GATE 2019 CE (CE1) – Question 60
Two reservoirs are connected by a full-running siphon of total length 5000 m and diameter 0.10 m. The inlet leg to the summit is 2000 m and reservoir surfaces differ by 5 m. Minimum permissible absolute summit pressure is 2.5 m water, atmospheric pressure 10.3 m water, friction factor f = 0.02 throughout and g = 9.81 m/s². Considering only major losses by Darcy–Weisbach, find maximum summit elevation h above the upper reservoir (m), to one decimal place.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 5.7 to 5.9
Explanation
Overall reservoir head difference equals friction loss: $5=(fL/D)V^2/(2g)$. Here $fL/D=1000$, so velocity head is 0.005 m. Inlet-leg friction loss is $(2000/5000)(5)=2$ m. Bernoulli to the summit gives $$h=10.3-2.5-2-0.005=5.795\ \mathrm m.$$ Rounded maximum height is **5.8 m**.