Project ForgeFluid Mechanics
Bernoulli's Equation & Flow
GATE 2021
Medium
A cylindrical jet of water (density=1000 kg/m³, diameter D=1 cm) impinges at the center of a flat circular plate resting on a linear spring (spring constant k=1 kN/m) and spreads radially outwards. If the spring shows a steady deflection of 1 cm upon impingement, the velocity of the incoming jet is ___ m/s (round off to one decimal place).
11.28 m/s(± 0.15 accepted)
Explanation
Force needed to hold the plate = spring force = kx = 1000×0.01=10 N. For a jet impinging normally on a flat plate deflecting radially, F=ρAV². A=πD²/4=π(0.01)²/4=7.854×10⁻⁵ m². V²=F/(ρA)=10/(1000×7.854×10⁻⁵)=127.3, V≈11.28 m/s.
Source: GATE ME 2021 Session 1 (ME-1) (2021)
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