Question 1

A circular plate of radius r feet is submerged vertically in a tank of fluid that weighs w pounds per cubic foot. The center of the circle is  feet below the surface of the fluid. The fluid force on the surface of the plate is given by  Find the fluid force on the circular plate as shown in the figure given  feet and  feet. Round your answer to one decimal place.

Accepted Answer

A

Question 2

A rectangular plate of height h feet and base b feet is submerged vertically in a tank of fluid that weighs w pounds per cubic foot. The center of the plate is k feet below the surface of the fluid. The fluid force on the surface of the plate is given by  Find the fluid force on the rectangular plate as shown in the figure given  feet and  feet. Round your answer to one decimal place.

Accepted Answer

D

Question 3

The figure is the vertical side of a form for poured concrete that weighs 140.7 pounds per cubic foot. Dimensions in the figure are in feet. Determine force on this part of the concrete form

Accepted Answer

A

Question 4

Find the fluid force on the vertical side of the tank, where the dimensions are given in feet. Assume that the tank is full of water. Note: The density of water is 62.4 lbs per cubic foot.

Accepted Answer

To find the fluid force on the vertical side of the tank, we need to use the formula F = ρghA, where ρ is the density of water (62.4 lbs/ft³), g is the acceleration due to gravity (32.2 ft/s²), h is the height of the water level (10 ft), and A is the area of the vertical side (20 ft x 10 ft = 200 ft²).

F = (62.4 lbs/ft³) x (32.2 ft/s²) x (10 ft) x (200 ft²) = 4,032,960 lbs

Therefore, the fluid force on the vertical side of the tank is 4,032,960 lbs, which corresponds to answer choice C.

Question 5

The figure is the vertical side of a form for poured concrete that weighs 140.7 pounds per cubic foot. Dimensions in the figure are in feet. Determine force on this part of the concrete form.

Accepted Answer

The answer of The figure is the vertical side of...

Question 6

Find the fluid force on the vertical side of the tank, where the dimensions are given in feet. Assume that the tank is full of water. Note: The density of water is 62.4 lbs per cubic foot.

Accepted Answer

The answer of Find the fluid force on the vertical...

Question 7

A cylindrical gasoline tank is placed so that the axis of the cylinder is horizontal. Find the fluid force on a circular end of the tank if the tank is full, assuming that the diameter is  feet and the gasoline weighs  pounds per cubic foot. (Evaluate one integral by a geometric formula and the other by observing that the integrand is an odd function.) Round your answer to two decimal places.

Accepted Answer

The answer of A cylindrical gasoline tank is placed so...

Question 8

A porthole on a vertical side of a submarine (submerged in seawater) is  square  . Find the fluid force on the porthole, assuming that the center of the square is  feet below the surface.

Accepted Answer

The answer of A porthole on a vertical side of...

Question 9

The vertical cross section of an irrigation canal is modeled by  where x is measured in feet and  corresponds to the center of the canal. Use the integration capabilities of a graphing utility to approximate the fluid force against a vertical gate used to stop the flow of water if the water is  feet deep. Round your answer to three decimal places.

Accepted Answer

The answer of The vertical cross section of an irrigation...

Question 10

Find the fluid force of a square vertical plate submerged in water, where  meters and the weight-density of water is 9800 newtons per cubic meter.

Accepted Answer

The fluid force on a submerged plate is determined by the formula F = ρghA, where ρ is the density of the fluid, g is the acceleration due to gravity, h is the depth of the fluid, and A is the area of the plate. In this case, ρ = 9800 kg/m³, g = 9.8 m/s², h = 11 meters, and A = 1m x 1m = 1m². Plugging these values into the formula gives F = 9800 x 9.8 x 11 x 1 = 1,068,680 N or 1.07 MN. Therefore, the best choice is C, 11eaa595_64e8_a6d1_a696_813de579df99_TB4584_11_TB4584_11.

Question 11

A cylindrical gasoline tank is placed so that the axis of the cylinder is horizontal. Find the fluid force on a circular end of the tank if the tank is half full, assuming that the diameter is  feet and the gasoline weighs 42 pounds per cubic foot.

Accepted Answer

The answer of A cylindrical gasoline tank is placed so...

Question 12

Find the fluid force of a triangular vertical plate submerged in water, where the dimensions are given in meters  and the weight-density of water is 9800 newtons per cubic meter.

Accepted Answer

The answer of Find the fluid force of a triangular...

Question 13

Find the fluid force on the vertical side of the tank, where the dimensions are given in feet. Assume that the tank is full of water. Note: The density of water is 62.4 lbs per cubic foot.

Accepted Answer

The answer of Find the fluid force on the vertical...

Question 14

The area of the top side of a piece of sheet metal is 9 square feet. The sheet metal is submerged horizontally in 8 feet of water. Find the fluid force on the top side. Round your answer to one decimal place.

Accepted Answer

The fluid force on a submerged surface is given by the formula $F = \rho g h A$, where $\rho$ is the density of the fluid (in this case, water, which is approximately 62.4 lb/ft$^3$), $g$ is the acceleration due to gravity (which is generally taken as 32.2 ft/s$^2$ but is not needed here since the density already accounts for gravity), $h$ is the depth of the fluid, and $A$ is the area of the surface. Given that the depth $h = 8$ feet and the area $A = 9$ square feet, the fluid force $F$ can be calculated as follows:$$F = 62.4 \, \text{lb/ft}^3 \times 8 \, \text{ft} \times 9 \, \text{ft}^2 = 4,492.8 \, \text{lb}.$$Therefore, the fluid force on the top side of the sheet metal is 4,492.8 lb.

Question 15

Find the buoyant force of a rectangular solid of the given dimensions submerged in water so that the top side is parallel to the surface of the water. The buoyant force is the difference between the fluid forces on the top and bottom sides of the solid. Round your answer to two decimal places.

Accepted Answer

The answer of Find the buoyant force of a rectangular...

Quiz 7: Section 7: Applications of Integration

The figure is the vertical side of a form for poured concrete that weighs 140.7 pounds per cubic foot. Dimensions in the figure are in feet. Determine force on this part of the concrete form

Find the fluid force on the vertical side of the tank, where the dimensions are given in feet. Assume that the tank is full of water. Note: The density of water is 62.4 lbs per cubic foot.

The figure is the vertical side of a form for poured concrete that weighs 140.7 pounds per cubic foot. Dimensions in the figure are in feet. Determine force on this part of the concrete form.

Find the fluid force on the vertical side of the tank, where the dimensions are given in feet. Assume that the tank is full of water. Note: The density of water is 62.4 lbs per cubic foot.

A porthole on a vertical side of a submarine (submerged in seawater) is square . Find the fluid force on the porthole, assuming that the center of the square is feet below the surface.

Find the fluid force of a square vertical plate submerged in water, where meters and the weight-density of water is 9800 newtons per cubic meter.

A cylindrical gasoline tank is placed so that the axis of the cylinder is horizontal. Find the fluid force on a circular end of the tank if the tank is half full, assuming that the diameter is feet and the gasoline weighs 42 pounds per cubic foot.

Find the fluid force of a triangular vertical plate submerged in water, where the dimensions are given in meters and the weight-density of water is 9800 newtons per cubic meter.

Find the fluid force on the vertical side of the tank, where the dimensions are given in feet. Assume that the tank is full of water. Note: The density of water is 62.4 lbs per cubic foot.

The area of the top side of a piece of sheet metal is 9 square feet. The sheet metal is submerged horizontally in 8 feet of water. Find the fluid force on the top side. Round your answer to one decimal place.

Find the buoyant force of a rectangular solid of the given dimensions submerged in water so that the top side is parallel to the surface of the water. The buoyant force is the difference between the fluid forces on the top and bottom sides of the solid. Round your answer to two decimal places.