Question

A swimming pool measures 5.0 m long x 4.0 m wide x 3.0 mdeep.

Compute the force exerted by the water against a) thebottom; b)
either end. (Hint: Calculate the force on athin,
horizontal strip at a depth h, and integratethis over the
end of the pool.) Do not include the force due to
airpressure.

Answer 1

a) 588,000 N

b) 294000 N

Step-by-step explanation:

Given that

Density of water = 1000kg/m3

(g) = 9.8m/s2

volume is given as (V)= 5m*4m*3m

a) force will be equal to weight of water

`W = mg  = \rho g V = 1000* 9.8 * (5*4*3) = 588,000 kg m/s^2`

b) at either end

`P = (F)/(A) = P_o + \rho gh`

`dF = PdA`

`dF = \rho g w \int h dh`

`F = \rho g w (h^2)/(2)`

`F = \rho g A (h)/(2)` [A = wh]

`F = 1000* 9.8 * 5* 4 *(3)/(2)`

F = 294000 N