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Hydraulics Engineering

 

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 (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 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 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 symbols used 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.

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

Table A.1.  Overview of SI 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.
Table A.2.  Relationship of Mass and Weight.
  MassWeight or Force of Gravity Force
English slug pound pound
pound-masspound-forcepound-force
metrickilogramnewtonnewton
Table A.3.  Derived Units With Special Names.
QuantityNameSymbolExpression
FrequencyhertzHzs-1
ForcenewtonNkg × m/s2
Pressure, stresspascalPaN/m2
Energy, work, quantity of heatjouleJN × m
Power, radiant fluxwattWJ/s
Electric charge, quantitycoulombCA × s
Electric potentialvoltVW/A
CapacitancefaradFC/V
Electric resistanceohmΩV/A
Electric conductancesiemensSA/V
Magnetic fluxweberWbV × s
Magnetic flux densityteslaTWb/m2
InductancehenryHWb/A
Luminous fluxlumenlmcd × sr
Illuminanceluxlxlm/m2
Table A.4. Useful Conversion Factors.
QuantityFrom English UnitsTo Metric UnitsMultiplied by*
LengthMilekm1.609
yardm0.9144
footm0.3048
inchmm25.4
Areasquare milekm22.590
acrem24047
acrehectare0.4047
square yardm20.8361
square footm20.092 90
square inchmm2645.2
Volumeacre footm31 233
cubic yardm30.7646
cubic footm30.028 32
cubic footL (1000 cm3)28.32
100 board feetm30.2360
gallonL (1000 cm3)3.785
cubic inchcm316.39
MassLbkg0.4536
kip (1000 lb)metric ton (1000 kg)0.4536
Mass/unit lengthplfkg/m1.488
Mass/unit areapsfkg/m24.882
Mass densitypcfkg/m316.02
ForcelbN4.448
kipkN4.448
Force/unit lengthplfN/m14.59
klfkN/m14.59
Pressure, stress, modulus of elasticitypsfPa47.88
ksfkPa47.88
psikPa6.895
ksiMPa6.895
Bending moment, torque, moment of forceft-lbN · m1.356
ft-kipkN · m1.356
Moment of masslb · ftkg · m0.1383
Moment of inertialb · ft2kg · m20.042 14
Second moment of areaIn4mm4416 200
Section modulusIn3mm316 390
Powerton (refrig)kW3.517
Btu/skW1.054
hp (electric)W745.7
Btu/hW0.2931
Volume rate of flowft3/sm3/s0.028 32
cfmm3/s0.000 471 9
cfmL/s0.4719
mgdm3/s0.0438
Velocity, speedft/sm/s0.3048
Accelerationf/s2m/s20.3408
Momentumlb · ft/seckg · m/s0.1383
Angular momentumlb · ft2/skg · m2/s0.042 14
Plane angledegreerad0.017 45
mrad17.45
* 4 significant figures; underline denotes exact conversion
Table A.5.  Prefixes.
Submultiples
deci10-1d
centi10-2c
milli10-3m
micro10-6μ
nano10-9n
pica10-12p
femto10-15f
atto10-18a
zepto10-21z
yocto10-24y
 
Multiples
deka 101 da
hecto 102 h
kilo 103 k
mega 106 M
giga 109 G
tera 1012 T
peta 1015 P
exa 1018 E
zetta 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
Celcius 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.  Sediment Particles Grade Scale.
SizeApproximate Sieve Mesh
Openings Per Inch
Class
MillimetersMicronsInches 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--------0.6-0.32 1/2----Medium gravel
8-4--------0.3-0.1655Fine gravel
4-2--------0.16-0.08910Very fine gravel
2-12.00-1.002000-1000----1618Very coarse sand
1-1/21.00-0.501000-500----3235Coarse sand
1/2-1/40.50-0.25500-250----6060Medium sand
1/4-1/80.25-0.125250-125----115120Fine sand
1/8-1/160.125-0.062125-62----250230Very fine sand
1/16-1/320.062-0.03162-31------------Coarse silt
1/32-1/640.031-0.01631-16------------Medium silt
1/64-1/1280.016-0.00816-8------------Fine silt
1/128-1/2560.008-0.0048-4------------Very fine silt
1/256-1/5120.004-0.00204-2------------Coarse clay
1/512-1/10240.0020-0.00102-1------------Medium clay
1/1024-1/20480.0010-0.00051-0.5------------Fine clay
1/2048-1/40960.0005-0.00020.5-0.24------------ Very fine clay
Table A.8.  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 0.133 7 0.004 951 0.003 785 3.068 E - 6 1.547 E - 6
Cubic Foot 1,728 28.32 7.481 1 0.037 04 0.028 32 22.96 E - 6 11.57 E - 6
Cubic Yard 46,660 764.5 202.0 27 1 0.746 6 619.8 E - 6 312.5 E - 6
Meter3 61,020 1,000 264.2 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
Discharge (Flow Rate, Volume/Time)
Unit 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
Meter3/Second 15,850 1,000 70.04 35.31 22.82 1
Updated: 12/08/2014

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