A trough cross-section is a 2-foot-high and 4-foot-wide rectangle. If the trough 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) $500$
B) $2,500$
C) $3,200$
D) $3,960$
E) $4,500$

Question

A trough cross-section is a 2-foot-high and 4-foot-wide rectangle. If the trough 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) $500$
B) $2,500$
C) $3,200$
D) $3,960$
E) $4,500$

Quizplus · Accepted Answer

The force due to hydrostatic pressure on one end of the trough can be calculated using the formula for hydrostatic pressure, $P = \rho gh$, where $\rho$ is the density of the fluid, $g$ is the acceleration due to gravity (which is approximately $32.2 \, \text{ft/s}^2$ but is not needed in this calculation since the density given already accounts for gravity), and $h$ is the depth of the fluid. The force is then $F = PA$, where $A$ is the area of the surface being pushed on by the fluid.Given that the density of water is $62.5 \, \text{lb/ft}^3$, the height of the water (which is the same as the height of the trough) is $2 \, \text{ft}$, and the width of the trough (which will be the width of the end being pushed on by the water) is $4 \, \text{ft}$, the area $A$ of one end of the trough is $2 \, \text{ft} \times 4 \, \text{ft} = 8 \, \text{ft}^2$.The force due to hydrostatic pressure on one end of the trough is calculated as:$$F = \rho ghA = 62.5 \, \text{lb/ft}^3 \times 2 \, \text{ft} \times 8 \, \text{ft}^2 = 500 \, \text{lb}.$$Thus, the correct answer is $500$ pounds.

A Trough Cross-Section Is a 2-Foot-High and 4-Foot-Wide Rectangle 500500500 B) 2,5002,5002,500

A Trough Cross-Section Is a 2-Foot-High and 4-Foot-Wide Rectangle $500$ B) $2,500$