A composite plate comprises a triangular area (1) and rectangular area (2) as shown in the figure. The triangular plate experiences forces due to the liquids of densities `rho_(1)` and the rectangular plate experiences the force due to liquid of density `rho_(2)`. Find the hydrostatic forces on (a) area `1`, (b) area `2`, (c) total composite area of the plate. Assume `rho_(1)=rho` and `rho_(2)=2rho`.

Answer

`7/3rhogh^(2)b`

Explanation

The hydrostatic force on the triangular area is
`F_(1)=rho_(1)gh_(C_(1))A_(1)`

where `rho_(1)=rho, y_(C_(1))=2h/3` and `A_(1)=(bh)/2`. This gives
`F_(1)=(rhogh^(2)b)/3`
b. The hydrostatic force on the rectangular area is
`F_(2)=(rho_(1)gh_(1)+rho_(2)ghy_(C_(2)))A_(2)`
Substituting `rho_(1)=rho,h_(1)=h, rho_(2)=2rho, y_(C_(2))=h//2` and `A_(2)=bh` we have `F_(2)=rhogh^(2)b`.
c. The total hydrostatic force on the composite patch is
`F=F_(1)+F_(2)=(rho)/3gh^(2)b+2rhogh^(2)b=7/3rhogh^(2)b`