Final answer:
To express the hydrostatic force against one side of the plate, we use the pressure exerted by the water on that side. By calculating the pressure at each infinitesimally small vertical section of the plate and summing them up using an integral, we can determine the total force. The hydrostatic force against one side of the plate can be expressed as (7p/6) * ∫ 06 y dy.
Step-by-step explanation:
To express the hydrostatic force against one side of the plate, we need to calculate the pressure exerted by the water on that side.
The pressure exerted by a fluid depends on its density, depth, and acceleration due to gravity. In this case, the fluid is water with a weight density of 62.5 lb/ft³.
Since the top of the plate is 2 ft below the surface, the depth of the plate is (6 - 2) ft = 4 ft.
To express the force as an integral, we need to sum up the pressure at each infinitesimally small vertical section of the plate.
Let y be the height of each infinitesimally small vertical section from the bottom of the plate.
Since the plate is triangular, the width of each section is y*(7/6) ft.
The force on each section is given by the pressure (p) times the area (A), which is p * y*(7/6).
To express this as an integral, we integrate from y = 0 to y = 6 ft (the height of the plate).
Therefore, the hydrostatic force against one side of the plate is:
F = ∫ 06 p * y*(7/6) dy = (7p/6) * ∫ 06 y dy