A 6-m-high, 4-m-wide rectangular gate is located at the end of an open freshwater tank (...

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

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.