GATE Papers >> Civil >> 2017 >> Question No 48

Question No. 48 Civil | GATE 2017

A sluice gate used to control the flow in a horizontal channel of unit width is shown in the figure.

It is observed that the depth of flow is 1.0 m upstream of the gate , while the depth is 0.2 m downstream of the gate. Assuuming a smooth flow transition across the sluice gate, i.e, without any energy loss, and the acceleration due to gravity as 10 m/s2, the discharge (in m3/s, up to two decimal places) passing under the sluice gate is _______

Answer : 0.80 to 0.83

Solution of Question No 48 of GATE 2017 Civil Paper

There is no energy loss so

E1 = E2

$\begin{array}{l}{\mathrm y}_1+\frac{\mathrm v_1^2}{2\mathrm g}={\mathrm y}_2+\frac{\mathrm v_2^2}{2\mathrm g}\\1+\frac{\mathrm Q^2}{2\mathrm{gA}_1^2}=0.2+\frac{\mathrm Q^2}{2\mathrm{gA}_2^2}\\\frac{\mathrm Q^2}{2\mathrm g}\left[\frac1{\mathrm A_2^2}-\frac1{\mathrm A_2^1}\right]=1-0.2\\\frac{\mathrm Q^2}{2\times10}\left[\frac1{0.2^2}-\frac1{1^2}\right]=0.8\\\mathrm Q^2=\frac{16}{24}\\\mathrm Q^2=\frac23\\\mathrm Q=0.82\;\mathrm m^3/\mathrm s\end{array}$

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