1. An aquarium 6 ft long, 3 ft wide, and 5 ft deep is full of water. (Recall that the weight density of water is 62.5 lb/ft3.)
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.
2. A 2-ft-high and 6-ft-wide rectangular plate is submerged vertically in water so that the top is 1 ft below the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Recall that the weight density of water is 62.5 lb/ft3.)
3. A semicircular plate with radius 10 m is submerged vertically in water so that the top is 2 m above the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Round your answer to the nearest whole number. Use 9.8 m/s2 for the acceleration due to gravity. Recall that the weight density of water is 1000 kg/m3.)
4. An equilateral triangular plate with sides 4 m is submerged vertically in water so that the base is even with the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Round your answer to the nearest whole number. Use 9.8 m/s2 for the acceleration due to gravity. Recall that the weight density of water is 1000 kg/m3.)
5. A hemispherical plate with diameter 6 ft is submerged vertically 1 ft below the surface of the water. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Round your answer to the nearest whole number. Recall that the weight density of water is 62.5 lb/ft3.)
6. A hemispherical plate with diameter 6 ft is submerged vertically 1 ft below the surface of the water. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Round your answer to the nearest whole number. Recall that the weight density of water is 62.5 lb/ft3.)
7. A trapezoidal plate with height h and bases a and 2a is submerged vertically in water as shown. Express the hydrostatic force against one side of the plate as an integral and evaluate it.
8. A cube with 20-cm-long sides is sitting on the bottom of an aquarium in which the water is one meter deep. (Round your answers to the nearest whole number. Use 9.8 m/s2 for the acceleration due to gravity. Recall that the weight density of water is 1000 kg/m3.)
a. Estimate the hydrostatic force on the top of the cube.
b. Estimate the hydrostatic force on one of the sides of the cube.
9. A swimming pool is 30 ft wide and 60 ft long and its bottom is an inclined plane, the shallow end having a depth of 4 ft and the deep end, 11 ft. Assume the pool is full of water. (Round your answers to the nearest whole number. Recall that the weight density of water is 62.5 lb/ft3.)
a. Estimate the hydrostatic force on the shallow end.
b. Estimate the hydrostatic force on the deep end.
c. Estimate the hydrostatic force on one of the sides.
d. Estimate the hydrostatic force on the bottom of the pool.