Question

Please solve number 2 urgently

What is the trapezoidal rule?

1. Derive the formula of the falling head equation. 2. Compare the theoretical and experimental forces on the sluice gate of w-0.5ft with Q-0.145 cfs and upstream depth =0.719A and down stream depth=0.073 ft. The pizometric head is given as Dh. Z () 0 0.020.040.08 0.120.16 Dh (t)0.50.520.540.570.530.5

Answer 1

Assume Steady incompressible flow with no variation across the width W. then the inlet and outlet mass flow balance is m = rho V1H1W = rho V2H2W or V2 = (H1/H2)*V1 We may use gauge pressure for convenience because a uniform atmospheric pressure causes no force. By equating the net horizontal force sigma F_x = -F_gate + P_1 A_1 - P_2 A_2 = m(V_2 - V_1) or -F_gate + gamma H_1 /2(H_1 W) - gamma H_2 /2(H_2 W) = m(H_1 /H_2 * nu_1 - nu_1) m = rho H_1 W nu_1 solve for F_gate and eliminate V2 using the mass flow relation. The desired result is F_gate = 1/2 rho gwh_1^2 (1-(h_2^2/h_1^2)) - rho h_1 w nu_1^2 (h1/h2 - 1) now if we apply energy (bernoullies) equation to the 2 points at the free surface (p1 = p2 = 0) p1/gamma + V1^2 /2g + h_1 = p2/gamma + V2^2 /2g + h_2 eliminate V2 using the mass flow relation then