A trough is filled with a liquid of density 875 kg/m3. The ends of the trough are equilateral triangles with sides 14 m long and vertex at the bottom. Find the hydrostatic force on one end of the trough. (Use 9.8 m/s2 for the acceleration due to gravity.) Show all your steps clearly.

Rectangle Gate AB has length L and width b into the paper is hinged at B and has negligible weight. The liquid level, water, h does not reach the top of the gate for an angle theta. Find an equation for the force P, required to keep the gate in equilibrium. Solve for width, b. In the figure. (hint: draw a free-body diagram for the left and right side of the gate separately)

The tank is filled with water. Suppose that h=4.0 m. Solve the problem using the integration method. Determine the resultant force acting on the trapezoidal plate C and determine the location of the center of pressure measured from the top of the tank.

The figure below shows a container filled with a liquid of density p up to a height of 4R. The container is of unit width into the plane of the screen and AB is half a parabola with a height of kR and a base of R. Determine the magnitude and direction of the vertical component Fy of the hydrostatic force acting on the curved surface AB if k = 2, R = 0.5 m, p = 1000 kg/m³ and the gravitational acceleration g = 9.81 m/s². Note that Fy is positive if it acts upwards and is negative if it acts downwards. Geometric properties of a half-parabola are also given below. Fy= 1. [-6.7362, -6.3438 kN. 4R h ထမ 35 b Liquid Р X Half-Parabola BR KR A = 3bh 1xc=²bh³ |yxc=hb³ |yy,c=²7/531 2 h63