The weight of the gate separating the two fluids is such that the system shown i

Question

The weight of the gate separating the two fluids is such that the system shown in Fig. 3-91 is at static equilibrium. If it is known that F1/F2 = 1.70, determine h/H.  See figure below.

a test of your equation, let = 1.25 m, b = 1 m, t = 0.2m, w = 1 m, g = 9.807 m/s2, rho = 998.3 kg/m3, and theta = 30 degree. If your equation is correct, you should get a force of 11.4 kN. The weight of the gate separating the two fluids is such that the system shown in Fig. P3-91 is at static equilibrium. If it is known that F1/F2 = 1.70, determine h/H. FIGURE P3-91 Consider a 1-m wide inclined gate of negligible

Explanation / Answer

Assume width = 1.

Average pressure on left side = 1/2*(860*g*H)

Force on left side F1 = 1/2*(860*g*H) *(H/Sin alpha *1)

Similrly, F2 = 1/2*(1250*g*h) *(h/Sin alpha *1)

F1/F2 = (860/1250)*(H/h)^2

Thus, h/H = sqrt [(860/1250) / 1.7]

h/H = 0.636

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