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Hydraulic Design of Energy Dissipators for Culverts and Channels
Hydraulic Engineering Circular Number 14, Third Edition

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. Table A.7 gives the sediment grade scale and Table A.8 gives some common equivalent hydraulic units.

Table A.1. Overview of SI.
 UnitsSymbol
Base unitslengthmeterm
masskilogramkg
timeseconds
temperature*kelvinK
electrical currentampereA
luminous intensitycandelacd
amount of materialmolemol
Derived units ** 
Supplementary unitsangles in the planeradianrad
solid anglessteradiansr
* Use degrees Celsius (°C), which has a more common usage than kelvin.
** Many derived units exist; several will be discussed in this session.
Table A.2 Relationship of Mass and Weight.
 MassWeight or Force of GravityForce
Customaryslugpoundpound
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
deka101da
hector102h
kilo103k
mega106M
giga109G
tera1012T
peta1015P
exa1018E
zeta1021Z
yotto1024Y
Table A.6. Physical Properties of Water at Atmospheric Pressure in SI Units
TemperatureDensitySpecific WeightDynamic ViscosityKinematic ViscosityVapor PressureSurface Tension1Bulk Modulus
CentigradeFahrenheitkg/m3N/m3N · s/m2m2/sN/m2 abs.N/mGN/m2
32°1,0009,8101.79 x 10-31.79 x 10-66110.07561.99
41°1,0009,8101.51 x 10-31.51 x 10-68720.07492.05
10°50°1,0009,8101.31 x 10-31.31 x 10-61,2300.07422.11
15°59°9999,8001.14 x 10-31.14 x 10-61,7000.07352.16
20°68°9989,7901.00 x 10-31.00 x 10-62,3400.07282.20
25°77°9979,7818.91 x 10-48.94 x 10-73,1700.07202.23
30°86°9969,7717.97 x 10-48.00 x 10-74,2500.07122.25
35°95°9949,7517.20 x 10-47.24 x 10-75,6300.07042.27
40°104°9929,7326.53 x 10-46.58 x 10-77,3800.06962.28
50°122°9889,6935.47 x 10-45.53 x 10-712,3000.0679 
60°140°9839,6434.66 x 10-44.74 x 10-720,0000.0662 
70°158°9789,5944.04 x 10-44.13 x 10-731,2000.0644 
80°176°9729,5353.54 x 10-43.64 x 10-747,4000.0626 
90°194°9659,4673.15 x 10-43.26 x 10-770,1000.0607 
100°212°9589,3982.82 x 10-42.94 x 10-7101,3000.0589 
1Surface tension of water in contact with air
Table A.7. Physical Properties of Water at Atmospheric Pressure in SI Units
TemperatureDensitySpecific WeightDynamic ViscosityKinematic ViscosityVapor PressureSurface Tension1Bulk Modulus
FahrenheitCentigradeSlug/ft3Weight lb/ft3lb-sec/ft2ft2/seclb/in2lb/ftlb/in2
32°1.94062,4160.374 x 10-41.93 x 10-50.090.00518287,000
39.24.0°1.94062,4240    
40°4.4°1.94062,4230.3231.670.120.00514296,000
50°10.0°1.94062,4080.2731.410.180.00508305,000
60°15.6°1.93962,3660.2351.210.260.00504313,000
70°21.1°1.93662,3000.2051.060.360.00497319,000
80°26.7°1.93462,2170.1800.9290.510.00492325,000
90°32.2°1.93162,1180.1600.8280.700.00486329,000
100°37.8°1.92761,9980.1430.7410.950.00479331,000
120°48.9°1.91861,7190.1170.6101.690.0466332,000
140°60°1.90861,3860.09790.5132.89  
160°71.1°1.89661,0060.08350.440.4.74  
180°82.2°1.88360,5860.07260.3857.51  
200°93.3°1.86960,1350.06370.34111.52  
212°100°1.84759,8430.05930.31914.70  
1Surface tension of water in contact with air
Table A.8. Sediment Particles Grade Scale.
SizeApproximate Sieve Mesh Opening per InchClass
MillimetersMicronsInchesTylerU.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 ½-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-.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.9. Common Equivalent Hydraulic Units
Volume
UnitEquivalent
cubic inchliteru.s. galloncubic footcubic yardcubic meteracre-footsec-foot-day
liter61.0210.264 20.035 310.001 3080.001810.6 E - 9408.7 E - 9
u.s. gallon231.03.78510.13370.004 9510.003 7853.068 E - 61.547 E - 6
cubic foot172828.327.48110.037 040.028 3222.96 E - 611.57 E - 6
cubic yard46,660764.6202.02710.746 6619.8 E - 6312.5 E - 6
meter361,0201000264.235.311.3081810.6 E - 6408.7 E - 6
acre-foot75.27 E + 61,233,000325,90043 5601.6131 23310.504 2
sec-foot-day149.3 E + 62,447,000646,40086 4003 2002 4471.9831
Table A.9. Common Equivalent Hydraulic Units (con't)
Discharge (Flow Rate, Volume/Time)
UnitEquivalent
gallon/minliter/secacre-foot/dayfoot3/secmillion gal/daymeter3/sec
gallon/minute10.063 090.004 4190.002 2280.001 44063.09 E - 6
liter/second15.8510.070 050.035 310.022 820.001
acre-foot/day226.314.2810.504 20.325 90.014 28
feet3/second448.828.321.98310.646 30.028 32
million gal/day694.443.813.0681.54710.043 82
meter3/second15,850100070.0435.3122.831
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Contact:

Cynthia Nurmi
Resource Center (Atlanta)
404-562-3908
cynthia.nurmi@dot.gov

Updated: 04/07/2011
 

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