A trough is filled with a liquid of density 855 kg/ . The ends of the trough are equilateral triangles with sides m long and vertex at the bottom. Find the hydrostatic force on one end of the trough.

Question

A trough is filled with a liquid of density 855 kg/  . The ends of the trough are equilateral triangles with sides  m long and vertex at the bottom. Find the hydrostatic force on one end of the trough.

Quizplus · Accepted Answer

The area of one end of the trough can be found by using the formula for the area of an equilateral triangle: $(\sqrt{3}/4)s^2$, where $s$ is the length of the side. Plugging in $s=11\sqrt{3}/3$, we get an area of $33\sqrt{3}$ square meters.

The hydrostatic pressure at any depth $h$ is given by $P=h\rho g$, where $\rho$ is the density of the liquid and $g$ is gravitational acceleration. Since the vertex of the triangle is at the bottom of the trough, the depth at any point on the end of the trough is simply the height of the equilateral triangle, which is $11\sqrt{3}/2$ meters.

Thus, the pressure at any point on this end of the trough is $P=h\rho g = (11\sqrt{3}/2)(855)(9.81) \approx 41611$ Pascal.

Finally, we can use the formula for hydrostatic force to find the force exerted by the liquid on this end of the trough: 
$F = P A = (41611)(33\sqrt{3}) \approx 4434217$ Newtons.

Converting to the provided answer choices, we get choice C: $11eaa3e5_5534_4ab0_9f8f_e9346b90830c_TB5971_11$.

A Trough Is Filled with a Liquid of Density 855