440 Chapter 7: Applications of Integration
7.7 Fluid Pressure and Fluid Force
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. 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.
a. 4,492.8 lb
b. 4,420.8 lb
c. 4,348.8 lb
d. 4,622.4 lb
e. 4,838.4 lb
____ 2. 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.
a. 561.60 lb
b. 748.80 lb
c. 2,246.40 lb
d. 249.60 lb
e. 187.20 lb
7.7 Fluid Pressure and Fluid Force 441
____ 3. 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.
b.
c.
d.
e.
____ 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.
a.
b.
c.
d.
e.
442 Chapter 7: Applications of Integration
____ 5. 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.
b.
c.
d.
e.
____ 6. 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.
b.
c.
d.
e.
7.7 Fluid Pressure and Fluid Force 443
____ 7. 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.
a.
b.
c.
d.
e.
____ 8. 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.
b.
c.
d.
e.
444 Chapter 7: Applications of Integration
____ 9. 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.
b.
c.
d.
e.
____ 10. 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.
a.
b.
c.
d.
e.
____ 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 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.
a.
b.
c.
d.
e.
7.7 Fluid Pressure and Fluid Force 445
____ 12. 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.
b.
c.
d.
e.
446 Chapter 7: Applications of Integration
____ 13. 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.
a.
b.
c.
d.
e.
____ 14. 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.
a.
b.
c.
d.
e.
____ 15. 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.
a.
b.
c.
d.
e.
7.7 Fluid Pressure and Fluid Force 447
7.7 Fluid Pressure and Fluid Force
Answer Section