Exam 7: Section 7: Applications of Integration

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

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.

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.

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.

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.

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.

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 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.

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.

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

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 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.