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A pipe of 324 mm diameter, having fiction coefficient as 0.04, connects two reservoirs with 15 m difference in their water levels through a 1500 m long pipe. What will be the discharge through the pipe?
1. 104 Ips
2. 134 Ips
3. 165 Ips
4. 196 Ips

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Correct Answer - Option 1 : 104 Ips

Concept:

According to Darcy’s Weisbach equation:

\({\rm{Head\;loss}} = {{\rm{h}}_{\rm{f}}} = \frac{{{\rm{fL}}{{\rm{V}}^2}}}{{2{\rm{gD}}}}\)

 Where,

f = friction factor of the pipe, L = Length of the pipe, V = velocity of water through the pipe

g = gravitational acceleration, D = diameter of the pipe

Calculation:

Given: f = 0.04, L = 1500 m, D = 324 mm

The head lose in pipe is balanced by the difference in water levels of tank i.e. h = 15

\(15 = \frac{{0.04{\rm{\;}}\; \times {\rm{\;}}1500{\rm{\;}}{{\rm{V}}^2}}}{{2\; \times \;9.81\; \times \;0.324}}\)

⇒ V = 1.26 m/s

Discharge, Q = AV

\(Q = \frac{\pi }{4} \times {0.324^2} \times 1.26\) = 0.104 m3/s

Discharge in pipe, Q = 0.104 m3/s or 104 l/s

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