A trough cross-section is a 6-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) $2,250$
B) $3,500$
C) $4,500$
D) $5,000$
E) $5,550$

Question

A trough cross-section is a 6-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) $2,250$
B) $3,500$
C) $4,500$
D) $5,000$
E) $5,550$

Quizplus · Accepted Answer

The force due to hydrostatic pressure is calculated by integrating the pressure over the area. The pressure at depth $ y $ is $ 62.5y $. The force is $ \int_0^6 62.5y \times 4 \, dy = 4 \times 62.5 \times \frac{6^2}{2} = 4,500 $ pounds.

A Trough Cross-Section Is a 6-Foot-High and 4-Foot-Wide Rectangle 2,2502,2502,250 B) 3,5003,5003,500

A Trough Cross-Section Is a 6-Foot-High and 4-Foot-Wide Rectangle $2,250$ B) $3,500$