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

• sting10
In summary, a student is working on an assignment about Torricelli's law and is having trouble with a bowl described by the function squareroot(1/0.11*h) and a hole with a radius of 0.004m. Despite using the relevant formula, integrating it, and conducting experiments, the estimated time for the bowl to drain (1200s) is incorrect. The student is using the formula dh/dt*A(h)=-0.6*B*squareroot(2*g*h) in Maple 13, but it is not giving a reasonable solution. The student also asks for clarification on what squareroot(1/0.11*h) represents and the purpose of the -0.6
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.

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.

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!

## 1. What is Torricelli's Law?

Torricelli's Law, also known as Torricelli's Theorem, is a physics principle that explains the flow of a liquid out of an opening in a container. It states that the speed of the liquid leaving the container is directly proportional to the square root of the height of the liquid in the container.

## 2. How is Torricelli's Law used in this investigation?

In this investigation, Torricelli's Law is used to study the flow of liquid out of a bowl with a hole. By measuring the height of the liquid in the bowl and the flow rate of the liquid out of the hole, we can verify the accuracy of Torricelli's Law and make calculations to predict the flow rate at different heights.

## 3. What materials are needed for this investigation?

The materials needed for this investigation include a bowl with a hole, water, a ruler or measuring tape, a stop watch, and a container to catch the water.

## 4. What are the steps for conducting this investigation?

The steps for conducting this investigation are as follows:

1. Fill the bowl with water to a certain height and mark the water level on the bowl.
2. Place the bowl over the container to catch the water.
3. Start the stop watch and measure the time it takes for the water to reach a certain height in the container.
4. Repeat the experiment with different water levels and record the data.
5. Use Torricelli's Law to calculate the theoretical flow rate and compare it to the experimental data.

## 5. What are some potential sources of error in this investigation?

Some potential sources of error in this investigation include human error in measuring the time and water level, variations in the size of the hole in the bowl, and external factors such as air resistance. It is important to conduct multiple trials and take an average to minimize these errors and increase the accuracy of the results.

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