# GATE Papers >> Mechanical >> 2017 >> Question No 139

Question No. 139

The arrangement shown in the figure measures the velocity V of a gas of density 1 kg/m2 flowing through a pipe. The acceleration due to gravity is 9.81 m/s2. If the manometric fluid is water (density 1000 kg/m3) and the velocity V is 20 m/s, the differential head h (in mm) between the two arms of the manometer is__________

##### Answer : 19 to 21

Solution of Question No 139 of GATE 2017 Mechanical Paper

$\begin{array}{l}{\mathrm S}_\mathrm m=1000\mathrm{kg}/\mathrm m^3\\\mathrm S=1\;\mathrm{kg}/\mathrm m^3\\\mathrm x=\mathrm h\left(\frac{{\mathrm S}_\mathrm m}{\mathrm S}-1\right)=\mathrm h\left(\frac{1000}1-1\right)=999\mathrm h\\\mathrm V=\sqrt{2\mathrm{gx}}\\20=\sqrt{2\times9.81.\;\mathrm x}\Rightarrow\mathrm x=2.38\;\mathrm m\\\mathrm h=\frac{\mathrm x}{999}=20.4\;\mathrm{mm}\end{array}$

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