GATE 2021 AE – Question 50
A stationary cart carries a water tank and deflector. A 5 cm diameter jet of speed 10 m/s is deflected through 60° as shown. With water density 1000 kg/m³, the horizontal restraining force is ___ N.
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Correct answer: 97.71 to 98.69
Explanation
Take the **tank, the jet and the deflector as one system**. The restraining force on the cart must balance the net rate at which horizontal momentum leaves the system.
**Jet mass flow rate and speed.** With a 5 cm diameter jet at 10 m/s:
$$A=\frac\pi4(0.05)^2=1.9635\times10^{-3}\text{ m}^2,\qquad\dot m=\rho AV=1000\times1.9635\times10^{-3}\times10=19.635\text{ kg/s}.$$
**Momentum balance** (horizontal). The fluid leaves the deflector at the same speed $V$, turned through $60^\circ$, so the outgoing horizontal velocity is $V\cos60^\circ$. The jet is formed in the tank, where the fluid is at rest, so no horizontal momentum enters. The restraining force equals the outgoing horizontal momentum flux:
$$F=\dot m\,V\cos60^\circ=19.635\times10\times0.5=\mathbf{98.2\ N}.$$