A trough is filled with a liquid of density $855 \mathrm {~kg} / \mathrm { m } ^ { 3 }$. The ends of the trough are equilateral triangles with sides $8 \mathrm {~m}$ long and vertex at the bottom. Find the hydrostatic force on one end of the trough.
A) $8.36 \times 10 ^ { 5 } \mathrm {~N}$
B) $5.36 \times 10 ^ { 5 } \mathrm {~N}$
C) $6.36 \times 10 ^ { 5 } \mathrm {~N}$
D) $7.36 \times 10 ^ { 5 } \mathrm {~N}$
E) $4.36 \times 10 ^ { 5 } \mathrm {~N}$

Question

Quizplus · Accepted Answer

The hydrostatic force on one end of the trough can be calculated using the formula $F = \rho g h A$, where $\rho$ is the density of the liquid, $g$ is the acceleration due to gravity (approximately $9.8 \, \text{m/s}^2$), $h$ is the depth of the liquid, and $A$ is the area of the surface. For an equilateral triangle, the area $A = \frac{\sqrt{3}}{4} \times \text{side}^2$, and the height $h$ (for the purpose of calculating pressure at the centroid) is $\frac{\sqrt{3}}{2} \times \text{side}$. Substituting the given values, the force can be calculated, leading to the correct answer.

A Trough Is Filled with a Liquid of Density 855 kg/m3855 \mathrm {~kg} / \mathrm { m } ^ { 3 }855 kg/m3

A Trough Is Filled with a Liquid of Density $855 \mathrm {~kg} / \mathrm { m } ^ { 3 }$