Question

An aquarium 5 ft long, 2 ft wide, and 3 ft deep is full of water. (Recall that the weight density of water is 62.5 lb/ft^³) (a) Find the hydrostatic pressure on the bottom of the aquarium. (b) Find the hydrostatic force on the bottom of the aquarium. (c) Find the hydrostatic force on one end of the aquarium.

Answer 1

The hydrostatic pressure on the bottom of the aquarium is approximately 600 lb/ft². The hydrostatic force on the bottom of the aquarium is approximately 6000 lb. The hydrostatic force on one end of the aquarium is approximately 3600 lb.

Step-by-step explanation:

To calculate the hydrostatic pressure on the bottom of the aquarium, we can use the formula P = hpg, where P is the pressure, h is the height of the fluid column, p is the density of the fluid, and g is the acceleration due to gravity. In this case, the height of the fluid column is equal to the depth of the aquarium, which is 3 ft. The density of water is 62.5 lb/ft³. Plugging these values into the formula, we get P = (3 ft) * (62.5 lb/ft³) * (32.2 ft/s²), which gives us a pressure of approximately 600 lb/ft².

To calculate the hydrostatic force on the bottom of the aquarium, we can use the formula F = PA, where F is the force, P is the pressure, and A is the area. The area of the bottom of the aquarium is equal to the length times the width, which is (5 ft) * (2 ft). Plugging the pressure value we calculated earlier, we get F = (600 lb/ft²) * (5 ft * 2 ft), which gives us a force of approximately 6000 lb.

To calculate the hydrostatic force on one end of the aquarium, we can use the same formula as before, but this time we need to calculate the pressure at the end of the aquarium. Since the pressure at any depth in a fluid is equal to the weight density times the depth, we can calculate the pressure at the end of the aquarium as P = (3 ft) * (62.5 lb/ft³) * (32.2 ft/s²). Plugging this pressure value and the area of the end of the aquarium (2 ft * 3 ft) into the formula, we get F = (600 lb/ft²) * (2 ft * 3 ft), which gives us a force of approximately 3600 lb.

Answer 2

The hydrostatic pressure on the bottom of the aquarium is 1905 lb/ft². The hydrostatic force on the bottom of the aquarium is 19050 lb. The hydrostatic force on one end of the aquarium is 11430 lb.

Step-by-step explanation:

To find the hydrostatic pressure on the bottom of the aquarium, we can use the formula P = hpg, where P is the pressure, h is the height of the fluid column, p is the density of the fluid, and g is the acceleration due to gravity. In this case, the height of the fluid column is 3 ft and the density of water is 62.5 lb/ft^3. Plugging in these values, we get P = (3 ft)(62.5 lb/ft^3)(32.2 ft/s^2) = 1905 lb/ft^2.

To find the hydrostatic force on the bottom of the aquarium, we can use the formula F = PA, where F is the force, P is the pressure, and A is the area. The area of the bottom of the aquarium is (5 ft)(2 ft) = 10 ft^2. Plugging in the value of pressure we just calculated, we get F = (1905 lb/ft^2)(10 ft^2) = 19050 lb.

To find the hydrostatic force on one end of the aquarium, we can use the same formula F = PA, but this time the area is (2 ft)(3 ft) = 6 ft^2. Plugging in the value of pressure we calculated earlier, we get F = (1905 lb/ft^2)(6 ft^2) = 11430 lb.