Environmental Engineering CIV2257 Hydraulic Systems Environmental Engineering CIV2257

Review of Basic Concepts Density, ρ = mass / volume [kg/m³] ρ = 1000 kg/m³ for water ρg = 62.4 lb/ft³ for water Pressure = force / area [N / m² = Pa] Pressure = ρ g h [kg/m³ * m/s² * m = Pa] Flowrate, Q = Velocity x Area = VA [m³/s]

Continuity Equation Flow entering = Flow exiting the system … or what goes in must come out. Q1 = Q2 V1A1 = V2A2

General Energy Equation P1/ρg + z1 + v1²/2g + hA – hR – hL = P2/ρg + z2 + v2²/2g where hL represents the friction losses of flowing fluid through pipe, valves and fittings. The General Energy Equation must be written in the direction of flow (for the h signs to be correct)

Hazen-Williams Formula Popular for water systems … … but the fluid must be water, in pipe sizes between 2” and 6 ft in diameter, with a velocity < 10 ft/s, and a flowing temperature of 60°F; … and it ignores minor losses in the system; … and be sure you use the correct formula for SI or Imperial units. … and the Hazen-Williams Coefficient (C) can vary from source to source.

Hazen-Williams Formula SI Units hL = 0.002131 L (100/C)1.85 Q 1.85/D4.8655 Imperial Units hL = 0.002083 L (100/C)1.85 Q 1.85/D4.8655 where C = Hazen-Williams Coefficient Q = flowrate [gpm or m³/s] D = diameter [inches or m] L = length [feet or m]

Hazen-Williams Coefficient (*Can vary depending on the source) Type of Pipe Hazen-Williams Coefficient, C Asbestos cement 140 Concrete 100 – 130, use 100 Copper 130 – 140, use 130 Plastic 130 – 150, use 130 Glass 130 New welded steel 120 New riveted steel 110 Corrugated steel 60 Ductile Iron: Cement Lined 130 – 150, use 140 New, unlined 5-year old, unlined 20-year old, unlined 100 Texts range in values.

Darcy’s Equation For laminar or turbulent flow: hL = ƒ x L/D x v²/2g where: hL is the energy loss due to friction [m] L is the length of pipe [m] D is the diameter of the pipe [m] v is the average velocity [m/s] ƒ is the friction factor [dimensionless] Can be used for long, straight sections of pipe for both laminar and turbulent flow.

Table 9.1, p.243

Table 9.2, Moody Diagram, Mott, p.244

Sch. 40 Steel Pipe

Centrifugal Pumps

Centrifugal Pumps

Pump Curve (Usually for a given pump model operating at a given speed [rpm]) Head-Discharge Curve Shows the relationship of flowrate and head delivered from shutoff head to run-out conditions for a range of impeller sizes. Efficiency Shows the pump efficiency depending on design conditions. Power Shows the motor horsepower required. NPSHR Shows the net positive suction head required (NPSHR) to prevent cavitation. Difference between the suction pressure and the saturation pressure of the fluid being pumped.

Pump Curve

Pump Curve http://www.alard-equipment.com/p-z/thomsen/thomsen8_curve3450.jpg

Pump Curve http://www.zoeller.com/imagesZep/a00416.gif

Centrifugal Pumps Power (required) = ρ g Q hL Power (motor) = Power (required) / efficiency (Efficiency is found on the pump curve and varies for manufacturer and design of pump)

Example Flowrate of pump at A = 1600 gpm Outflow at B=1100 gpm and C=900 gpm. Find rate of discharge from storage. C = 100

Example Outflow at B=800 gpm and C=650 gpm. The pressure at C = 40 psig Find rate of discharge from storage, and size the pump. C = 100

Open Channel Flow

Open Channel Flow Flow through pipe or through channels that is open to the atmosphere.

Manning’s Equation (metric) Q = vA = 1.00 A R2/3 S1/2 n R is the hydraulic radius [m] A is the x-sectional area [m² S is the slope of the channel n (Manning’s number) is a factor that relates the condition of the surface (like pipe roughness) v = Q/A can be substituted into Manning’s equation.

Manning’s Equation (Imperial) Q = vA = 1.49 A R2/3 S1/2 n R is the hydraulic radius [ft] A is the x-sectional area [ft²] S is the slope of the channel n (Manning’s number) is a factor that relates the condition of the surface (like pipe roughness) v = Q/A can be substituted into Manning’s equation.

Manning’s Number Channel Description Manning’s Number Glass, copper, plastic (smooth surfaces) 0.010 Unpainted steel, planed wood 0.012 Painted steel, coated cast iron 0.013 Smooth asphalt, trowel-finished concrete Black iron pipe, clay sewer pipe 0.014 Float-finished concrete, concrete pipe 0.015 Formed, unfinished concrete 0.017 Smooth earth 0.018 Clean excavated earth 0.022 Corrugated metal storm drain 0.024 Natural channel (stones & weeds) 0.030 Natural channel (light brush) 0.050 Natural channel (tall grasses and reeds) 0.060 Natural channel (heavy brush_ 0.100

Circular Pipe Diagram

Flow Measurement

Flow Measurement Closed Channel Venturi Meter

Venturi Meter Calculations PA/γ + zA + vA²/2g = PB/γ + zB + vB²/2g (PA- PB)/ γ + (zA- zB) = (vB²- vA²)/2g From continuity, substitute: vAAA = vBAB (PA- PB)/γ + (zA- zB) = ((vAAA/AB)²-vA²)/2g … Solve for vA

Flow Measurement Open Channel Parshall Flume good for wastewater with suspended and floating solids.

Parshall Flume Calculations Q = 4BH1.522(B^0.026) Where Q = Flowrate [ft³/s] B = Throat width [ft] H = Upper head [ft]

Summary Use Hazen-Williams Formula (cautiously) for closed pipe design. Use Manning’s Equation for open channel flow. Centrifugal pumps must be designed for flowrate and required head with a consideration for motor power and NPSHR.