Force on a Submerged Sheet In Exercises 1 and 2, the area

Force on a Submerged Sheet In Exercises 1 and 2, the area of the top side of a piece of sheet metal is given. The sheet metal is submerged horizontally in 5 feet of water. Find the fluid force on the top side. 3 square feet

Force on a Submerged Sheet In Exercises 1 and 2, the area of the top side of a piece of sheet metal is given. The sheet metal is submerged horizontally in 5 feet of water. Find the fluid force on the top side. 16 square feet

Buoyant Force In Exercises 3 and 4, 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.

Buoyant Force In Exercises 3 and 4, 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.

Fluid Force on a Tank Wall In Exercises 510, 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. Rectangle

Fluid Force on a Tank Wall In Exercises 510, 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. Triangle

Fluid Force on a Tank Wall In Exercises 510, 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. Trapezoid

Fluid Force on a Tank Wall In Exercises 510, 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. Semicircle

Fluid Force on a Tank Wall In Exercises 510, 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. Parabola

Fluid Force on a Tank Wall In Exercises 510, 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. Semiellipse

Fluid Force of Water In Exercises 1114, find the fluid force on the vertical plate submerged in water, where the dimensions are given in meters and the weight-density of water is 9800 newtons per cubic meter. Square

Fluid Force of Water In Exercises 1114, find the fluid force on the vertical plate submerged in water, where the dimensions are given in meters and the weight-density of water is 9800 newtons per cubic meter. Square

Fluid Force of Water In Exercises 1114, find the fluid force on the vertical plate submerged in water, where the dimensions are given in meters and the weight-density of water is 9800 newtons per cubic meter. Triangle

Fluid Force of Water In Exercises 1114, find the fluid force on the vertical plate submerged in water, where the dimensions are given in meters and the weight-density of water is 9800 newtons per cubic meter. Rectangle

Force on a Concrete Form In Exercises 1518, the figure is the vertical side of a form for poured concrete that weighs 140.7 pounds per cubic foot. Determine the force on this part of the concrete form. Rectangle

Force on a Concrete Form In Exercises 1518, the figure is the vertical side of a form for poured concrete that weighs 140.7 pounds per cubic foot. Determine the force on this part of the concrete form. Semiellipse

Force on a Concrete Form In Exercises 1518, the figure is the vertical side of a form for poured concrete that weighs 140.7 pounds per cubic foot. Determine the force on this part of the concrete form. Rectangle

Force on a Concrete Form In Exercises 1518, the figure is the vertical side of a form for poured concrete that weighs 140.7 pounds per cubic foot. Determine the force on this part of the concrete form. Triangle

Fluid Force of Gasoline 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 3 feet and the gasoline weighs 42 pounds per cubic foot.

Fluid Force of Gasoline Repeat Exercise 19 for a tank that is full. (Evaluate one integral by a geometric formula and the other by observing that the integrand is an odd function.)

Fluid Force on a Circular Plate A circular plate of radius feet is submerged vertically in a tank of fluid that weighs pounds per cubic foot. The center of the circle is feet below the surface of the fluid. Show that the fluid force on the surface of the plate is (Evaluate one integral by a geometric formula and the other by observing that the integrand is an odd function.)

Fluid Force on a Circular Plate Use the result of Exercise 21 to find the fluid force on the circular plate shown in each figure. Assume the plates are in the wall of a tank filled with water and the measurements are given in feet. (a) (b)

Fluid Force on a Rectangular Plate A rectangular plate of height feet and base feet is submerged vertically in a tank of fluid that weighs pounds per cubic foot. The center is feet below the surface of the fluid, where Show that the fluid force on the surface of the plate is

Fluid Force on a Rectangular Plate Use the result of Exercise 23 to find the fluid force on the rectangular plate shown in each figure. Assume the plates are in the wall of a tank filled with water and the measurements are given in feet. (a) (b)

Submarine Porthole A porthole on a vertical side of a submarine (submerged in seawater) is 1 square foot. Find the fluid force on the porthole, assuming that the center of the square is 15 feet below the surface.

Submarine Porthole Repeat Exercise 25 for a circular porthole that has a diameter of 1 foot. The center is 15 feet below the surface.

Modeling Data The vertical stern of a boat with a superimposed coordinate system is shown in the figure. The table shows the width of the stern at indicated values of Find the fluid force against the stern if the measurements are given in feet.

Irrigation Canal Gate The vertical cross section of an irrigation canal is modeled by where 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 3 feet deep.

In Exercises 29 and 30, use the integration capabilities of a graphing utility to approximate the fluid force on the vertical plate bounded by the -axis and the top half of the graph of the equation. Assume that the base of the plate is 12 feet beneath the surface of the water 23  y23 423 x

In Exercises 29 and 30, use the integration capabilities of a graphing utility to approximate the fluid force on the vertical plate bounded by the -axis and the top half of the graph of the equation. Assume that the base of the plate is 12 feet beneath the surface of the water x2 28  y2 16 x 1

Think About It (a) Approximate the depth of the water in the tank in Exercise 5 if the fluid force is one-half as great as when the tank is full. (b) Explain why the answer in part (a) is not 3 2.

Define fluid pressure.

Define fluid force against a submerged vertical plane region.