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