Flowmetry Analysis (relating height to flow rate)

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SUMMARY

The discussion centers on calculating the instantaneous height of a liquid in a cylinder during simultaneous filling and emptying. The user employs Torricelli's theorem and the continuity equation, utilizing a cylinder area of 5 cm² and an orifice area of 0.5 cm². Despite calculating volume using V=Qt and height with H=V/A, the user expresses uncertainty about the modeling approach. The need for a more accurate method to assess flow rates and heights is evident.

PREREQUISITES
  • Understanding of fluid dynamics principles, specifically Torricelli's theorem.
  • Familiarity with the continuity equation in fluid mechanics.
  • Basic knowledge of calculus for instantaneous rate calculations.
  • Experience with volume and area calculations in geometric contexts.
NEXT STEPS
  • Research advanced applications of Torricelli's theorem in varying flow conditions.
  • Explore numerical methods for solving differential equations related to fluid dynamics.
  • Learn about the impact of orifice size on flow rate and liquid height.
  • Investigate simulation tools for modeling fluid flow in real-time scenarios.
USEFUL FOR

This discussion is beneficial for students in fluid dynamics, engineers working on hydraulic systems, and anyone involved in modeling liquid flow in containers.

Minoui11
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Hello!

1. Homework Statement
I need to find the instantaneous height of a liquid during the simultaneous filling and emptying (through a hole) of a cylinder. I have varying Qin at incremental time of 1 sec. with cylinder area=5 cm and orifice area=0.5 cm.

Homework Equations


Torricelli's theorem
Continuity equation[/B]

The Attempt at a Solution


1) Used V=Qt to find volume for each flow rate.
2) Calculated H=V/A.
3) Used torricelli's theorem to calculate Qout.

But this doesn't seem to me like the correct modeling of the problem and am stuck on how to go about it.
 
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