Question

A trough of length 6 ft has for its vertical cross section an isosceles trapezoid. The upper and lower bases are 6 ft and 2 ft respectively and the altitude is 2 ft. If the trough is full of water, find the force on the slant side of the trough.

Answer 1

Given:

b = 2 ft = 0.61 m;

h = 2 ft = 0.61 m;

w = 6 ft = 1.83 m;

l = 6 ft = 1.83 m.

Find the force perpendicular to the vertical plane equal to the slant side in height and width:

$$F_p=\frac12\rho gh(hw)=\frac12·1000·9.8·0.61(1.83·0.61)=\\=3320\text{ N}.$$

Find the volume above the slant:

$$V=\frac14 (w-b)hl=0.34\text{ m}^3.$$

The weight of water above the slant side:

$$w=V\rho g= 3330\text{ N}.$$

The magnitude of the force is

$$R=\sqrt{w^2+F_p^2}=4700\text{ N}.$$