Mass of water reaching the plate per sec = \(\frac{{dm}}{{dt}}\)

\( = Av\rho = A({v_1} + {v_2})\rho \)\( = \frac{V}{{{v_2}}}({v_1} + {v_2})\rho \)

(\(v = {v_1}\, + \,{v_2}\, = \) velocity of water coming out of jet w.r.t. plate)

(\(A = \) Area of cross section of jet \( = \frac{V}{{{v_2}}}\))

\(\therefore F = \frac{{dm}}{{dt}}v = \frac{V}{{{v_2}}}({v_1} + {v_2})\rho \times ({v_1} + {v_2})\) \( = \rho \left[ {\frac{V}{{{v_2}}}} \right]{({v_1} + {v_2})^2}\)