# Math Help - Hydrostatic Pressure and Force.

1. ## Hydrostatic Pressure and Force.

A trough is filled with a liquid of density $840 kg/m^3$. The end of the trough are equilateral triangles with sides $8 m$ long and vertex at the bottom. Find the hydrostatic force on one end of the trough.

I think, am not sure the areas that am going to sum up, will they be the equaliteral triangles, also why do the say at one end? How is this picture supposed to look like? Thank You !

2. Originally Posted by zangestu888
A trough is filled with a liquid of density $840 kg/m^3$. The end of the trough are equilateral triangles with sides $8 m$ long and vertex at the bottom. Find the hydrostatic force on one end of the trough.

I think, am not sure the areas that am going to sum up, will they be the equaliteral triangles, also why do the say at one end? How is this picture supposed to look like? Thank You !
The pressure at a depth $D$ in the trough is $\rho g D$. At a depth $D$ the width of the trough is:

$w(D)=8-2 D/\sqrt{3}$

so the force on the end of the trough is:

$
F=\int_{D=0}^{4\sqrt{3}} [\rho g D]\times w(D) \ dD
$

or

$
F=\int_{D=0}^{4\sqrt{3}} [\rho g D] \times (8-2 D/\sqrt{3})\ dD
$

.