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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4

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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
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