Calculating Hole Size for Desired Flow Rate in Tank/Reservoir

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SUMMARY

This discussion focuses on calculating the hole size required to achieve a specific flow rate in a tank or reservoir, given the pressure at a certain point. The relationship between pressure (P), hole area (s), and fluid velocity (v) is established using energy conservation principles. The formula derived is P = (ρv²)/2, where ρ represents the density of the liquid. This approach assumes negligible friction, simplifying the calculation of the hole size necessary for the desired flow rate.

PREREQUISITES
  • Understanding of fluid dynamics principles
  • Knowledge of energy conservation in fluid systems
  • Familiarity with basic equations of motion
  • Concept of pressure and its relation to flow rate
NEXT STEPS
  • Study the Bernoulli's equation and its applications in fluid mechanics
  • Learn about the effects of friction in fluid flow and how to account for it
  • Explore the relationship between hole diameter and flow rate using the orifice equation
  • Investigate the impact of varying liquid densities on flow calculations
USEFUL FOR

Engineers, fluid mechanics students, and anyone involved in designing tanks or reservoirs for fluid flow applications will benefit from this discussion.

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Specifically, I have a certain flow rate in (volume/sec) and I know the pressure of the resevoir at a certain point. If there is a hole in the tank/resevoir at that point, how big should it be to achieve the given certain flow rate?
 
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If you may ignore friction, the easiest approach is to use energy conservation. Kinetic energy of liquid flowing out must be equal to work done by pressure pushing this volume out:

P - pressure, s - area of the hole, v - velocity [itex]\rho[/itex] - density of the liquid
[tex]Psv = \rho sv\frac{v^2}{2}[/tex]
thus
[tex]P = \frac{\rho v^2}{2}[/tex]
 


pressure = potential energy
 

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