Hydrostatic Pressure: Calculate Force on Cylindrical Tank

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SUMMARY

The discussion focuses on calculating the hydrostatic pressure exerted on a flat side of a cylindrical tank with a base radius of 9.4 meters, partially filled with a liquid of density 1260 kg/m³ to a depth of 14 meters. The force exerted on the tank's side is derived from the equation F = ∫(from -9.4 to 9.4) (14 - y) * 2(88.36 - y²)^(1/2) dy. Participants emphasize the necessity of defining depth as a function of y to accurately integrate the pressure over the area of the tank's end. Proper setup of the integral is crucial for determining the correct force calculation.

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  • Understanding of hydrostatic pressure principles
  • Familiarity with integration techniques in calculus
  • Knowledge of cylindrical geometry and its properties
  • Ability to apply the concept of variable depth in pressure calculations
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  • Review hydrostatic pressure calculations in fluid mechanics
  • Study integration of variable functions in calculus
  • Learn about cylindrical coordinate systems and their applications
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Students in engineering or physics, particularly those studying fluid mechanics, as well as educators and professionals involved in pressure-related calculations in cylindrical tanks.

africanmasks
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Homework Statement


A cylindrical tank, with base radius 9.4 meter, lies on its side and is partially filled with a liquid whose density is \sigma=1260 kilograms per cubic meter. The liquid fills the tank to a maximum depth of 14 meters. Determine the amount of force (in Newtons) exerted on a flat side of the tank.

Homework Equations



F=\sigmadA

The Attempt at a Solution



I need help setting it up.

So far I have:

F= int (from -9.4 to 9.4) (14-y) 2(88.36-y^2)^(1/2)

Is that right? Or should be from 0 to 14?
 
Last edited:
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The pressure is a variable function of the depth. You have to integrate the pressure over the area of the end of the tank.
 
africanmasks said:
I have everything set-up, but I don't know what the depth is. Is it just 14 or y-14?

You need to let the depth be a function of y. You might be able to use y-14, but you will definitely need a y somewhere (finding depth as a function of y can be tricky and was one of the hardest things for me for these kinds of pressure problems since there can be more than one way to set it up).
 

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