GATE 2026 ES – Question 55
A cylindrical roller gate of diameter 6.0 m and length 10.0 m sits on a dam as shown. Water is about to spill over the gate. Find the resultant water force as $n\times10^6$ N, reporting n to two decimals. Use $g=9.81\,\mathrm{m/s^2}$,$\rho=1000\,\mathrm{kg/m^3}$ and $\pi=3.14$.
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Correct answer: 2.00 to 2.50
Explanation
The wetted surface is the upstream semicylinder of radius 3 m. The horizontal component equals the force on its vertical projection: $F_H=\rho g(6\cdot10)(3)=1.7658\times10^6$ N. The vertical component is upward and equals the weight of water displaced by the upstream half-cylinder: $F_V=\rho g(\pi3^2/2)(10)=1.386153\times10^6$ N. These components are perpendicular, so $F=\sqrt{F_H^2+F_V^2}\approx2.24488\times10^6$ N. Answer **2.24**.