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

[sting10]

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.

 

[ideasrule]

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.

 

[kerimek]

Hello there,

Firstly, I would like to commend you for taking on the challenge of solving Torricelli's Law and investigating a bowl with a hole. It is a complex and interesting topic in fluid mechanics.

After reviewing your homework statement and equations, I believe there may be a few factors that could be affecting your results. Firstly, the formula you are using is a simplified version of Torricelli's Law, which assumes a constant cross-sectional area. However, in this case, the cross-sectional area is not constant due to the presence of a hole in the bottom of the bowl. This could be causing discrepancies in your calculations.

Additionally, the formula you are using assumes ideal conditions, which may not be the case in a real-world scenario. Factors such as friction, viscosity, and turbulence can impact the rate at which the bowl drains.

I would recommend considering these factors and perhaps using a more advanced formula, such as the Bernoulli equation, to account for the changing cross-sectional area and other factors. Additionally, conducting more experiments and adjusting your parameters could help you arrive at a more accurate result.

I hope this helps and good luck with your assignment!