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Design For Fish Passage at Roadway - Stream Crossings: Synthesis Report


Appendix A

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 include the kilometer (1000 m), the centimeter (1m/100) and the millimeter (1 m/1000). The second base unit relevant to highway applications is the kilogram, a measure of mass that is the inertia 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 Customary (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 Customary to SI units. The symbols used in this table for metric (SI) 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.

Table A.6 provides physical properties of water at atmospheric pressure in SI units, A.7 in customary units. Table A.8 gives the sediment grade scale and Table A.9 and A.10 give some common equivalent hydraulic units.

Table A.1 Overview of SI
  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 steradiasr

* Use degrees Celsius (°C), which has a more common usage Kelvin.
** Many derived units exist; several will be discussed in this session.

Table A.2 Relationship of Mass and Weight
  Mass Weight or Force of Gravity Force
Customary 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
Capacitance farad F C/V
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

* 4 significant figures; underline denotes exact conversion

Table A.4 Useful Conversion Factors (continued)
Quantity From English Units To Metric Units Multiplied by*
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 A m 1.356
ft-kip kN A 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
mrad 17.45

* 4 significant figures; underline denotes exact conversion

Table A.5 Prefixes
Submultiples Multiples
deci 10-1 d deka 101 da
centi 10-2 c hector 102 h
milli 10-3 m kilo 103 k
micro 10-6 μ mega 106 M
nano 10-9 n giga 109 G
pica 10-12 p tera 1012 T
femto 10-15 f peta 1015 P
atto 10-18 a exa 1018 E
zepto 10-21 z zeta 1021 Z
yocto 10-24 y 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
0° 32° 1,000 9,810 1.79 x 10-3 1.79 x 10-6 611 0.0756 1.99
5° 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 (Customary 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° 0° 1.940 62,416 0.374 x 10-4 1.93 x 10-5 0.09 0.00518 287,000
39.2 4.0° 1.940 62,424 0
40° 4.4° 1.940 62,423 0.323 1.67 0.12 0.00514 296,000
50° 10.0° 1.940 62,408 0.273 1.41 0.18 0.00508 305,000
60° 15.6° 1.939 62,366 0.235 1.21 0.26 0.00504 313,000
70° 21.1° 1.936 62,300 0.205 1.06 0.36 0.00497 319,000
80° 26.7° 1.934 62,217 0.180 0.929 0.51 0.00492 325,000
90° 32.2° 1.931 62,118 0.160 0.828 0.70 0.00486 329,000
100° 37.8° 1.927 61,998 0.143 0.741 0.95 0.00479 331,000
120° 48.9° 1.918 61,719 0.117 0.610 1.69 0.0466 332,000
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

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 ½ - 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 86 400 3 200 2 447 1.983 1
Table A.10 Common Equivalent Hydraulic Units (continued)
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 0.325 9 0.014 28
feet3/second 448.8 28.32 1.983 1 0.646 3 0.028 32
million gal/day 694.4 43.81 3.068 1.547 1 0.043 82
meter3/second 15,850 1000 70.04 35.31 22.83 1
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Updated: 04/07/2011

Contact:

Bert Bergendahl
720-963-3754
Bart.Bergendahl@dot.gov
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