Question

In: Civil Engineering

"Two reservoirs 1200 m apart are connected by a 50-cm smooth concrete pipe. If the two...

"Two reservoirs 1200 m apart are connected by a 50-cm smooth concrete pipe. If the two reservoirs have an elevation difference of 5 m, determine the discharge (20 degree C) in the pipe by the Darcy Weisbach equation, (b) the Hazen- Williams equation, (c) the Manning equation. Assume minor losses are negligible and verify your results with computer software."

Solutions

Expert Solution

Distance between reservoir, that is the length of pipe, l = 1200m

Diameter of pipe, Dc = 0.5m (full flow condition is assumed)

head loss, h_l = 5m

Discharge, Q, as per Darcy Weisbach equation

S=f*8π2g+Q2Dc5

S à hydraulic slope (h_l/l)

f à Darcy friction factor; Re = 2000

f=64Re
f = .032 (for laminar flow)

therefore, substituting in the above equation, Q = 0.00699 m³/s

Computer Analysis Using EPANET

Used two pipes of 600m length and .5m dia for successful analysis. Below is the screenshot of the results as per each equation:

as per Darcy Weisbach equation

as per Hazen- Williams equation

Discharge, Q, as per Hazen- Williams equation

S=10.67*Q1.852C1.852*d14.87045

Cà Roughness coefficient, C = 100.

Q = 0.00159 m³/s

Discharge, Q, as per Manning equation

Q=.312n*D83*S1/2

D = A/P ; S=.5/1200; n = 0.015

Q = 0.00165 m³/s

Ally Wells answered 1 year ago

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