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Debris Control Structures Evaluation and Countermeasures Hydraulic Engineering Circular No. 9

Appendix A - Metric System, Conversions, and Water Properties

Metric System, Conversion Factors, and Water Properties

The following information is summarized from the Federal Highway Administration, National Highway Institute (NHI) Course No. 12301, "Metric (SI) Training for Highway Agencies." For additional information, refer to the Participant Notebook for NHI Course No. 12301.

In SI there are seven base units, many derived units and two supplemental units (Table A.1). Base units uniquely describe a property requiring measurement. One of the most common units in civil engineering is length, with a base unit of meters in SI. Decimal multiples of meter includes the kilometer (1000 m), the centimeter (1 m/100) and the millimeter (1 m/1000). The second base unit relevant to highway applications is the kilogram, a measure of mass which is the inertial of an object. There is a subtle difference between mass and weight. In SI, mass is a base unit, while weight is a derived quantity related to mass and the acceleration of gravity, sometimes referred to as the force of gravity. In SI the unit of mass is the kilogram and the unit of weight/force is the Newton. Table A.2 illustrates the relationship of mass and weight. The unit of time is the same in SI as in the English system (seconds). The measurement of temperature is Centigrade. The following equation converts Fahrenheit temperatures to Centigrade, °C = 5/9 (°F - 32).

Derived units are formed by combining base units to express other characteristics. Common derived units in highway drainage engineering include area, volume, velocity, and density. Some derived units have special names (Table A.3).

Table A.4 provides useful conversion factors from English to SI units. The abbreviations presented in this table for metric units, including the use of upper and lower case (e.g., kilometer is "km" and a Newton is "N") are the standards that should be followed. Table A.5 provides the standard SI prefixes and their definitions.

Tables A.6 and A.7 provide physical properties of water at atmospheric pressure in SI and English systems of units, respectively. Table A.8 gives the sediment grade scale and Table A.9 gives some common equivalent hydraulic units.

 Units Symbol Base units length meter m mass kilogram kg time second s temperature* kelvin K electrical current ampere A luminous intensity candela cd amount of material mole mol Derived units ** Supplementary units angles in the plane radian rad solid angles steradian sr * Use degrees Celsius (_C), which has a more common usage than kelvin. ** Many derived units exist; several will be discussed in this session.

 Mass Weight or Force of Gravity Force English slug pound pound pound-mass pound-force pound-force metric kilogram newton newton

Table A.3. Derived Units With Special Names.
Quantity Name Symbol Expression
Frequency hertz Hz s-1
Force newton N Kg · m/s2
Pressure, stress pascal Pa N/m2
Energy, work, quantity of heat joule J N · m
Power, radiant flux watt W J/s
Electric charge, quantity coulomb C A · s
Electric potential volt V W/A
Electric resistance ohm Ω V/A
Electric conductance siemens S A/V
Magnetic flux weber Wb V · s
Magnetic flux density tesla T Wb/m2
Inductance henry H Wb/A
Luminous flux lumen lm cd · sr
Illuminance lux lx lm/m2

Table A.4. Useful Conversion Factors.
Quantity From English Units To Metric Units Multiplied by*
Length Mile km 1.609
yard m 0.9144
foot m 0.3048
inch mm 25.4
Area square mile km2 2.590
acre m2 4047
acre hectare 0.4047
square yard m2 0.8361
square foot m2 0.092 90
square inch mm2 645.2
Volume acre foot m3 1 233
cubic yard m3 0.7646
cubic foot m3 0.028 32
cubic foot L (1000 cm3) 28.32
100 board feet m3 0.2360
gallon L (1000 cm3) 3.785
cubic inch cm3 16.39
Mass Lb kg 0.4536
kip (1000 lb) metric ton (1000 kg) 0.4536
Mass/unit length plf kg/m 1.488
Mass/unit area psf kg/m2 4.882
Mass density pcf kg/m3 16.02
Force lb N 4.448
kip kN 4.448
Force/unit length plf N/m 14.59
klf kN/m 14.59
Pressure, stress, modulus of elasticity psf Pa 47.88
ksf kPa 47.88
psi kPa 6.895
ksi MPa 6.895
Bending moment, torque, moment of force ft-lb N · m 1.356
ft-kip kN · m 1.356
Moment of mass lb · ft kg · m 0.1383
Moment of inertia lb · ft2 kg · m2 0.042 14
Second moment of area In4 mm4 416 200
Section modulus In3 mm3 16 390
Power ton (refrig) kW 3.517
Btu/s kW 1.054
hp (electric) W 745.7
Btu/h W 0.2931
Volume rate of flow ft3/s m3/s 0.028 32
cfm m3/s 0.000 471 9
cfm L/s 0.4719
mgd m3/s 0.0438
Velocity, speed ft/s m/s 0.3048
Acceleration f/s2 m/s2 0.3408
Momentum lb · ft/sec kg · m/s 0.1383
Angular momentum lb · ft2/s kg · m2/s 0.042 14
Plane angle degree rad 0.017 45
* 4 significant figures; underline denotes exact conversion

Table A.5. Prefixes
Submultiples
deci 10-1 d
centi 10-2 c
milli 10-3 m
micro 10-6 μ
nano 10-9 n
pica 10-12 p
femto 10-15 f
atto 10-18 a
zepto 10-21 z
yocto 10-24 y
Multiples
deka 101 da
hector 102 h
kilo 103 k
mega 106 M
giga 109 G
tera 1012 T
peta 1015 P
exa 1018 E
zeta 1021 Z
yotto 1024 Y

Table A.6. Physical Properties of Water at Atmospheric Pressure in SI Units
Temperature Density Specific Weight Dynamic Viscosity Kinematic Viscosity Vapor Pressure Surface Tension1 Bulk Modulus
Centigrade Fahrenheit kg/m3 N/m3 N · s/m2 m2/s N/m2 abs. N/m GN/m2
32° 1,000 9,810 1.79 x 10-3 1.79 x 10-6 611 0.0756 1.99
41° 1,000 9,810 1.51 x 10-3 1.51 x 10-6 872 0.0749 2.05
10° 50° 1,000 9,810 1.31 x 10-3 1.31 x 10-6 1,230 0.0742 2.11
15° 59° 999 9,800 1.14 x 10-3 1.14 x 10-6 1,700 0.0735 2.16
20° 68° 998 9,790 1.00 x 10-3 1.00 x 10-6 2,340 0.0728 2.20
25° 77° 997 9,781 8.91 x 10-4 8.94 x 10-7 3,170 0.0720 2.23
30° 86° 996 9,771 7.97 x 10-4 8.00 x 10-7 4,250 0.0712 2.25
35° 95° 994 9,751 7.20 x 10-4 7.24 x 10-7 5,630 0.0704 2.27
40° 104° 992 9,732 6.53 x 10-4 6.58 x 10-7 7,380 0.0696 2.28
50° 122° 988 9,693 5.47 x 10-4 5.53 x 10-7 12,300 0.0679
60° 140° 983 9,643 4.66 x 10-4 4.74 x 10-7 20,000 0.0662
70° 158° 978 9,594 4.04 x 10-4 4.13 x 10-7 31,200 0.0644
80° 176° 972 9,535 3.54 x 10-4 3.64 x 10-7 47,400 0.0626
90° 194° 965 9,467 3.15 x 10-4 3.26 x 10-7 70,100 0.0607
100° 212° 958 9,398 2.82 x 10-4 2.94 x 10-7 101,300 0.0589
1Surface tension of water in contact with air

Table A.7. Physical Properties of Water at Atmospheric Pressure in SI Units
Temperature Density Specific Weight Dynamic Viscosity Kinematic Viscosity Vapor Pressure Surface Tension1 Bulk Modulus
Fahrenheit Centigrade Slug/ft3 Weight lb/ft3 lb-sec/ft2 ft2/sec lb/in2 lb/ft lb/in2
32° 1.940 62,416 0.374 x 10-4 1.93 x 10-5 0.09 0.00518 1.99
39.2 4.0° 1.940 62,424 0
40° 4.4° 1.940 62,423 0.323 1.67 0.12 0.00514 2.05
50° 10.0° 1.940 62,408 0.273 1.41 0.18 0.00508 2.11
60° 15.6° 1.939 62,366 0.235 1.21 0.26 0.00504 2.16
70° 21.1° 1.936 62,300 0.205 1.06 0.36 0.00497 2.20
80° 26.7° 1.934 62,217 0.180 0.929 0.51 0.00492 2.23
90° 32.2° 1.931 62,118 0.160 0.828 0.70 0.00486 2.25
100° 37.8° 1.927 61,998 0.143 0.741 0.95 0.00479 2.27
120° 48.9° 1.918 61,719 0.117 0.610 1.69 0.0466 2.28
140° 60° 1.908 61,386 0.0979 0.513 2.89
160° 71.1° 1.896 61,006 0.0835 0.440. 4.74
180° 82.2° 1.883 60,586 0.0726 0.385 7.51
200° 93.3° 1.869 60,135 0.0637 0.341 11.52
212° 100° 1.847 59,843 0.0593 0.319 14.70
1Surface tension of water in contact with air, weight of sea water approximately 63.93 lb/ft3 @ 15°C

Table A.8. Sediment Particles Grade Scale.
Size Approximate Sieve Mesh Opening per Inch Class
Millimeters Microns Inches Tyler U.S. Standard
4000-2000 ---- ---- 160-80 ---- ---- Very large boulders
2000-1000 ---- ---- 80-40 ---- ---- Large boulders
1000-500 ---- ---- 40-20 ---- ---- Medium boulders
500-250 ---- ---- 20-10 ---- ---- Small boulders
250-130 ---- ---- 10-5 ---- ---- Large cobbles
130-64 ---- ---- 5-2.5 ---- ---- Small cobbles
64-32 ---- ---- 2.5-1.3 ---- ---- Very coarse gravel
32-16 ---- ---- 1.3-0.6 ---- ---- Coarse gravel
16-8 ---- ---- 0.6-0.3 2 1/2 ---- Medium gravel
8-4 ---- ---- 0.3-0.16 5 5 Fine gravel
4-2 ---- ---- 0.16-0.08 9 10 Very fine gravel
2-1 2.00-1.00 2000-1000 ---- 16 18 Very coarse sand
1-1/2 1.00-0.50 1000-500 ---- 32 35 Coarse sand
1/2-1/4 0.50-0.25 500-250 ---- 60 60 Medium sand
1/4-1/8 0.25-0.125 250-125 ---- 115 120 Fine sand
1/8-1/16 0.125-0.062 125-62 ---- 250 230 Very fine sand
1/16-1/32 0.062-0.031 62-31 ---- ----   Coarse silt
1/32-1/64 0.031-0.016 31-16 ---- ---- ---- Medium silt
1/64-1/128 0.016-0.008 16-8 ---- ---- ---- Fine silt
1/128-1/256 0.008-0.004 8-4 ---- ---- ---- Very fine silt
1/256-1/512 0.004-.0020 4-2 ---- ---- ---- Coarse clay
1/512-1/1024 0.0020-0.0010 2-1 ---- ---- ---- Medium clay
1/1024-1/2048 0.0010-0.0005 1-0.5 ---- ---- ---- Fine clay
1/2048-1/4096 0.0005-0.0002 0.5-0.24 ---- ---- ---- Very fine clay

Table A.9. Common Equivalent Hydraulic Units
Volume
Unit Equivalent
cubic inch liter u.s. gallon cubic foot cubic yard cubic meter acre-foot sec-foot-day
liter 61.02 1 0.264 2 0.035 31 0.001 308 0.001 810.6 E - 9 408.7 E - 9
u.s. gallon 231.0 3.785 1 0.1337 0.004 951 0.003 785 3.068 E - 6 1.547 E - 6
cubic foot 1728 28.32 7.481 1 0.037 04 0.028 32 22.96 E - 6 11.57 E - 6
cubic yard 46,660 764.6 202.0 27 1 0.746 6 619.8 E - 6 312.5 E - 6
meter3 61,020 1000 264.2 35.31 1.308 1 810.6 E - 6 408.7 E - 6
acre-foot 75.27 E + 6 1,233,000 325,900 43 560 1.613 1 233 1 0.504 2
sec-foot-day 149.3 E + 6 2,447,000 646,400 66 400 3 200 2 447 1.983 1

Table A.9. Common Equivalent Hydraulic Units (con't)
Discharge (Flow Rate, Volume/Time)
Unit Equivalent
gallon/min liter/sec acre-foot/day foot3/sec million gal/day meter3/sec
gallon/minute 1 0.063 09 0.004 419 0.002 228 0.001 440 63.09 E - 6
liter/second 15.85 1 0.070 05 0.035 31 0.022 82 0.001
acre-foot/day 226.3 14.28 1 0.504 2 325 9 0.014 28
feet3/second 448.8 28.32 1.983 1 0.646 3 0.028 32
meter3/second 15,850 1000 70.04 35.31 22.83 1

Updated: 09/22/2014

United States Department of Transportation - Federal Highway Administration