A swimming pool measures a length of 5.70 m, width 4.20 m, and depth 2.90 m.?

Question

Compute the force (in Newtons) exerted by the water against either end of the pool. Do not include the force due to air pressure.

Answer 1

If you have some calc background then you can set up the equation of force on the sides of the pool (does not include atmospheric pressure)


dF= P dA
P- pressure
dA - differential area based on depth
and
P= pgy (from y=-2.9 to y= 0)
p - water mass density
g - acceleration due to gravity
y - position below the surface level

dA= Ldy
putting it together we have
dF= pgLy dy
integrated from y=-2.9 to y= 0 we have

F= 0.5 pgL (y)^2 where y=-2.9 m

F1 = (5.7)(2.9)^2 pg
F2 = (4.2)(2.9)^2 pg