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Fluid Force - Integral Calculation

Fluid Force - Integral Calculation

Author: Richard Enderton

Students will be able to calculate fluid force on a vertical flat surface.

The packet consists of an instructional video, a video with examples, a problem set and other resources.

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Students should be familiar with using definite integrals as summations.

Fluid Force

This video develops the concept of using an integral to calculate the total fluid force on a vertical surface.

Source: self-created video

Fluid Force Calculation Examples

This video walks through some examples of calculating fluid force.

Source: self-created video

Problem Set

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 y equals x squared minus 4 and the x-axis (measurements in ft). (1064.96 lbs)



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 x squared over 16 plus y squared over 4 equals 1. 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)

Additional Resources

Where Do I Go From Here?



Definite Integrals Solid of Revolution - Shell Method