Question

A tank of square cross section `(2mxx2m)` is filled with water up to a height of `2.5 m`. Find the thrust experienced by the vertical and botom of the tank `(g=10m//s^(2))`.

Answer 1

Thrust at the bottom surface
The pressure is uniformly distrubed over the bottom surface.
Thrust `=` Pressure `xx` Area
`=(2.5rhog)A=2.5xx(1xx10^3)[10(2xx2)]`

Thrust at the vertical surface:
On a vertical surface in contact with the liquid the pressure is not the same at all points. Points at greater depth experience the larger pressures and hence the greater thrust. Consider a vertical surface `ABCD(lxxh)` in contact with the liquid of height `h`.
Divide the vertical surface `ABCD` into rectangular strips of height `dx` and area `ldx`. Then
`F=intPdA=int_(0)^(A)(xrhog)ldx=(rhog/(h^(2)))/2`
Expressing `F` as `F=[h/2rhog]=(rhog/h^(2))/2`
`F=` [Pressure at `CG` of vertical surface `xx` [Area of surface]
`=(2.5/2xxrhoxxg)(2xx2.5)`
`=2.5/2xx10^(-3)xx10xx5=6.25xx10^(4)`