HW-Hydraulic calculations

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University of Akron *

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MISC

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Mechanical Engineering

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Apr 3, 2024

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docx

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Exercise 1: A 200m aluminum pipe of 3 inches diameter (internal) will be used to convey 10 l/s to your farm. The absolute roughness of the pipe (e) is equal to 0.0015 mm; Water density 𝜌 = 1,000 kg/m 3 ; and water viscosity μ= 1.14x10 3 ‐ Kg/ms (or Pa.s) at 15 o C . Calculate the expected velocity of the flow (m/s) in the pipe d = 3 in = 0.0763 m q = 10 l/s = 0.01 m3/s V = Q/A = 0.01 x 4/ (pi x 0.0763^2) V = 2.1871 m/s Using Reynolds number, determine the type of flow. R = Rho x V x d / μ R = (1000 x 2.1871 x 0.0763)/ 1.14x10 3 ‐ R = 146,382.2193 ; Turbulent flow Use Moody diagram to find the friction loss factor (f) of Darcy Weisbach ‐ Relative Roughness = 0.0015 / 76.3 = 0.0000197 f = 0.017 Calculate the total friction losses in the pipe using Darcy Weisbach equation ‐ h = fLV^2/2gd h = 0.017 x 200 x 2.1871^2/(2 x 9.81 x 0.0763) h = 10.864 m If the desired pressure at the end of the pipe is 20m. Calculate the power (kW) of the pump. Assume a pump efficiency equivalent to 75%. Pressure applied = 20 + 10.864 = 30.864 m Power = Discharge x Pressure / (367 x Efficiency)

q = 10 l/s = 0.01 m3/s = 36 m3/h Power = ( 36 x 30.864) / (367 x 0.75) Power = 4.037 kW If the pump is to be powered using a diesel motor, calculate the motor power needed (kW) assuming a motor efficiency equivalent to 40%. Motor Power = power of pump / Motor efficiency = 4.037/ 0.4. = 10.093 kW The selected motor consumes 0.4 liter of diesel to produce 1 kW.h. The annual operation time of the pump is estimated to 3,600 hours. At diesel price of 1.45 $/liter, determine you annual diesel cost. Energy consumed = 10.093 x 3600 = 36,334.8 kWh Liters consumed = 0.4 x 36,334.8 = 14,533.92 liters Annual diesel cost = 14,533.92 x 1.45 = $ 21,074.18 Page 1 of 2

Page 2 of 2 Exercise 2: Drip irrigation Crop: Each tree will have 2 drippers of 4 l/h each. How many drippers per lateral are needed ? Number of trees per lateral = 113/2.35 = 48 trees Drippers = 48 x 2 = 96 drippers Laterals are made of 3/4 inch PVC pipe on which on line 4 l/h drippers will be used. Calculate the friction losses along the lateral d = ¾ in = 0.01905 m Using Colebrook Write Equation excel sheet Friction losses = 0.5 m How many laterals the manifold has to carry? Number of laterals = 120/2.35 = 51 The minimum operational pressure of the dripper should not be lower than 1 bar (H =10m). Difference in operating pressure between the most downstream end dripper (lowest pressure = 10m) and the most upstream end pressure (highest pressure) should not exceed 20% (∆H <20m), as this will correspond to discharge variation equivalent to 10% (∆Q/Q = 10%). Determine the appropriate pipe diameter for the manifold. Select the pipe size from the following table (commercially available pipe size) Friction losses cannot exceed 2 – 0.5 = 1.5 m Using Colebrook Write Equation excel sheet Diameter = 0.0659 m = 2.594 Therefore 2.75 in (2 ¾ ) pipe is selected

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Assume the 35m conveyance pipe will have the same diameter as your manifold. Calculate the friction losses in the conveyance pipe. Using Colebrook Write Equation excel sheet; Pipe diameter = 2.75 in = 0.06985 m Fiction losses = 0. 99 m Ignore the friction losses in the tube well and assume a pump efficiency of 75%, calculate the pump power (kW) needed to operate the system. Add 10% of total friction losses to account for head losses in junctions, gates, flow meters, filtering system … Pressure Up stream = Minimum dripper pressure + Friction losses in pipe + Friction losses in filters and juntions + Field topography + Difference in elevation between field and water source Pressure Up stream = 10 + ( 0.5 + 1.5 + 0.99) + 0.1 x ( 0.5 + 1.5 + 0.99) + 0 + 50 Pressure Up stream = 63.289 m Power = Discharge x Pressure / (367 x Efficiency) Power = ( 19.584 x 63.289) / (367 x 0.75) Power = 4.503 kW Select the power needed to run the pump using an electrical motor (efficiency of 90%) Motor Power = power of pump / Motor efficiency = 4.503/ 0.9. = 5.003 kW On an average year you will apply 350mm of water to your orchard. Based on your design, what will be your annual energy bill assuming the cost of 1kW.h of electricity is 0.2 $. Time = Volume/ Discharge Time = (0.35 x 113 x 120)/ 19.584 = 242.34 hrs Energy consumed by pump = 5.003 x 242. 34 = 1,212.43 kWh Annual electricity cost = 0.2 x 1 ,212.43 = $ 242.486