a rectangular plate 120 ft long and 80 ft wide is submerged vertically with the longer edge in the surface of the water find the force on one side of the plate
To find the force on one side of the submerged rectangular plate, we need to calculate the hydrostatic force acting on it. The hydrostatic force is determined by the pressure difference between the top and bottom surfaces of the plate.
Here's how you can calculate it step by step:
1. Determine the depth of submersion:
The longer edge of the rectangular plate is submerged, so the depth of submersion is equal to the width of the plate, which is 80 ft.
2. Calculate the pressure at the top surface of the plate:
The pressure at any depth in a fluid is given by the formula:
Pressure = density × gravity × depth
In this case, we need to determine the pressure at the top surface of the plate, which is at the surface of the water. Since the plate is vertically submerged, the depth is 0 ft. The density of water is approximately 62.4 lb/ft³, and the acceleration due to gravity is 32.2 ft/s².
Using the formula, the pressure at the top surface is:
Pressure_top = density × gravity × depth
= 62.4 lb/ft³ × 32.2 ft/s² × 0 ft
= 0 lb/ft²
The pressure at the top surface is 0 lb/ft² because it is exposed to atmospheric pressure.
3. Calculate the pressure at the bottom surface of the plate:
The pressure at the bottom surface of the plate is equal to the hydrostatic pressure at that depth, which is determined by the depth of submersion. In this case, the depth of submersion is 80 ft.
Using the same formula as above, the pressure at the bottom surface is:
Pressure_bottom = density × gravity × depth
= 62.4 lb/ft³ × 32.2 ft/s² × 80 ft
= 160,512 lb/ft²
4. Calculate the force on one side of the plate:
The force on one side of the plate is equal to the pressure difference between the top and bottom surfaces multiplied by the area of the plate. Since the top surface pressure is 0 lb/ft², we can ignore it in this case.
The area of the plate is the product of its length and width:
Area = length × width
= 120 ft × 80 ft
= 9,600 ft²
The force on one side of the plate is:
Force = pressure difference × area
= (Pressure_bottom - Pressure_top) × Area
= (160,512 lb/ft² - 0 lb/ft²) × 9,600 ft²
= 1,536,921,600 lb
Therefore, the force on one side of the submerged rectangular plate is approximately 1,536,921,600 lb.