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
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calculation of pressure forces on submerged plates
First result takes you to an example of a rectangular plate submerged in the way your question describes.
To find the force on one side of the plate, we first need to calculate the pressure exerted by the water on the plate.
Pressure is defined as force per unit area, so we can calculate the force on the plate by multiplying the pressure by the area of the plate.
The pressure at a certain depth in a fluid is given by the equation:
Pressure = density × acceleration due to gravity × depth
In this case, the depth is the width of the plate (80 ft) since the longer edge is in the surface of the water.
Let's assume the density of the water to be 62.4 lbs/ft³ (typical value).
The force on one side of the plate can be calculated as follows:
Force = Pressure × Area
Area = length × width
Substituting the given values:
Area = 120 ft × 80 ft = 9,600 ft²
Pressure = density × acceleration due to gravity × depth
= 62.4 lbs/ft³ × 32.2 ft/s² × 80 ft
≈ 201,216 lbs/ft² (pounds per square foot)
Force = Pressure × Area
= 201,216 lbs/ft² × 9,600 ft²
≈ 1,932,710,400 lbs (pounds)
Therefore, the force on one side of the plate is approximately 1,932,710,400 pounds.
To find the force on one side of the submerged rectangular plate, we can use the equation:
Force = Pressure * Area
1. Find the area of the submerged side of the plate:
Since the plate is submerged vertically with the longer edge in the surface of the water, only the width of the plate is submerged.
Area = Length * Width
Length = 120 ft
Width = 80 ft
Area = 120 ft * 80 ft
2. Find the pressure exerted on the submerged side of the plate:
The pressure exerted at a certain depth in a fluid is given by the equation:
Pressure = Density * Gravitational Acceleration * Depth
Since the plate is submerged vertically, the depth is the same as the width of the plate:
Depth = Width
The density of water is approximately 62.4 lb/ft³.
The gravitational acceleration is approximately 32.2 ft/s².
Pressure = 62.4 lb/ft³ * 32.2 ft/s² * Width
3. Calculate the force on one side of the plate using the found area and pressure:
Force = Pressure * Area
Force = (62.4 lb/ft³ * 32.2 ft/s² * Width) * (120 ft * 80 ft)
By plugging in the appropriate values for the width, you can calculate the force on one side of the submerged plate.