Water Resources and Environmental Hydraulics · Environmental Hydraulics · 2 marks · Numerical answer
Reservoirs differ10 m in level and connect through 50 m of .10 m pipe, friction factor .02. Replace the final25 m with .20 m pipe of the same material. Ignore minor losses. Find discharge increase in percent, to one decimal.
At fixed friction factor, Darcy head loss is proportional to $Q^2\sum L/D^5$. Old resistance is 50/.1⁵; new is 25/.1⁵+25/.2⁵. Thus $Q_n/Q_o=\sqrt{2/(1+1/32)}=1.392621$. Increase=**39.3%**. The10 m driving head cancels in the ratio.
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