A trough whose cross-section is a right isosceles triangle whose base is 4 feet long and altitude is 4 feet long is filled with water of density 62.5 pounds per cubic foot. The force, in pounds, due to hydrostatic pressure on one end of the trough is

A) $680$
B) $\frac { 2,000 } { 3 }$
C) $550$
D) $\frac { 2,000 } { 7 }$
E) $300$

Question

A trough whose cross-section is a right isosceles triangle whose base is 4 feet long and altitude is 4 feet long is filled with water of density 62.5 pounds per cubic foot. The force, in pounds, due to hydrostatic pressure on one end of the trough is

A) $680$
B) $\frac { 2,000 } { 3 }$
C) $550$
D) $\frac { 2,000 } { 7 }$
E) $300$

Quizplus · Accepted Answer

The force due to hydrostatic pressure on one end of the trough can be calculated using the formula for hydrostatic pressure, $P = \rho g h$, where $\rho$ is the density of the fluid, $g$ is the acceleration due to gravity (which can be considered as part of the density unit in this context since the density is given in pounds per cubic foot, incorporating gravitational force), and $h$ is the depth of the fluid. The force on one end of the trough is the integral of pressure over the area of that end. Given the shape of the trough and the uniform density of water, the force can be calculated as the product of the density of water, the gravitational acceleration (implicitly included in the given density), and the volume of water acting at the centroid of the triangular end. The volume of water is $\frac{1}{2} \times \text{base} \times \text{height}$ for the triangle, and the centroid is located at $\frac{1}{3}$ the height from the base for a right triangle. The correct calculation involves integrating this pressure over the area, but given the options and the setup, the answer that corresponds to the correct application of principles is $\frac{2,000}{3}$ pounds, recognizing that the force is proportional to the volume of water and its depth.

A Trough Whose Cross-Section Is a Right Isosceles Triangle Whose 680680680

A Trough Whose Cross-Section Is a Right Isosceles Triangle Whose $680$