Fluid Force - Integral Calculation

Students should be familiar with using definite integrals as summations.

1. For each exercise, a vertical side of a tank is shaped as described. Calculate the fluid force on the side described. Assume the tank is filled to the top with water (62.4 lbs per cubic ft)

a. A rectangle of height 4 ft and width 5 ft  (2496 lbs)

b. An isosceles trapezoid with parallel sides of length 3 ft and 4 ft. The parallel sides are horizontal and the shorter side is down. The distance between the parallel sides is 2 ft. (416 lbs)

c. The region bounded by  and the x-axis (measurements in ft). (1064.96 lbs)

2.

a. A vertical circular porthole in an observation ship has diameter 1 ft. It is placed so that the center of the of the porthole is 2 ft below the surface of the ocean. Calculate the fluid force on the porthole (seawater: 64.0 lbs per cubic ft). (100.531 lbs)

b. What would be the fluid force on the same window if it was horizontal rather than vertical? (100.531 lbs)

3. One side of a form for poured concrete is the bottom half of the ellipse . Determine the fluid force on the plate when the form is filled, using 140.7 lbs per cubic ft for concrete. (1500.8 lbs)

4. A vertical plate is submerged in water (62.4). The plate is shaped as a square with length side 3 ft. The plate hangs from its corner and that top corner is 2 ft below the surface of the water. What is the fluid force on the plate? (2314.53 lbs)

5. A tanker truck is transporting gasoline (41 lbs per cubic ft) The tank is in the form of right cylinder with the round ends vertical. The radius of the tank is 3 ft and the distance between the bases is 15 ft. What is the fluid force on one end of the tank when it is full? (3477.74 lbs)

Paul’s Online Notes

http://tutorial.math.lamar.edu/Classes/CalcII/HydrostaticPressure.aspx

Wolfram Alpha

www.wolframalpha.com