For the system in Problem P6.6, suppose your design requirement was to minimize the force necessary to hold the gate closed. Would you rather put the hinge at the top of the gate or at the bottom? Support your answer.

Problem P6.6

A 6-m-high, 4-m-wide rectangular gate is located at the end of an open freshwater tank (Figure P6.6). The gate is hinged at the top and held in place by a force F. From Equation (6.4), the pressure is proportional to the depth of the water, and the average pressure p_avg exerted on the gate by the water is

where Δp is the difference in pressure between the bottom of the gate (p₁) and the surface (p₀). The resulting force of the water on the gate is

F_water = p_avg A

where A is the area of the gate the water acts upon. The resulting force acts 2 m from the bottom of the gate because the pressure increases with depth. Determine the force required to hold the gate in place.

Figure P6.6

Ap Pavg 2