Question

A rectangular swimming pool is 8 m ✕ 34 m in area. The depth varies uniformly from 1 m in the shallow to 3 m in the deep end. (a) Determine the pressure at the deep end of the pool and at the shallow end. (b) What is the net force on the bottom of the pool due to the water in the pool? (Ignore the effects of the air above the pool for this part.)

Answer 1

Given

   rectangular swimming pool of dimensions w = 8m, l=34 m

   depth varying uniformly at shallow 1 m, at deep end 3 m

a) force at shallow end is F = (rho*w*h/2)(2x1+h)

here h = x2-x1, x1 is height on the surface of the pool = 0 m, x is at a height here x2= 1m

   substituting the values   

   F = (1000*8*1/2)(2*0+1) = 4000 N

at deep end

   F = (rho*w*h/2)(2x1+h)
   F = (1000*8*3/2)(0+3)
   F = 36000 N

b) total force is

using the formula

   F = 0.5*rho*w (sqrt(l^2+(d1-d2)^2))(d1+d2)
here d1 = 1m, d2 = 3 m

   F = 0.5*1000*8(sqrt(34^2+(3-1)^2))(3+1)
   F = = 544940 N