Solving Torricelli's Law: Investigating a Bowl with a Hole

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SUMMARY

This discussion focuses on solving Torricelli's Law for a bowl described by the function squareroot(1/0.11*h) with a hole of radius 0.004m. The user reports an unrealistic drainage time of 1200 seconds when applying the formula dh/dt*A(h)=-0.6*B*squareroot(2*g*h), where B represents the cross-sectional area. The bowl's depth is 0.11m, and the user seeks clarification on the meaning of squareroot(1/0.11*h) and the significance of the coefficient -0.6 in the equation. The discussion highlights the need for accurate integration and understanding of the variables involved.

PREREQUISITES
  • Understanding of Torricelli's Law and fluid dynamics
  • Familiarity with calculus, specifically integration techniques
  • Knowledge of cross-sectional area calculations
  • Experience using Maple 13 for mathematical computations
NEXT STEPS
  • Investigate the derivation of Torricelli's Law and its applications in fluid mechanics
  • Learn how to accurately compute cross-sectional areas for irregular shapes
  • Explore integration techniques for solving differential equations in fluid dynamics
  • Review the use of Maple 13 for solving complex mathematical problems
USEFUL FOR

Students studying fluid dynamics, mathematicians working on differential equations, and anyone involved in physics or engineering applications related to fluid flow and drainage systems.

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Homework Statement



ok, I am doing an assignment on torricellis law but I have run into a big problem. I have a bowl which can be described by the function:

squareroot(1/0.11*h). This bowl has a hole in the bottom of a radius of 0.004m. But when I use the relavant formula and integrate it, it says it takes 1200s to drain it. The bowl has a depth of 0.11m. have done experiments and this is far from correct.

Homework Equations



I use the following formula:

dh/dt*A(h)=-0.6*B*squareroot(2*g*h)

where B is the crosssectional area.

I use maple 13 to try to solve it, but it won't give anything reasonable.
 
Physics news on Phys.org
What does squareroot(1/0.11*h) represent? Cross-sectional area?

Also, in dh/dt*A(h)=-0.6*B*squareroot(2*g*h), what's the -0.6 for? Show us in detail how you got 1200 s.
 

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