Units and Quantities

CVEG 3213 HydraulicsCVEG 3213 HydraulicsLecture: Units and Quantities Lecture: Units and Quantities

Units and QuantitiesUnits and Quantities massmass

kg, g, mg, kg, g, mg, gg(microgram)(microgram)

• 1 kg = 1000 g = 101 kg = 1000 g = 1033g ; 1 g = 0.001 kg = 10g ; 1 g = 0.001 kg = 10-3-3 kg kg• 1 kg = 10001 kg = 1000..1000 mg = 101000 mg = 1066 (a million) mg (a million) mg• 1 1 g = 10g = 10-6-6 g g

1 kg = 2.2 lb1 kg = 2.2 lb• note: lb is actually a weight (force)note: lb is actually a weight (force)

F = ma F = ma

volumevolume 1 cubic foot = ft1 cubic foot = ft33 = 7.48 gal = 7.48 gal 1 gal = 3.8 L1 gal = 3.8 L 1 m1 m33 = 1000 L = 1000 L 1 mL = 1 cm1 mL = 1 cm33 = 1 cc = 1 cc

Units and QuantitiesUnits and Quantities Density: Density: = mass per volume = mass per volume

Water density = Water density = ww = 1 g/mL = 1 kg/L = 1 g/mL = 1 kg/L • = 62.4 lb/cubic foot= 62.4 lb/cubic foot*(see below)*(see below)

slightly temperature dependentslightly temperature dependent considered incompressible (very slightly compressible)considered incompressible (very slightly compressible)

Unit weight of water: Unit weight of water: ww = weight per volume = weight per volume ““specific weight”specific weight” weight is a force = mass x accelerationweight is a force = mass x acceleration

• = mass x g= mass x g g = 9.8 m/sg = 9.8 m/s22 = 32.2 ft/s = 32.2 ft/s33

ww = = ww..g g

• = 1000 kg/m= 1000 kg/m33 . . 9.8 m/s9.8 m/s22 = 9800 N/m = 9800 N/m33 = = 9.8 kN/m9.8 kN/m33 • = 1.94 slugs/ft= 1.94 slugs/ft33 .. 32.2 ft/s 32.2 ft/s22 = = 62.4 lb/ft62.4 lb/ft33

Units and QuantitiesUnits and Quantities Density of liquids Density of liquids

(pcf) SG

Ethyl Alcohol 49.3 0.79

Gasoline 42.5 0.68

Glycerin 78.6 1.26

Mercury 847 13.57

SAE 20 Oil 57 0.91

Seawater 64 1.03

Water 62.4 1.00

Units and QuantitiesUnits and Quantities

Solid densitySolid density• density of sand = 2.6 g/cmdensity of sand = 2.6 g/cm33 = 2600 kg/m = 2600 kg/m33 • concrete density = 2400 kg/mconcrete density = 2400 kg/m3 3 (150 lb/ft(150 lb/ft33), ),

SG = 2.4SG = 2.4

Dry bulk density of soil or solidsDry bulk density of soil or solids• Mass per volume (including voids)Mass per volume (including voids)• Approximately ~ 1.4 – 1.8 g/mLApproximately ~ 1.4 – 1.8 g/mL


Pressure = force per areaPressure = force per area N/mN/m22 = Pa (Pascal) = Pa (Pascal)

• often use kPaoften use kPa• atmospheric P: 1 atm = 101.325 kPaatmospheric P: 1 atm = 101.325 kPa

psi = lb/inpsi = lb/in22 • 1 atm = 14.7 psi1 atm = 14.7 psi


Pressure exerted by a 1-ft diameter Pressure exerted by a 1-ft diameter column of water 34 ft highcolumn of water 34 ft high Pressure = force (weight) per areaPressure = force (weight) per area

• wt = volume x unit wt (wt = volume x unit wt (ww)) volume = area x ht volume = area x ht

• area = area = /4 x dia/4 x dia22 = 3.14/4 x (1ft) = 3.14/4 x (1ft)22 = 0.785ft = 0.785ft22 • Vol = 0.785ftVol = 0.785ft22 x 34ft = 26.7ft x 34ft = 26.7ft33 = 200 gal = 200 gal

wt = 26.7ftwt = 26.7ft33 x 62.4 lb/ft x 62.4 lb/ft33 = 1666 lb = 1666 lb

• Pressure = wt/areaPressure = wt/area = 1666 lb / 0.785 ft= 1666 lb / 0.785 ft22 = 2122 lb/ft = 2122 lb/ft22 = 14.7 psi = 1.00 atm = 14.7 psi = 1.00 atm


Pressure exerted by a 10-ft square column Pressure exerted by a 10-ft square column of water 34 ft highof water 34 ft high Pressure = force (weight) per areaPressure = force (weight) per area

• wt = volume x unit wt (wt = volume x unit wt (ww)) volume = area x ht volume = area x ht

• area = 10ft x 10 ft = 100ftarea = 10ft x 10 ft = 100ft22 • Vol = 100ftVol = 100ft22 x 34ft = 3400ft x 34ft = 3400ft33 = 25430 gal = 25430 gal

wt = 3400ftwt = 3400ft33 x 62.4 lb/ft x 62.4 lb/ft33 = 212,160 lb = 212,160 lb

• Pressure = wt/areaPressure = wt/area = 212,160 lb / 100 ft= 212,160 lb / 100 ft22 = 2122 lb/ft = 2122 lb/ft22 = 14.7 psi = 1.00 atm = 14.7 psi = 1.00 atm


Velocity and distanceVelocity and distance If you drive 50 mph for two hours, how far do If you drive 50 mph for two hours, how far do

you go?you go?• 2 hr x 50 mi/hr = 100 mi (duh)2 hr x 50 mi/hr = 100 mi (duh)

If you drive 120 miles in 3 hours, what’s your If you drive 120 miles in 3 hours, what’s your average speed?average speed?• 120 mi / 3 hr = 40 mph 120 mi / 3 hr = 40 mph

distance = v distance = v .. t is important t is important• pipe flowpipe flow• stream flowstream flow


Concentration: CConcentration: C Concentration isConcentration is Mass per Volume Mass per Volume

• mass of chemical or solids per volume of solutionmass of chemical or solids per volume of solution• mg/L (milligram per liter)mg/L (milligram per liter)• 1 mg/L = 1 lb per 1 mg/L = 1 lb per __________ gal gal

1 L/mg x 1000 mg/g x 1000 g/kg x 2.2 kg/lb x 1 gal/3.8 L1 L/mg x 1000 mg/g x 1000 g/kg x 2.2 kg/lb x 1 gal/3.8 L = 120,000 gal/lb or 1 lb per 120,000 gal = 120,000 gal/lb or 1 lb per 120,000 gal

• 1 1 g/L (microgram per liter) = 1/1000 x mg/Lg/L (microgram per liter) = 1/1000 x mg/L


mg/L versus ppm (parts per million)mg/L versus ppm (parts per million) ppm is mass/massppm is mass/mass

• e.g., mg per million mg = mg/kge.g., mg per million mg = mg/kg

• waterwater = 1 kg/L, = 1 kg/L, 1 L of water weighs 1 kg1 L of water weighs 1 kg so a mg/L ~ ppmso a mg/L ~ ppm

Units and QuantitiesUnits and Quantities Flow: QFlow: Q

Flow is Volume per TimeFlow is Volume per Time• mm33/s , ft/s , ft33/s = cfs, gal/min = gpm/s = cfs, gal/min = gpm• MGD = million gallons per dayMGD = million gallons per day

note: 7.48 gal per ftnote: 7.48 gal per ft33

• 1 cfs = _____ MGD1 cfs = _____ MGD 1 ft1 ft33/s x 60 s/min x 60 min/hr x 24 hr/day /s x 60 s/min x 60 min/hr x 24 hr/day

x 7.48 gal/ftx 7.48 gal/ft33 x 1 million/10 x 1 million/1066 = 0.65 MGD= 0.65 MGD

• Beaver Water Plant = ?Beaver Water Plant = ? 40 – 60 MGD40 – 60 MGD

Units and QuantitiesUnits and Quantities Mass transportedMass transported

Mass/Time = QMass/Time = Q..CC• vol/time x mass/vol = mass/timevol/time x mass/vol = mass/time

If Fayetteville wastewater plant discharges 18 MGD of If Fayetteville wastewater plant discharges 18 MGD of water containing 2 mg/L phosphorus, how much water containing 2 mg/L phosphorus, how much phosphorus (kg, lbs) is discharged per day and per year?phosphorus (kg, lbs) is discharged per day and per year?

• Mass/Time = QMass/Time = Q..C = 18 x 10C = 18 x 1066 gal/day x 2 mg/L gal/day x 2 mg/L x 3.8 L/gal x 1g/1000 mg x 1kg/1000 g x 3.8 L/gal x 1g/1000 mg x 1kg/1000 g = 137 kg/day= 137 kg/day x 365 = ~ 50,000 kg/yrx 365 = ~ 50,000 kg/yr

• 18 MGD x 2 mg/L x (8.34 lb/MG)/mg/L18 MGD x 2 mg/L x (8.34 lb/MG)/mg/L = 300 lb/day= 300 lb/day

• x 1 kg/2.2 lb = 137 kg/dayx 1 kg/2.2 lb = 137 kg/day

Units and Quantities

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