Did you know Sophia has tons of great content that aligns with the CCSS and NGSS standards? Get a jump on incorporating them into your everyday teaching.
Students should be familiar with using definite integrals as summations.
This video develops the concept of using an integral to calculate the total fluid force on a vertical surface.
Source: self-created video
This video walks through some examples of calculating fluid force.
Source: self-created video
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
Even when I do it in my calculator, the answer after the integrals is incorrect
On the second video with the trapezoid fluid pressure, it all makes sense, however when I do the math for the actual integral, I foiled it and integrated and do not get the same answer. I'm really confused and don't understand how I'm setting it up right but getting it wrong, still. I know it sounds dumb but can you please do the math out for the integrals?
Sophia's online courses not only save you money, but credits are also eligible for transfer to over 2,000 colleges and universities.*