

US gpd

4.39 10-8

0.0000026

0.000158

0.000044

0.0026

0.158

US gpm

0.000063

0.00379

0.227

0.0630

3.785

227.1

cfm

0.00047

0.028

1.699

0.472

28.32

1698.99

Imp gpd

5.26 10-8

0.0000032

0.000189

0.0000526

0.00316

0.1895

Imp gpm

0.000076

0.0046

0.272

0.076

4.55

272.7

Select the "from" unit in the left column and  follow the row until the "to" unit column. 

Example - Convert from m3/h to Imperial gallons per minute (Imp gpm)

Volume flow in m3/h must be multiplied with

3.67

to convert to Imp gpm.

Alternatively use the online fluid flow calculator below.

Alternative Flow Units

1 Cubic metres/second =  22643 Barrel (oil)/h
1 Cubic metres/second =  6.29 Barrel (oil)/s
1 Cubic metres/second =  3.6 10
9 Cubic centimeter/hour
1 Cubic metres/second =  6 10
7 Cubic centimetre/minute
1 Cubic metres/second =  10
6 Cubic centimetre/second
1 Cubic metres/second =  127133 Cubic feet/hour
1 Cubic metres/second =  2119 Cubic feet/minute
1 Cubic metres/second =  35.3 Cubic feet/second
1 Cubic metres/second =  3600 Cubic meters/hour
1 Cubic metres/second =  60 Cubic meters/minute
1 Cubic metres/second =  4709 Cubic yards/hour
1 Cubic metres/second =  78.5 Cubic yards/minute
1 Cubic metres/second =  1.31 Cubic yards/second
1 Cubic metres/second =  13198 Gallon water/minute (UK)
1 Cubic metres/second =  15850 Gallon water/minute (US)
1 Cubic metres/second =  951019 Gallons (FI)/hour (US)
1 Cubic metres/second =  15850 Gallons (FI)/minute (US)
1 Cubic metres/second =  264.2 Gallons (FI)/second (US)
1 Cubic metres/second =  19005330 Gallons/day (UK)
1 Cubic metres/second =  791889 Gallons/hour (UK)
1 Cubic metres/second =  13198 Gallons/minute (UK)
1 Cubic metres/second =  219.97 Gallons/second (UK)
1 Cubic metres/second =  3600000 Litre/hour
1 Cubic metres/second =  60000 Litre/minute
1 Cubic metres/second =  1000 Litre/second
1 Cubic metres/second =  131981 Pounds water/minute
1 Cubic metres/second =  93097 Ton of water (metric)/24hrs

Horsepower Definition for Pumps, Fans and Turbines

A definition of British Horse Power for pumps, fans and turbines and how to convert to other common units

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Horsepower

Horsepower is the imperial (British) unit of power. A horsepower is the ability to do work at the rate of

Note that Power is "Work per unit time" and work is "Force through distance". In gravity systems Force is Weight - mass multiplied with gravity.

The total horsepower developed by water falling from a given height is the product of the mass flow rate in pounds per minute times the falling height in feet divided by 33,000. It can be expressed as:

Php = mmin h g / 33000 (1)

where

Php = power (horsepower, hp)

mmin = mass flow rate per minute (lbm/min)

h = head or height (ft)

g = acceleration of gravity (32 ft/s2)

(1) can alternatively be expressed as:

Php = msec h g / 550 (1b)

where

msec = mass flow rate per second (lbm/s)

(1) can also be expressed as:

Php = γ Q h / 33000 (1c)

where

Q = volume flow rate (ft3/min)

γ = specific weight (lbf/ft3) (weight is force)

Water Horsepower for Flow in gal/min

Water horsepower for flow in gal/min can be expressed as:

Pwhp = SG Qgal h / 3960 (1d)

where

Q = volume flow rate (gpm)

SG = specific gravity

h = head (ft)

SG for water is 1.001 at 32oF and 0.948 at 240oF.

Shaft or Brake Horsepower

The brake horsepower is the amount of real horsepower going to the pump, not the horsepower used by the motor. In the metric system the unit kilowatts (kW) is used.

Due to hydraulic, mechanical and volumetric losses in a pump or turbine the actual horsepower available for work on or from the fluid is less than the total horsepower supplied.

Shaft or Brake Horsepower for a Pump or Fan

The brake horse power - bhp - for a pump or fan can be expressed as:

Pbhp = ( γ Q h / 33000 ) / η (2)

where

Pbhp = brake horse power (horsepower, hp)

Q = volume flow rate (ft3/min, cfm)

η = overall efficiency

Shaft or Brake Horsepower for a Turbine

The brake horse power - bhp - for a turbine can be expressed as:

Pbhp = η ( γ Q h / 33000 ) (2b)

Input Horsepower to the Electrical Motor

The input horsepower to the electrical motor for a pump or fan can be expressed as:

Php_el = Pbhp / ηe (3)

or

Php_el = (m h / 33000) / (η ηe) (3b)

where

Php_el = input power to the electrical motor

ηe = mechanical efficiency of the electrical motor

Horsepower in Kilowatts and other Units

Horsepower can be converted to other common units as:

Transforming horsepower to kiloWatt can be expressed as:

PkW = 0.746 Php (4)

where

PkW = power (kW)

Together with the equations above it's possible to express (4) in many common combinations as:

PkW = 0,746 (m h / 33000) / η ηe (5)

Inches and Decimal Equivalents

Decimal equivalents of eights, sixteenths, thirty-seconds and sixty-fourths of an inch

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The table below can be used to convert inches to the decimal equivalents or vice verca.

Eights

1/8

0.125

1/4

0.250

3/8

0.375

1/2

0.500

5/8

0.625

3/4

0.750

7/8

0.875

Sixteenths

1/16

0.0625

3/16

0.1875

5/16

0.3125

7/16

0.4375

9/16

0.5625

11/16

0.6875

13/16

0.8125

15/16

0.9375

Thirty-seconds

1/32

0.03125

3/32

0.09375

5/32

0.15625

7/32

0.21875

9/32

0.28125

11/32

0.34375

13/32

0.40625

15/32

0.46875

17/32

0.53125

19/32

0.59375

21/32

0.65625

23/32

0.71875

25/32

0.78125

27/32

0.84375

29/32

0.90625

31/32

0.96875

Sixty-fourths

1/64

0.015625

3/64

0.046875

5/64

0.078125

7/64

0.109375

9/64

0.140625

11/64

0.171875

13/64

0.203125

15/64

0.234375

17/64

0.265625

19/64

0.296875

21/64

0.328125

23/64

0.359375

25/64

0.390625

27/64

0.421875

29/64

0.453125

31/64

0.484375

33/64

0.515625

35/64

0.546875

37/64

0.578125

39/64

0.609375

41/64

0.640625

43/64

0.671875

45/64

0.703125

47/64

0.734375

49/64

0.765625

51/64

0.796875

53/64

0.828125

55/64

0.859375

57/64

0.890625

59/64

0.921875

61/64

0.953125

63/64

0.984375

Length Units Converter

Convert between common length units like meters, feet, inches, nautical miles and many more

Length Unit Conversion Table

The table below can be used to convert between some common length units:

Multiply with

Convert from

Convert to

inches

feet

yards

miles

nautical miles

cables

meter

39.37

3.28

1.09

6.21 10-4

5.4 10-3

5.4 10-3

decimeter

3.937

0.328

0.109

6.21 10-5

5.4 10-4

5.4 10-4

centimeter

0.394

0.0328

0.0109

6.21 10-6

5.4 10-5

5.4 10-5

millimeter

0.039

0.00328

0.00109

6.21 10-7

5.4 10-6

5.4 10-6

micrometer

3.9 10-5

3.28 10-6

1.09 10-6

6.2 10-10

5.4 10-10

5.4 10-9

nanometer

3.9 10-8

3.28 10-9

1.09 10-9

6.21 10-13

5.4 10-13

5.4 10-12

ångströms

3.9 10-9

3.28 10-10

1.09 10-10

6.21 10-14

5.4 10-14

5.4 10-13

hectometer

3937

328

109.4

0.0621

0.054

0.54

kilometer

39370

3280

1094

0.621

0.54

0.54

inch

1

0.083

0.0278

1.58 10-5

1.37 10-5

1.37 10-4

foot

12

1

0.33

1.89 10-4

1.65 10-4

1.65 10-3

yard

36

3

1

5.7 10-4

4.9 10-4

4.9 10-3

mile

63398

5283

1761

1

0.87

8.7

nautical mile

72908

6076

2025

1.15

1

10

cable

7291

607.6

203

0.11

0.1

1


Multiply with

Convert from

Convert to

meters

decimeters

centimeters

millimeters

micrometers

nanometers

ångströms

hectometers

kilometers

meter

1

10

100

1000

106

109

1010

0.01

0.001

decimeter

0.1

1

10

100

105

108

109

0.001

0.0001

centimeter

0.01

0.1

1

10

104

107

108

0.0001

0.00001

millimeter

0.001

0.01

0.1

1

103

106

107

0.00001

0.000001

micrometer

10-6

10-5

10-4

10-3

1

103

104

10-8

10-9

nanometer

10-9

10-8

10-7

10-6

10-3

1

10

10-11

10-12

ångströms

10-10

10-9

10-8

10-7

10-4

0.1

1

10-12

10-13

hectometer

100

1000

104

105

108

1011

1012

1

0.1

kilometer

1000

104

105

106

109

1012

1013

10

1

inch

0.0254

0.254

2.54

25.4

2.54 104

2.54 107

2.54 108

2.54 10-4

2.54 10-5

foot

0.3048

3.048

30.48

304.8

3.05 105

3.05 108

3.05 109

3.05 10-3

3.05 10-4

yard

0.914

9.14

91.4

914

9.14 105

9.14 108

9.14 109

9.14 10-3

9.14 10-4

mile

1610

1.61 104

1.61 105

1.61 106

1.61 107

1.61 1012

1.61 1013

1.61 102

1.61

nautical mile

1852

1.85 104

1.85 105

1.85 106

1.85 107

1.85 1012

1.85 1013

1.85 102

1.85

cable

185

1.85 103

1.85 104

1.85 105

1.85 106

1.85 1011

1.85 1012

1.85

0.185

Note that since the metrification of the inch the inch has been specified as exactly 25.4 mm.

Other Length Units

1 meter = 118.106 barleycoms

Mass and Weight

What is weight and what is mass? An explanation of the difference between weight and mass

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Mass and weight are two common, and often misused and misunderstood terms in mechanics and fluid mechanics.

The fundamental relation between the mass and the weight is defined from the Newton's Second Law and can be expressed in SI-units as

F = m a (1)

where

F = force (N)

m = mass (kg)

a = acceleration (m/s2)

Mass

Mass is a measure of the amount of material in an object, being directly related to the number and type of atoms present in the object. Mass does not change with a body's position, movement or alteration of its shape unless material is added or removed.

The mass is a fundamental property of an object, a numerical measure of its inertia and a fundamental measure of the amount of matter in the object.

Weight

Weight is the gravitational force acting on a body mass. Transforming Newton's Second Law regarding the weight as a force due to gravity gives

w = m g (2)

where

w = weight (N)

m = mass (kg)

g = acceleration of gravity (m/s2)

The handling of mass and weight depends on the systems of units that is used. The most common systems of units are the

The International System - SI

In the SI system the mass unit is the kg and since the weight is a force - the weight unit is the newton (N). Equation (2) for a body with 1 kg mass can then be expressed as:

w = 1 (kg) 9.807 (m/s2) = 9.807 (N) (2b)

where

9.807 (m/s2) = standard gravity close to earth in the SI system

As a result:

The British Gravitational System - BG

The British Gravitational System of units is used by engineers in the English-speaking world with the same relation to the foot - pound - second system as the meter kilogram - force second system (SI) has to the meter - kilogram - second system. For engineers who deals with forces, instead of masses, it's convenient to use a system that has as its base units length, time, and force, instead of length, time and mass.

The three base units are the foot, the second, and the pound-force.

In the BG system the mass unit is the slug and is defined from the Newton's Second Law (1). The unit of mass, the slug, is derived from the pound-force by defining it as the mass that will accelerate at 1 foot per second per second when a 1 pound-force acts upon it:

1 lb = (1 slug)(1 ft/s2)

In other words, 1 lb force acting on 1 slug mass will give the mass an acceleration of 1 ft/s2.

The weight of the mass from equation (2) in BG units can be expressed as:

w (lb) = m (slugs) g (ft/s2)

With a standard gravity 32.174 ft/s2 - the mass of 1 slug weights 32.174 lb.

The English Engineering System - EE

In the English Engineering system of units the primary dimensions are are force, mass, length, time, and temperature. The units for force and mass are defined independently:

In the EE system 1 lb of force will give a mass of 1 lbm a standard acceleration of 32.174 ft/s2.

Since the EE system operates with these units of force and mass, the Newton's Second Law can be modified to

F = m a / gc (3)

where

gc = a proportionality constant

or transformed to weight

w = m g / gc (4)

The proportionality constant gc makes it possible to define suitable units for force and mass. We can transform (4) to

1 lb = (1 lbm)(32.174 ft/s2) / gc

or

gc = (1 lbm)(32.174 ft/s2)/(1 lb)

Since 1 lb force gives a mass of 1 lbm an acceleration of 32.174 ft/s2 and a mass of 1 slug an acceleration of 1 ft/s2, then

1 slug = 32,174 lbm

Example - Weight versus Mass

A car's mass is 1,644 kg. The weight can be calculated:

w = (1,644 kg)(9.807 m/s2) = 16.122,7 N = 16.1 kN

In other words - there is a force of 16.1 kN between the car and the earth.

Moment of Inertia

The moment of inertia of a body depends on the mass of the object, its shape and its relative point of rotation

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Moment of inertia is the name given to rotational inertia. For a point mass the moment of inertia is just the mass times the square of perpendicular distance to the rotation axis

I = m r2 (1)

where

I = moment of inertia (lbm ft2, kg m2)

m = mass (lbm, kg)

r = distance between axis and rotation mass (ft, m)

That point mass relationship are basis for all other moments of inertia since any object can be built up from a collection of point masses.

I = ∑i mi ri2 = m1 r12 + m2 r22 + ..... (2)

Some Typical Bodies and their Moment of Inertia

Inertia of Cylinder

Thin-walled hollow cylinder:

A thin-walled hollow cylinder is comparable with the point mass (1) and can be expressed as:

I = m r2 (3a)

where

m = mass of the hollow (lbm, kg)

r = distance between axis and the thin walled hollow (ft, m)

ro = distance between axis and outside hollow (ft, m)

Hollow cylinder:

I = 1/2 m ( ri2 + ro2) (3b)

where

m = mass of hollow (lbm, kg)

ri = distance between axis and inside hollow (ft, m)

ro = distance between axis and outside hollow (ft, m)

Solid cylinder:

I = 1/2 m r2 (3c)

where

m = mass of cylinder (lbm, kg)

r = distance between axis and outside cylinder (ft, m)

Inertia of Sphere

Thin-walled hollow sphere:

I = 2/3 m r2 (4a)

where

m = mass of sphere hollow (lbm, kg)

r = distance between axis and hollow (ft, m)

Solid sphere:

I = 2/5 m r2 (4b)

where

m = mass of sphere (lbm, kg)

r = radius in sphere (ft, m)

Moment of Inertia - General Formula

The Inertia formula may be generally expressed as

I = k m r2 (5)

where

k = inertial constant - depending on the shape of the body

Natural Trigonometric Functions

Sine, Cosine and Tangent - Natural Trigonometric Functions

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Natural trigonometric functions are expressed as

sin θ = cos (π / 2 - θ) (1)

cos θ = cos (π / 2 - θ) (2)

tan θ = sin θ / cos θ = 1 / cot θ = cot (π / 2 - θ) (3)

cot = 1 / tan θ = cos θ / sin θ = tan(π / 2 - θ) (4)

Trigonometric functions ranging 0 to 90 degrees are tabulated below:

Pressure Units Converter

Convert between common pressure units like Pa,  bar, atmosphere, pound square feet, psi and more - with converting tables

Pressure Converting Tables

The tables below can be used to convert between some common pressure units:

Multiply by

Convert from

Convert to

Pa (N/m2)

bar

atmosphere

mm Hg

mm H2O

m H2O

kg/cm2

Pa (N/m2)

1

10-5

9.87 10-6

0.0075

0.1

10-4

1.02 10-5

bar

105

1

0.987

745

1.0197 104

10.197

1.0197

atmosphere

1.01 105

1.013

1

759.9

10132

10.13

1.03

mm Hg

133.3

1.33 10-3

1.32 10-3

1

13.3

0.013

1.36 10-3

mm H2O

10

0.000097

9.87 10-5

0.075

1

0.001

1.02 10-4

m H2O

104

0.097

9.87 10-2

75

1000

1

0.102

kg/cm2

9.8 104

0.98

0.97

735

10000

10

1

pound square feet

47.8

4.78 10-4

4.72 10-4

0.36

4.78

4.78 10-3

4.88 10-4

pound square inches (psi)

6897

0.069

0.068

51.7

689.7

0.690

0.07

inches Hg

3377

0.0338

0.033

25.33

337.7

0.337

0.034

inches H2O

248.8

2.49 10-3

2.46 10-3

1.87

24.88

0.0249

0.0025

 

Multiply by

Convert from

Convert to

pound square feet

pound square inches (psi)

inches Hg

inches H2O

Pa (N/m2)

0.021

1.45 10-4

2.96 10-4

4.02 10-3

bar

2090

14.50

29.61

402

atmosphere

2117.5

14.69

29.92

407

mm Hg

2.79

0.019

0.039

0.54

mm H2O

0.209

1.45 10-3

2.96 10-3

0.04

m H2O

209

1.45

2.96

40.2

kg/cm2

2049

14.21

29.03

394

pound square feet

1

0.0069

0.014

0.19

pound square inches (psi)

144.1

1

2.04

27.7

inches Hg

70.6

0.49

1

13.57

inches H2O

5.2

0.036

0.074

1

Some other Pressure Units

1 Pa (N/m2) = 0.0000102 Atmosphere (metric)
1 Pa (N/m
2) = 0.0000099 Atmosphere (standard)
1 Pa (N/m
2) = 0.00001 Bar
1 Pa (N/m
2) = 10 Barad
1 Pa (N/m
2) = 10 Barye
1 Pa (N/m
2) = 0.0007501 Centimeter of mercury (0 C)
1 Pa (N/m
2) = 0.0101974 Centimeter of water (4 C)
1 Pa (N/m
2) = 10 Dyne/square centimeter
1 Pa (N/m
2) = 0.0003346 Foot of water (4 C)
1 Pa (N/m
2) = 10-9 Gigapascal
1 Pa (N/m
2) = 0.01 Hectopascal
1 Pa (N/m
2) = 0.0002953 Inch of mercury (0 C)
1 Pa (N/m
2) = 0.0002961 Inch of mercury (15.56 C)
1 Pa (N/m
2) = 0.0040186 Inch of water (15.56 C)
1 Pa (N/m
2) = 0.0040147 Inch of water (4 C)
1 Pa (N/m
2) = 0.0000102 Kilogram force/centimetre2
1 Pa (N/m
2) = 0.0010197 Kilogram force/decimetre2
1 Pa (N/m
2) = 0.101972 Kilogram force/meter2
1 Pa (N/m
2) = 10-7 Kilogram force/millimeter2
1 Pa (N/m
2) = 10-3 Kilopascal
1 Pa (N/m
2) = 10-7 Kilopound force/square inch
1 Pa (N/m
2) = 10-6 Megapascal
1 Pa (N/m
2) = 0.000102 Meter of water (4 C)
1 Pa (N/m
2) = 10 Microbar (barye, barrie)
1 Pa (N/m
2) = 7.50062 Micron of mercury (millitorr)
1 Pa (N/m
2) = 0.01 Millibar
1 Pa (N/m
2) = 0.0075006 Millimeter of mercury (0 C)
1 Pa (N/m
2) = 0.10207 Millimeter of water (15.56 C)
1 Pa (N/m
2) = 0.10197 Millimeter of water (4 C)
1 Pa (N/m
2) =7.5006 Millitorr
1 Pa (N/m
2) = 1 Newton/square meter
1 Pa (N/m
2) = 32.1507 Ounce force (avdp)/square inch
1 Pa (N/m
2) = 0.0208854 Pound force/square foot
1 Pa (N/m
2) = 0.000145 Pound force/square inch
1 Pa (N/m
2) = 0.671969 Poundal/square foot
1 Pa (N/m
2) = 0.0046665 Poundal/square inch
1 Pa (N/m
2) = 0.0000099 Standard atmosphere
1 Pa (N/m
2) = 0.0000093 Ton (long)/foot2
1 Pa (N/m
2) = 10-7 Ton (long)/inch2
1 Pa (N/m
2) = 0.0000104 Ton (short)/foot2
1 Pa (N/m
2) = 10-7 Ton/inch2
1 Pa (N/m
2) = 0.0075006 Torr

Ounces and Pounds converted into Grams

Converting ounces (ozs.) and pounds (lbs.) into grams (g)

UK ounces (ozs.) and pounds (lbs.) can be converted into grams (g) with the table below:

Mass, Weight

Ounces

grams

1/4 (quarter)

7

1/2 (half)

14

3/4 (three quarters)

21

1

28.35

2

57

3

85

4 (quarter lb)

113

5

142

6

170

7

198

8 (half lb)

227

9

255 (1/4 kilo)

10

284

11

312

12 (3/4 lb)

340

13

369

14

397

15

425

16 (1 lb)

454

17

482

18

510 (1/2 kilo)

19

539

20 (1 1/4 lbs)

567

21

595

22

624

23

652

24 (1 1/2 lbs)

680

25

709

26

737

27

765 (3/4 kilo)

28 (1 3/4 lbs)

794

29

822

30

851

31

879

32 (2 lbs)

907

pH Definition

An introduction to pH

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pH can be viewed as an abbreviation for power of hydrogen or more completely, power of the concentration of the hydrogen ion.

The mathematical definition of pH is a bit less intuitive but in general more useful. It says that the pH is equal to to the negative logarithmic value of the Hydrogen ion (H+) concentration, or

pH = -log [H+]

pH is alternatively defined mathematically as the negative logarithmic value of the Hydroxonium ion (H3O+) concentration. Using the Bronsted-Lowry approach that would be

pH = -log [H3O+]

pH values are calculated in powers of 10. The hydrogen ion concentration of a solution with pH 1.0 is 10 times larger than in a solution with pH 2.0. The larger the hydrogen ion concentration, the smaller the pH.

In pure neutral water the concentration of hydrogen and hydroxide ions are both 10-7 equivalent per liter.

pH

Ion Concentration (gram equivalent per liter)

Type of Solution

0

1,0

Acid Solution - hydrogen ions - H+

1

0,1

2

0,01

3

0,001

4

0,0001

5

0,00001

6

0,000001

7

0,0000001

Neutral Solution

8

0,000001

Basic (alkaline) Solution - Hydroxide ions OH-

9

0,00001

10

0,0001

11

0,001

12

0,01

13

0,1

14

1,0


Common pH Values

pH values in some common products:

Product

pH

Battery Acid

0

HCl in stomach acid

1

Lemon juice, vinegar

2-3

Orange juice

3-4

Acid rain

4

Black coffee

5

Urine, salvia

6

Pure water

7

Sea water

8

Baking soda

9

Ammonia solution

10-11

Soapy water

12

Bleach

13

Oven cleaner

13-14

Drain cleaner

14



ppm - parts per million

ppm - parts per million - is commonly used as a unit of concentration





Parts per million - ppm -  is commonly used as a measure of small levels of pollutants in air, water, body fluids, etc. Parts per million is the mass ratio between the pollutant component and the solution and ppm is defined as

ppm = 1,000,000 mc / ms (1)

where

mc = mass of component (kg, lbm)

ms = mass of solution (kg, lbm)

In the metric system ppm can be expressed in terms of milligram versus kg where

Alternatively mass related units to measure very small concentration levels used are

An alternatively mass related unit to measure larger concentration levels are weight percent which can be expressed like

weight percent = 100 mc / ms (2)

Volume related Concentration Units

Mass per Unit Volume

The concentration of a component can be measured as mass per unit volume as mg/liter, mg/cm3, etc.

Weight of substance added to one unit volume of water to give one part per million (ppm)

1 ppm

    = 2.72 pounds per acre-foot

    = 1,233 grams per acre-foot

    = 1.233 kilograms per acre-foot

    = 0.0283 grams per cubic foot

    = 0.0000624 pounds per cubic foot

    = 0.0038 grams per US gallon

    = 0.058419 grains per US gallon

    = 0.07016 grains per Imperial gallon

    = 1 milligram per liter

    = 1 microlitre ( μL ) per liter

    = 0.001 gram per litre

    = 8.345 pounds per million gallons of water

Percent by Volume

Volume percent can be expressed as volume per unit volume as

percent by volume = 100 vc /(vc + vs) (3)

where

vc = volume component

vs = volume solvent

Molarity

Molarity is the number of moles of solute (substance of interest - pollution, etc.) dissolved in one liter (volume) of the solution.

Molality

Molality is the number moles of solute dissolved in one kg (mass) of the solution.

Prefix Names of Multiples and Submultiples of Units

Prefixes and decimal equivalents

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Prefix

Measure

Decimal equivalent

Exponential expression

Alto

one-quintillionth

0.000 000 000 000 000 001

E-18

Femto

one-quadrillionth

0.000 000 000 000 001

E-15

Pico

one-trillionth

0.000 000 000 001

E-12

Nano

one-billionth

0.000 000 001

E-9

Micro

one-millionth

0.000 001

E-6

Milli

one-thousandth

0.001

E-3

Centi

one-hundredth

0.01

E-2

Deci

one-tenth

0.1

E-1

Uni

one

1

E0

Deka

ten

10.0

E1

Hecto

one hundred

100.0

E2

Kilo

one thousand

1 000.0

E3

Mega

one million

1 000 000.0

E6

Giga

one billion

1 000 000 000.0

E9

Tera

one trillion

1 000 000 000 000.0

E1

Pressure

An introduction to pressure - the definition and presentation of common units as psi and Pa and the relationship between them - online pressure units converter

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The pressure in a fluid is defined as

"the normal force per unit area exerted on a imaginary or real plane surface in a fluid or a gas"

The equation for pressure can expressed as:

p = F / A (1)

where

p = pressure [lb/in2 (psi) or lb/ft2 (psf), N/m2 or kg/ms2 (Pa)]

F = force [1), N]

A = area [in2 or ft2, m2]

1) In the English Engineering System special care must be taken for the force unit. The basic unit for mass is the pound mass (lbm) and the unit for the force is the pound (lb) or pound force (lbf).

Absolute Pressure

The absolute pressure - pa - is measured relative to the absolute zero pressure - the pressure that would occur at absolute vacuum.

Gauge Pressure

A gauge is often used to measure the pressure difference between a system and the surrounding atmosphere. This pressure is often called the gauge pressure and can be expressed as

pg = pa - po (2)

where

pg = gauge pressure

po = atmospheric pressure

Atmospheric Pressure

The atmospheric pressure is the pressure in the surrounding air. It varies with temperature and altitude above sea level.

Standard Atmospheric Pressure

The Standard Atmospheric Pressure (atm) is used as a reference for gas densities and volumes. The Standard Atmospheric Pressure is defined at sea-level at 273oK (0oC) and is 1.01325 bar or 101325 Pa (absolute). The temperature of 293oK (20oC) is also used.

In imperial units the Standard Atmospheric Pressure is 14.696 psi.

Pressure Units

Since 1 Pa is a small pressure unit, the unit hectopascal (hPa) is widely used, especially in meteorology. The unit kilopascal (kPa) is commonly used designing technical applications like HVAC systems, piping systems and similar.

Some Pressure Levels

Some Alternative Units of Pressure

A torr (torr) is named after Torricelli and is the pressure produced by a column of mercury 1 mm high equals to 1/760th of an atmosphere. 1 atm = 760 torr = 14.696 psi

Pounds per square inch (psi) was common in U.K. but has now been replaced in almost every country except in the U.S. by the SI units. The Normal atmospheric pressure is 14.696 psi, meaning that a column of air on one square inch in area rising from the Earth's atmosphere to space weights 14.696 pounds.

The bar (bar) is common in the industry. One bar is 100,000 Pa, and for most practical purposes can be approximated to one atmosphere even if

1 Bar = 0.9869 atm

There are 1,000 millibar (mbar) in one bar, a unit common in meteorology.

1 millibar = 0.001 bar = 0.750 torr = 100 Pa

Pressure to Head Unit Converter

Convert between common units for pressure and head - lb/in2, atm, inch mercury, bars, Pa and more

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The table below can be used to convert between commonly used units for pressure and head.

Multiply by

to

from

lb/in2

lb/ft2

Atm

kg/cm2

kg/m2

in.
water (68
oF)

lb/in2

1

144

0.068046

0.070307

703.070

27.7276

lb/ft2

0.0069444

1

0.000473

0.000488

4088241

0.1926

Atm.

14.696

2116.22

1

1.0332

10332.27

407.484

kg/cm2

14.2233

2048.155

0.96784

1

10000

394.38

kg/m2

0.001422

0.204768

0.0000968

0.0001

1

0.03944

in.
water (68
oF)

0.036092

5.1972

0.002454

0.00253

25.375

1

ft.
water (68
oF)

0.432781

62.3205

0.029449

0.03043

304.275

12

in. mercury (32oF)

0.491154

70.7262

0.033421

0.03453

345.316

13.6185

mm
mercury (32
oF)

0.0193368

2.78450

0.0013158

0.0013595

13.59509

0.53616

Bars

14.5038

2088.55

0.98692

1.01972

10197.2

402.156

MPa

145.038

20885.5

9.8692

10.1972

101972.0

4021.56


Multiply by

to

from

ft.
water (68
oF)

in.
mercury (32
oF)

mm
mercury (32
oF)

Bars

MPa

lb/in2

2.3106

2.03602

51.7150

0.06895

0.006895

lb/ft2

0.01605

0.014139

0.35913

0.000479

0.0000479

Atm.

33.9570

29.921

760

1.01325

0.101325

kg/cm2

32.8650

28.959

735.559

0.98067

0.098067

kg/m2

0.003287

0.002896

0.073556

0.000098

0.0000098

in.
water (68
oF)

0.08333

0.073430

1.8651

0.00249

0.000249

ft.
water (68
oF)

1

0.88155

22.3813

0.029839

0.0029839

in. mercury (32oF)

1.1349

1

25.40005

0.033864

0.0033864

mm
mercury (32
oF)

0.044680

0.03937

1

0.001333

0.0001333

Bars

33.5130

29.5300

750.062

1

0.10

MPa

335.130

295.300

7500.62

10.0

1


Properties and State

Concepts of properties and state

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Property

Property is any characteristic or attribute which can be quantitatively evaluated. Pressure, temperature, velocity, energy, etc. are all properties.

Things that are done, like work or heat flow, are not properties.

State

The state of an object is its condition described by a list of properties. For example temperature and pressure may describe the state of a gas.

The list of properties necessary to describe the state of an object will vary with the object and the microscopic versus macroscopic view of the object.

Some common states and their often used properties:

State

Common Properties
to describe the state

Chemical

chemical composition, free charge, energy, entropy, etc.

Electromagnetic

electric field strength, magnetic dipole moment, charge, etc.

Esthetic

color, design, odor, etc

Geometric

length, width, breadth, volume, etc.

Hydrodynamic

pressure, shearing stress, strain rate, etc.

Kinematic

position, speed, acceleration, etc.

Thermodynamic

energy, temperature, volume, pressure, enthalpy, entropy, etc.

Radians

The radian - a unit of angle measure

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SI System

An introduction to the SI-system

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The SI system (Système International) is the modern metric system of measurement and the dominant system of international commerce and trade. SI units are gradually replacing Imperial and USCS units.

The SI is maintained by a small agency in Paris, the International Bureau of Weights and Measures (BIPM, for Bureau International des Poids et Mesures).

The SI system is founded on the

SI base units

The core of the SI system is a short list of base units defined in an absolute way without referring to any other units. The base units are consistent with the part of the metric system called the MKS system. The International System of Units (SI) is founded on seven base units.

Quantity

Name of Unit

Symbol

Length

meter

m

Mass

kilogram

kg

Time

second

s

Electrical current

ampere

A

Thermodynamic temperature

Kelvin

K

Luminous temperature

candela

cd

Amount of substance

mole

mol

SI supplementary units

Quantity

Name of Unit

Symbol

Plane angle

radian

rad

Solid angle

steradian

sr

SI derived units with special names and symbols acceptable in SI

Derived units are algebraic combinations of the seven base units and the two supplementary units with some of the combinations being assigned special names and symbols.

Quantity

Name of Unit

Symbol

Expression in terms of SI base units

Expression in terms of other units

Adsorbed radiation

gray

Gy

m2 s-2

J/kg

Electrical capacitance

farad

F

m-2 kg-1 s4 A2

C/V

Electrical charge

coulomb

C

A s

 

Electrical conductance

siemens

S

m-2 kg-1s3A2

A/V

Electrical inductance

Henry

H

m2 kg s-2 A-2

 

Electrical potential

volt

V

m2 kg s-3 A-1

W/A

Electrical resistance

ohm

w

m2 kg s-3 A-2

V/A

Force

Newton

N

kg ms-2

 

Frequency

hertz

Hz

s-1

 

Luminance

lux

lx

m-2cd sr

lm/m2

Luminous flux

lumen

lm

cd sr

 

Magnetic flux

weber

Wb

m2 kg s-2 A-1

V s

Magnetic flux density

tesla

T

kg s-2 A-1

Wb/m2

Power or radiant flux

watt

W

kg m2 s-3

J/s

Pressure

pascal

Pa

kg/(m s2) = (N/m2)

 

Radioactivity

bequerel

Bq

s-1

 

Work, energy, heat

joule

J

m2 kg s-2

N m

SI derived units described in terms of acceptable SI units

Derived units are algebraic combinations of the seven base units and the two supplementary units with some of the combinations being assigned special names and symbols. 

Quantity

Description

Symbol

Expression in terms of SI base units

acceleration

meter per second squared

m/s2

m s-2

area

square meter

m2

m2

coefficient of heat transfer (often used symbol h or U)

watt per square meter Kelvin

W/(m2 K)

kg s-3K-1

concentration (of amount of substance)

mole per cubic meter

mol/m3

mol m-3

current density (often used symbol r)

ampere per square meter

A/m2

A m-2

density (mass density)

kilogram per cubic meter

kg/m3

kg m-3

electrical charge density

columb per cubic meter

C/m3

m-3 s A

electric field strength

volt per meter

V/m

m kg s-3 A-1

electric flux density

columb per square meter

C/m2

m-2 s A

energy density

joule per cubic meter

J/m3

m-1 kg s-2

force

Newton

N or J/M

m kg s-2

heat capacity

joule per Kelvin

J/K

m2 kg s-2 K-1

heat flow rate (often used symbol Q or q)

watt

W or J/s

m2 kg s-3

heat flux density or irradiance

watt per square meter

W/m2

kg s-3

luminance

candela per square meter

cd/m2

cd m-2

magnetic field strength

ampere per meter

A/m

A m-1

modulus of elasticity (or Young?s modulus)

giga Pascal

GPa

10-9 m-1 kg s-1

molar energy

joule per mole

J/mol

m-2 kg s-2 mol-1

molar entropy (or molar heat capacity)

joule per mole Kelvin

J/(mol K)

m-2 kg s-2 K-1 mol-1

moment of force (or torque)

Newton meter

N m

m2 kg s-2

moment of inertia

kilogram meter squared

kg m2

kg m2

momentum

kilogram meter per second

kg m/s

kg m s-1

permeability

Henry per meter

H/m

m kg s-2 A-2

permitivity

farad per meter

F/m

m-3 kg-1 s4 A2

power

kilowatt

kW

10-3 m2 kg s-3

pressure (often used symbol P or p)

kilopascal

kPa

10-3 m-1 kg s-2

specific energy

joule per kilogram

J/kg

m2 s-2

specific heat capacity (or specific entropy, often used symbol c,p,cv or s)

joule per kilogram Kelvin

J/(kg K)

m2 s-2 K-1

specific volume

cubic meter per kilogram

m3/kg

m3 kg-1

stress

mega Pascal

MPa

10-6 m-1 kg s-2

surface tension

Newton per meter

N/m

kg s-2

thermal conductivity (often used symbol k)

watt per meter Kelvin

W/(m K)

m kg s-3 K-1

torque

Newton meter

N m

m2 kg s-2

velocity (or speed)

meters per second

m/s

m s-1

viscosity, absolute or dynamic (often used symbol m)

Pascal second

Pa s

m-1 kg s-1

viscosity, kinematic (often used symbol n)

square meter per second

m2/s

m2 s-1

volume

cubic meter

m3

m3

wave number

1 per meter

1/m

m-1

work (or energy heat, often used symbol W)

joule

J or N m

m2 kg s-2

The radian is the SI derived unit of angle.

There are 2 π (pi), about 6.283185 radians, in a complete circle.

The radian is defined as the angle subtended at the center of a circle by an arc of circumference equal in length to the radius of the circle.

Converting angular velocity to other units

Temperature

A short introduction to temperature - including Celsius, Fahrenheit, Kelvin and Rankine definitions - online temperature converter

Temperature (sometimes called thermodynamic temperature) is a measure of the average kinetic energy of a systems particles. Temperature is the degree of "hotness" ( or "coldness"), a measure of the heat intensity.

When two objects of different temperature are in contact, the warmer object becomes colder while the colder object becomes warmer. It means that heat flows from the warmer object to the colder one.

Degree Celsius (oC) and Degree Fahrenheit (oF)

Thermometer helps us determine how cold or how hot a substance is. Temperatures in science (and in most of the world) are measured and reported in degrees Celsius (oC). In the US, it is common to report temperature in degrees Fahrenheit (oF). On both the Celsius and Fahrenheit scales the temperature at which ice melts (water freezes) and the temperature at which water boils, are used as reference points.

On the Celsius scale there are 100 degrees between freezing point and boiling point of water, compared to 180 degrees on the Fahrenheit scale. This means that 1 oC = 1.8 oF.

Thus the following formulas can be used to convert temperature between the two scales:

tF = 1.8 tC + 32 = 9/5 tC + 32 (1)

tC = 0.56(tF -32) =5/9(tF - 32) (2)

where

tC = temperature in oC

tF = temperature in oF

Degree Celsius and degree Fahrenheit are compared in the table below:

Temperature

oC

oF

-20

-4

-15

5

-10

14

-5

23

0

32

5

41

10

50

15

59

20

68

25

77

30

86

35

95

40

104

45

113

50

122

Example - A patient with SARS (Severe Acute Respiratory Syndrome) has a temperature of 106 oF. What does this read on a Celsius thermometer?

tC = 5/9 (106-32)= 41.1 oC

Degree Kelvin - K

Another scale (common in science) is Kelvin, or the Absolute Temperature Scale. On the Kelvin scale the coldest temperature possible, -273 oC, has a value of 0 Kelvin (0 K) and is called the absolute zero. Units on the Kelvin scale are called Kelvins (K) and no degree symbol is used.
Because there are no lower temperatures the Kelvin scale do not have negative numbers.

A Kelvin equal in size to a Celsius unit: 1 K= 1 oC.

To calculate a Kelvin temperature, add 273 to the Celsius temperature:

tK = tC + 273.16 (3)

Example - What is normal body temperature of 37 oC on the Kelvin scale?

tK = tC + 273.16 = 37 + 273.16 = 310.16 K

Degree Rankine - R

In the English system the absolute temperature is in degrees Rankine (R), not in Fahrenheit:

tR = tF + 459.69 (4)

The Elements

The elements with name, symbol, atomic number and weight

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The elements from the periodic table - their name, symbol, atomic number and atomic weight:

Element Name

Element Symbol

Atomic Number

Atomic Weight1)

Actinium

Ac

89


Aluminum

Al

13

26.981538

Americium

Am

95


Antimony (Stibium)

Sb

51

121.760

Argon

Ar

18

39.948

Arsenic

As

33

74.92160

Astatine

At

85


Barium

Ba

56

137.327

Berkelium

Bk

97


Beryllium

Be

4

9.012182

Bismuth

Bi

83

208.98038

Boron

B

5

10.811

Bromine

Br

35

79.904

Cadmium

Cd

48

112.411

Calcium

Ca

20

40.078

Californium

Cf

98


Carbon

C

6

12.0107

Cerium

Ce

58

140.116

Cesium

Cs

55

132.90545

Chlorine

Cl

17

35.453

Chromium

Cr

24

51.9961

Cobalt

Co

27

58.933200

Copper

Cu

29

63.546

Curium

Cm

96


Dysprosium

Dy

66

162.50

Einsteinium

Es

99


Erbium

Er

68

167.259

Europium

Eu

63

151.964

Fermium

Fm

100


Fluorine

F

9

18.9984032

Francium

Fr

87


Gadolinium

Gd

64

157.25

Gallium

Ga

31

69.723

Germanium

Ge

32

72.64

Gold (Aurum)

Au

79

196.96655

Hafnium

Hf

72

178.49

Helium

He

2

4.002602

Holmium

Ho

67

164.93032

Hydrogen

H

1

1.00794

Indium

In

49

114.818

Iodine

I

53

126.90447

Iridium

Ir

77

192.217

Iron (Ferrum)

Fe

26

55.845

Krypton

Kr

36

83.798

Lanthanum

La

57

138.9055

Lawrencium

Lr

103


Lead (Plumbum)

Pb

82

207.2

Lithium

Li

3

6.941

Lutetium

Lu

71

174.967

Magnesium

Mg

12

24.3050

Manganese

Mn

25

54.9380

Mendelevium

Md

101


Mercury (Hydrargyrum)

Hg

80

200.59

Molybdenum

Mo

42

95.94

Neodymium

Nd

60

144.24

Neon

Nd

10

20.1797

Neptunium

Np

93


Nickel

Ni

28

58.6934

Niobium (Columbium)

Nb

41

92.90638

Nitrogen

N

7

14.0067

Nobelium

No

102


Osmium

Os

76

190.23

Oxygen

O

8

15.9994

Palladium

Pd

46

106.42

Phosphorus

P

15

30.973761

Platinum

Pt

78

195.078

Plutonium

Pu

94


Polonium

Po

84


Potassium (Kalium)

K

19

39.0983

Praseodymium

Pr

59

140.90765

Promethium

Pm

61


Protactinium

Pa

91


Radium

Ra

88


Radon

Rn

86


Rhenium

Re

75

186.207

Rhodium

Rh

45

102.90550

Rubidium

Rb

37

85.4678

Ruthenium

Ru

44

101.07

Samarium

Sm

62

150.36

Scandium

Sc

21

44.955910

Selenium

Se

34

78.96

Silicon

Si

14

28.0855

Silver (Argentum)

Ag

47

107.8682

Sodium (Natrium)

Na

11

22.989770

Strontium

Sr

38

87.62

Sulfur

S

16

32.065

Tantalum

Ta

73

180.9479

Technetium

Tc

43


Tellurium

Te

52

127.60

Terbium

Tb

65

158.92534

Thallium

Tl

81

204.3833

Thorium

Th

90

232.0381

Thulium

Tm

69

168.93421

Tin (Stannum)

Sn

50

118.710

Titanium

Ti

22

47.867

Tungsten (Wolfram)

W

74

183.84

Uranium

U

92

238.02891

Vanadium

V

23

50.9415

Xenon

Xe

54

131.293

Ytterbium

Yb

70

173.04

Yttrium

Y

39

88.90585

Zinc

Zn

30

65.409

Zirconium

Zr

40

91.224

1) Standard atomic weights (IUPAC 1997)

USCS - United States Customary System Units

United States Customary System Units or Imperial Units

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USCS - United States Customary System Units are the measuring units used in the U.S. consisting of the mile, foot, inch, gallon, second and pound. USCS are also called Imperial Units. Imperial or USCS units are gradually being replaced by SI units.

Velocity Units Converter

Convert between common velocity and speed units - with an online converter

Velocity Units Converting Table

The table below can be used to convert between some common velocity and speed units:

Multiply by

Convert from

Convert to

m/s

km/h

ft/min

ft/s

yards/min

mph

knots

m/s

1

3.6

196.9

3.28

65.6

2.24

1.94

km/h

0.278

1

54.68

0.91

18.23

0.62

0.54

ft/min

5.08 10-3

1.83 10-2

1

1.67 10-2

0.33

1.14 10-2

9.87 10-3

ft/s

0.305

1.097

60

1

20

0.682

0.592

yards/min

1.52 10-2

5.49 10-2

3

0.05

1

3.41 10-2

2.96 10-2

mph

0.45

1.609

88

1.47

29.33

1

0.869

knots

0.51

1.85

101.3

1.69

33.76

1.15

1

Some other common Velocity Units

Volume and Surface of some Common Solids

Surface and volume of solids like rectangular prism, cylinder, pyramid, cone and sphere

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Rectangular Prism

Volume of a rectangular prism can be expressed as

V = l b h (1)

where

V = volume of solid (m3, ft3)

l = length of rectangular prism (m, ft)

b = width of rectangular prism (m, ft)

h = height of rectangular prism (m, ft)

Surface of a rectangular prism can be expressed as

A = 2 (b h + h l + l b) (1b)

where

A = surface area of solid (m2, ft2)

Cylinder

Volume of a cylinder can be expressed as

V = π r2 h (2)

where

r = radius of cylinder (m, ft)

h = height of cylinder (m, ft)

Surface of a cylinder can be expressed as

A = 2 π r h + 2 π r2 (2b)

Pyramid

Volume of a pyramid can be expressed as

V = 1/3 l Ab (3)

where

Ab = area of base (m2, ft2)

h = perpendicular height of pyramid (m, ft)

Surface of a cylinder can be expressed as

A = ∑ sum of areas of triangles forming sides + Ab (3b)

where

the surface areas of the triangular faces will have different formulas for different shaped bases

Cone

Volume of a cone can be expressed as

V = 1/3 π r2 h (4)

where

r = radius of cone base (m, ft)

h = height of cone (m, ft)

Surface of a cone can be expressed as

A = π r l + π r2 (4b)

where

l = (r2 + h2)1/2 = length of cone side (m, ft)

Sphere

Volume of a sphere can be expressed as

V = 4/3 π r3 (5)

where

r = radius of sphere (m, ft)

Surface area of a sphere can be expressed as

A = 4 π r2 (5b)

Volume Units Converter

Convert between common volume units like cubic meters, cubic feet, cubic inches and many more

Volume Units Converting Table

The table below can be used to convert between common volume units. 

Multiply by

Convert from

Convert to

cubic inches

cubic feet

cubic yards

us liquid gallons

us dry gallons

imp liquid gallons

barrels (oil)

cups

fluid ounces (UK)

fluid ounces (US)

pints (UK)

cubic meters

6.1 104

35.3

1.308

264.2

227

220

6.29

4227

3.52 104

3.38 104

1760

cubic decimeters

61.02

0.035

1.3 10-3

0.264

0.227

0.22

0.006

4.23

35.2

33.8

1.76

cubic centimeters

0.061

3.5 10-5

1.3 10-6

2.64 10-4

2.27 10-4

2.2 10-4

6.29 10-6

4.2 10-3

3.5 10-2

3.34 10-2

1.76 103

cubic millimeters

6.1 10-5

3.5 10-8

1.31 10-9

2.64 10-7

2.27 10-7

2.2 10-7

6.3 10-9

4.2 10-6

3.5 10-5

3.4 10-5

1.76 10-6

hectoliters

6.1 103

3.53

0.13

26.4

22.7

22

0.63

423

3.5 103

3381

176

liters

61

3.5 10-2

1.3 10-3

0.26

0.23

0.22

6.3 10-3

4.2

35.2

33.8

1.76

centiliters

0.61

3.5 10-4

1.3 10-5

2.6 10-3

2.3 10-3

2.2 10-3

6.3 10-5

4.2 10-2

0.35

0.338

1.76 10-2

milliliters

6.1 10-2

3.5 10-5

1.3 10-6

2.6 10-4

2.3 10-4

2.2 10-4

6.3 10-6

4.2 10-3

3.5 10-2

3.4 10-2

1.76 10-3

cubic inches

1

5.79 10-4

2.1 10-5

4.3 10-3

3.7 10-3

3.6 10-3

10-4

6.9 10-2

0.58

0.55

2.9 10-2

cubic feet

1728

1

0.037

7.48

6.43

6.23

0.18

119.7

997

958

49.8

cubic yards

4.7 104

27

1

202

173.6

168.2

4.8

3232

2.69 104

2.59 104

1345

us liquid gallons

231

0.134

4.95 10-3

1

0.86

0.83

0.024

16

133.2

128

6.7

us dry gallons

268.8

0.156

5.76 10-3

1.16

1

0.97

0.028

18.62

155

148.9

7.75

imp liquid gallons

277.4

0.16

5.9 10-3

1.2

1.03

1

0.029

19.2

160

153.7

8

barrels (oil)

9702

5.61

0.21

42

36.1

35

1

672

5596

5376

279.8

cups

14.4

8.4 10-3

3.1 10-4

6.2 10-2

5.4 10-2

5.2 10-2

1.5 10-3

1

8.3

8

0.4

fluid ounces (UK)

1.73

10-3

3.7 10-5

7.5 10-3

6.45 10-3

6.25 10-3

1.79 10-4

0.12

1

0.96

5 10-2

fluid ounces (US)

1.8

10-3

3.87 10-5

7.8 10-3

6.7 10-3

6.5 10-3

1.89 10-4

0.13

1.04

1

0.052

pints (UK)

34.7

0.02

7.4 10-4

0.15

0.129

0.125

3.57 103

2.4

20

19.2

1

 

Multiply by

Convert from

Convert to

cubic meters

cubic decimeters

cubic centimeters

cubic millimeters

hectoliters

liters

centiliters

milliliters

cubic meters

1

103

106

109

10

103

105

106

cubic decimeters

10-3

1

103

106

0.01

1

100

103

cubic centimeters

10-6

10-3