GATE CE 2020 Set 1 — Question 61
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Water Resources Engineering → Flow Measurement → Applications of Bernoulli
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Question
A circular water tank of diameter has a circular orifice of diameter at the bottom. Water enters the tank steadily at a flow rate of and escapes through the orifice. The coefficient of discharge of the orifice is . Consider the acceleration due to gravity as and neglect frictional losses. The height of the water level (in m, round off to two decimal places) in the tank at the steady state, is ___________.
Correct answer
0.5 to 0.54
Solution
1.At steady state, the inflow rate equals the outflow rate: .
2.Inflow rate .
3.Outflow rate through the orifice , where is the orifice area and is the water height.
4.Orifice area .
5.Setting : .
6..
7..
8..
9..
10.Rounding to two decimal places, the height is .
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