Applications of Integrals - Fluid Forces (Vertical Plate)

An example that uses integration to calculate the fluid force on a vertical plate.

Category:

Education

Tags:

• calculus
• fluid
• force
• integration

[timmy11zoomsharecom]

shouldn't the force also depend on the tank size? If I had a pool with a glass on the side lets say at a height of 4, a certain force is acting on the glass. But lets say I make my pool 10 times longer, wouldn't the force be different?

[msumurph]

@timmy11zoomsharecom The length of the pool does not affect the force. The weight-density of the fluid, the length of the water along your plate, and the depth are what determine the force. We also do a trough problem similar to what you are describing that also illustrates this point, but I don't have a video for that yet.

[superstud2588]

or when you dont have an object... say you have a radius of 2ft and the tank is have filled with oil how do you find the fluid force of one side?

[msumurph]

@superstud2588 Not sure what shape you are describing. Is your tank a sphere of radius 2 ft? If so, it does not have sides. The technique in this video is used to calculate the fluid pressure on a thin plate, which is some flat surface.

[greywolf424]

@msumurph You messed up, the antiderivative of 3 - y is 3y - y^2 / 2

[msumurph]

@greywolf424 I know.  At about 5:01 into the video, I do fix it. :)

[FirstGradeCalculus]

Thanks! Please make more videos!

[92310CAMILLE]

salamat...(thanks:from the philippines)

[greywolf424]

@msumurph Yah, sorry posted before I got that far

[msumurph]

@superstud2588 Well, L is the strip length and it depends on the shape of the plate and the location of the y-axis. I usually draw the y-axis down the middle of the plate, If the plate is symmetric about the y-axis, L = 2x.  Of course, you'll have to write x in terms of y before you integrate.