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CVEG 3213 Hydraulics Lecture: Units and Quantities

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Units and Quantities mass kg, g, mg, g (microgram) kg, g, mg, g (microgram) 1 kg = 1000 g = 10 3 g ; 1 g = kg = kg1 kg = 1000 g = 10 3 g ; 1 g = kg = kg 1 kg = mg = 10 6 (a million) mg1 kg = mg = 10 6 (a million) mg 1 g = g1 g = g 1 kg = 2.2 lb 1 kg = 2.2 lb note: lb is actually a weight (force)note: lb is actually a weight (force) F = ma F = ma volume 1 cubic foot = ft 3 = 7.48 gal 1 cubic foot = ft 3 = 7.48 gal 1 gal = 3.8 L 1 gal = 3.8 L 1 m 3 = 1000 L 1 m 3 = 1000 L 1 mL = 1 cm 3 = 1 cc 1 mL = 1 cm 3 = 1 cc

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Units and Quantities Density: = mass per volume Water density = w = 1 g/mL = 1 kg/L Water density = w = 1 g/mL = 1 kg/L = 62.4 lb/cubic foot *(see below) = 62.4 lb/cubic foot *(see below) slightly temperature dependent slightly temperature dependent considered incompressible (very slightly compressible) considered incompressible (very slightly compressible) Unit weight of water: w = weight per volume “specific weight” “specific weight” weight is a force = mass x acceleration weight is a force = mass x acceleration = mass x g= mass x g g = 9.8 m/s 2 = 32.2 ft/s 3 g = 9.8 m/s 2 = 32.2 ft/s 3 w = w. g w = w. g = 1000 kg/m m/s 2 = 9800 N/m 3 = 9.8 kN/m 3= 1000 kg/m m/s 2 = 9800 N/m 3 = 9.8 kN/m 3 = 1.94 slugs/ft ft/s 2 = 62.4 lb/ft 3= 1.94 slugs/ft ft/s 2 = 62.4 lb/ft 3

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Units and Quantities Density of liquids (pcf) SG Ethyl Alcohol Gasoline Glycerin Mercury SAE 20 Oil Seawater Water

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Units and Quantities Solid density Solid density density of sand = 2.6 g/cm 3 = 2600 kg/m 3density of sand = 2.6 g/cm 3 = 2600 kg/m 3 concrete density = 2400 kg/m 3 (150 lb/ft 3 ),concrete density = 2400 kg/m 3 (150 lb/ft 3 ), SG = 2.4 SG = 2.4 Dry bulk density of soil or solids Dry 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

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Units and Quantities Pressure = force per area N/m 2 = Pa (Pascal) N/m 2 = Pa (Pascal) often use kPaoften use kPa atmospheric P: 1 atm = kPaatmospheric P: 1 atm = kPa psi = lb/in 2 psi = lb/in 2 1 atm = 14.7 psi1 atm = 14.7 psi

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Units and Quantities Pressure exerted by a 1-ft diameter column of water 34 ft high Pressure = force (weight) per area Pressure = force (weight) per area wt = volume x unit wt ( w )wt = volume x unit wt ( w ) volume = area x ht volume = area x ht area = /4 x dia 2 = 3.14/4 x (1ft) 2 = 0.785ft 2area = /4 x dia 2 = 3.14/4 x (1ft) 2 = 0.785ft 2 Vol = 0.785ft 2 x 34ft = 26.7ft 3 = 200 galVol = 0.785ft 2 x 34ft = 26.7ft 3 = 200 gal wt = 26.7ft 3 x 62.4 lb/ft 3 = 1666 lb wt = 26.7ft 3 x 62.4 lb/ft 3 = 1666 lb Pressure = wt/areaPressure = wt/area = 1666 lb / ft 2 = 2122 lb/ft 2 = 14.7 psi = 1.00 atm = 1666 lb / ft 2 = 2122 lb/ft 2 = 14.7 psi = 1.00 atm

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Units and Quantities Pressure exerted by a 10-ft square column of water 34 ft high Pressure = force (weight) per area Pressure = force (weight) per area wt = volume x unit wt ( w )wt = volume x unit wt ( w ) volume = area x ht volume = area x ht area = 10ft x 10 ft = 100ft 2area = 10ft x 10 ft = 100ft 2 Vol = 100ft 2 x 34ft = 3400ft 3 = galVol = 100ft 2 x 34ft = 3400ft 3 = gal wt = 3400ft 3 x 62.4 lb/ft 3 = 212,160 lb wt = 3400ft 3 x 62.4 lb/ft 3 = 212,160 lb Pressure = wt/areaPressure = wt/area = 212,160 lb / 100 ft 2 = 2122 lb/ft 2 = 14.7 psi = 1.00 atm = 212,160 lb / 100 ft 2 = 2122 lb/ft 2 = 14.7 psi = 1.00 atm

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Units and Quantities Velocity and distance If you drive 50 mph for two hours, how far do you go? If you drive 50 mph for two hours, how far do 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 average speed? If you drive 120 miles in 3 hours, what’s your average speed? 120 mi / 3 hr = 40 mph120 mi / 3 hr = 40 mph distance = v. t is important distance = v. t is important pipe flowpipe flow stream flowstream flow

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Units and Quantities Velocity and distance If you drive 50 mph for two hours, how far do you go? If you drive 50 mph for two hours, how far do 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 average speed? If you drive 120 miles in 3 hours, what’s your average speed? 120 mi / 3 hr = 40 mph120 mi / 3 hr = 40 mph distance = v. t is important distance = v. t is important pipe flowpipe flow stream flowstream flow

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Units and Quantities Concentration: Concentration: C Concentration Concentration is is Mass per Volume massmass of chemical or solids per volume of solution mg/Lmg/L (milligram per liter) 1mg/L = 1 lb per _____ _____ gal 1L/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 1 g/L g/L (microgram per liter) = 1/1000 x mg/L

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Units and Quantities mg/L versus ppm (parts per million) ppm is mass/mass ppm is mass/mass e.g., mg per million mg = mg/kge.g., mg per million mg = mg/kg water = 1 kg/L, water = 1 kg/L, 1 L of water weighs 1 kg 1 L of water weighs 1 kg so a mg/L ~ ppm so a mg/L ~ ppm

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Units and Quantities Flow: Q Flow is Volume per Time Flow is Volume per Time m 3 /s, ft 3 /s = cfs, gal/min = gpmm 3 /s, ft 3 /s = cfs, gal/min = gpm MGD = million gallons per dayMGD = million gallons per day note: 7.48 gal per ft 3 note: 7.48 gal per ft 3 1 cfs = _____ MGD1 cfs = _____ MGD 1 ft 3 /s x 60 s/min x 60 min/hr x 24 hr/day 1 ft 3 /s x 60 s/min x 60 min/hr x 24 hr/day x 7.48 gal/ft 3 x 1 million/10 6 x 7.48 gal/ft 3 x 1 million/10 6 = 0.65 MGD = 0.65 MGD Beaver Water Plant = ?Beaver Water Plant = ? 40 – 60 MGD 40 – 60 MGD

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Units and Quantities Mass transported Mass/Time = Q. C Mass/Time = Q. C vol/time x mass/vol = mass/timevol/time x mass/vol = mass/time If Fayetteville wastewater plant discharges 18 MGD of water containing 2 mg/L phosphorus, how much phosphorus (kg, lbs) is discharged per day and per year? If Fayetteville wastewater plant discharges 18 MGD of water containing 2 mg/L phosphorus, how much phosphorus (kg, lbs) is discharged per day and per year? Mass/Time = Q. C = 18 x 10 6 gal/day x 2 mg/L x 3.8 L/gal x 1g/1000 mg x 1kg/1000 gMass/Time = Q. C = 18 x 10 6 gal/day x 2 mg/L x 3.8 L/gal x 1g/1000 mg x 1kg/1000 g = 137 kg/day = 137 kg/day x 365 = ~ 50,000 kg/yr x 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

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