How Do You Calculate the Flow Rate from a Rectangular Opening in a Tank?

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SUMMARY

The discussion focuses on calculating the flow rate of water from a rectangular opening in a tank using Bernoulli's equation. The opening dimensions are defined by width W and height H2 - H1, where H1 and H2 represent specific distances from the tank's top. The user seeks assistance in determining the velocity of water at varying depths and integrating this to find the volume of water emerging per second. The solution involves understanding fluid dynamics principles and applying calculus to derive the flow rate accurately.

PREREQUISITES
  • Understanding of Bernoulli's equation in fluid dynamics
  • Basic calculus, specifically integration techniques
  • Knowledge of fluid velocity concepts at different depths
  • Familiarity with the principles of open-topped tank behavior
NEXT STEPS
  • Study the application of Bernoulli's equation in various fluid flow scenarios
  • Learn integration techniques for calculating variable flow rates
  • Explore the concept of velocity profiles in fluid dynamics
  • Research the effects of opening dimensions on flow rate in tanks
USEFUL FOR

Students in physics or engineering, particularly those studying fluid dynamics, as well as professionals involved in hydraulic engineering and water resource management.

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Homework Statement



A rectangular opening is cut into the side of a large open-topped water tank. The opening has width W and height H2 - H1, where H1 is the distance from the top of the tank to the top of the opening, and H2 is the distance from the top of the tank to the bottom of the opening. Determine the volume V of water that emerges from the opening per second.

You may assume that the surface area of the tank is extremely large compared to the area of the opening, but you should not assume that the water emerges from the opening with a single, uniform velocity.

Homework Equations



Bernoulli's equation

The Attempt at a Solution



So I first tried to get the velocity at H1 and H2 using Bernoulli's equation. Then I assume you have to integrate to account for the rate in between, but I'm having trouble setting up the integral. Help is appreciated, thanks.
 
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Can you find the velocity at any arbitrary depth y?
 

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