# A flat plate moves normally with a speed v1 towards a horizontal jet of water of uniform area of cross section…

Q: A flat plate moves normally with a speed v1 towards a horizontal jet of water of uniform area of cross section. The jet discharges water at the rate of volume V per second at a speed of v2. The density of water is ρ. Assume that water splashes along the surface of the plate at right angles to the original motion. The magnitude of the force acting on the plate due to the jet is

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Sol: Force acting on the plate is

$\large F = \frac{dp}{dt} = u_r \frac{dm}{dt}$

Av2 = V

$\large \frac{dm}{dt} = A(v_1 + v_2)\rho$

$\large \frac{dm}{dt} = \frac{Av_2}{v_2}(v_1 + v_2)\rho$

$\large \frac{dm}{dt} = \frac{V}{v_2}(v_1 + v_2)\rho$

(ur = v1 + v2 = velocity of water coming out of jet w.r.t plate)

$\large F = (v_1 + v_2)\frac{V}{v_2}(v_1 + v_2)\rho$

$\large F = \frac{V}{v_2}(v_1 + v_2)^2\rho$