A dam has been constructed of a large cylindrical pipe 10ft in diameter an 3ft long. Calcualte the net vertical and horizontal components of the fluid(water) force on this dam.
To calculate the net vertical and horizontal components of the fluid force on the dam, we need to consider the pressure of the water on the surface of the dam.
The formula to calculate the pressure exerted by a fluid is P = ρgh, where P represents pressure, ρ represents the density of the fluid, g represents the acceleration due to gravity, and h represents the depth of the fluid.
In this case, the fluid is water. The density of water is approximately 62.4 lb/ft^3, and the acceleration due to gravity is approximately 32.2 ft/s^2.
To calculate the net vertical component of the fluid force, we need to find the pressure at the midpoint of the dam. Since the dam is cylindrical, the midpoint is located at a depth of one-half the length of the cylinder, which is 3/2 ft.
Using the formula P = ρgh, we can calculate the pressure at the midpoint of the dam:
P_vertical = (62.4 lb/ft^3) * (32.2 ft/s^2) * (3/2 ft)
P_vertical ≈ 299.04 lb/ft^2
The net vertical component of the fluid force is equal to the pressure at the midpoint multiplied by the area of the dam. The area of a cylindrical surface can be calculated using the formula A = πr^2, where A represents the area and r represents the radius.
The radius of the dam is half of the diameter, so r = 10ft / 2 = 5ft.
Calculating the area:
A = π * (5ft)^2
A ≈ 78.54 ft^2
The net vertical component of the fluid force can be calculated as:
F_vertical = P_vertical * A
F_vertical ≈ (299.04 lb/ft^2) * (78.54 ft^2)
F_vertical ≈ 23,513.62 lb
So, the net vertical component of the fluid force on the dam is approximately 23,513.62 lb.
To calculate the net horizontal component of the fluid force, we can use the fact that the pressure exerted by a fluid is the same in all directions at the same depth. Therefore, the horizontal component of the fluid force is equal to the vertical component.
Thus, the net horizontal component of the fluid force on the dam is also approximately 23,513.62 lb.