A rectangular tank of dimensions 3 m 2 m 1 m is filled with water. Consider a vertical side of area 2 m 1 m and a horizontal strip of width x metre within this side, located at a depth of x metre from the water surface. Neglecting atmospheric pressure and using g = 10 m s ⁻² , determine the following values respectively: (i) the total force exerted by the water on the bottom surface of the tank, (ii) the force by the

Step-by-step solution

The density of water is = 1000 kg m ⁻³ and g = 10 m s ⁻² . The pressure at the bottom of the tank is P = g H = 1000 10 1 = 10000 N m ⁻² . The area of the bottom surface is A = 3 2 = 6 m ^2 . The total force exerted by the water on the bottom surface is F_ bottom = P A = 10000 6 = 60000 N . The vertical side has dimensions 2 m 1 m , so its width is 2 m and height is 1 m . The pressure at a depth x is P(x) = g x = 10000 x N m ⁻² . The area of the horizontal strip of width x is dA = 2 x m ^2 . The force on the strip i