# HELP Investigating the rate of discharge of water from a hole in a bucket

• ace121ace
In summary, the flow rate of water from a leaky bucket is relatively simple to calculate, but can be improved by finding a suitable formula or reference to equate the flow rate at different heights.
ace121ace
Hey guys, um I'm currently in grd 11, and for my physics assignment, I've chosen to investigate the flow rate of water from a leaky bucket. It is relatively simply however, I've been trying to find a suitable formula/s to equate the flow rate at different heights, ie, the volume of water over time, (the rate) and the water height. please note i don't want to cheat or anything, but a formula or a reference or something would be of great help, thanks in advance... :D
(I might add, the hole is at the bottom of the bucket, on the base, and also, i am aware that the size of the hole will make a difference, lol)(also, its the height of water in the bucket, not the height of the bucket itself, and the bucket is cylindrical)

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I am trying to investigate how the rate of the water leaving the bucket will change as the water level decreases, as less downward force is acting upon the hole,

Final result should look something like rate=c*height^n. You'll have to figure out what values for c and n work by taking measurements and trying to fit the data to the equation.

Once you have data, if you need help fitting it, feel free to ask.

K^2 said:
Final result should look something like rate=c*height^n. You'll have to figure out what values for c and n work by taking measurements and trying to fit the data to the equation.

Once you have data, if you need help fitting it, feel free to ask.

Thanx so much, and btw, what's c, and n, i mean what do the represent

They basically represent all of the variables you don't look at explicitly. There are a whole bunch of things going on here, so the formula will be mostly empirical.

Reason why it's probably going to be a power law dependence like this is because all of the limiting cases are simple power laws. For example, let's say the viscosity isn't a factor at all. In that case, rate=v*A, work done on fluid per unit time is v*A*P. Pressure P=rho*g*h. And energy lost to water flow is (1/2)rho*rate*v^2. So the equation to balance work being done v*A*rho*g*h=(1/2)rho*A*v^3. Or v=sqrt(2*g*h). That gives you rate ~ height^(1/2). On the other hand, if you force fluid through a long, narrow tube, you will get rate ~ height. (I'm not going to go through derivation, as it involves fluid mechanics.) In a realistic case, depending on which factors win out, the actual power will vary. And the actual dependence will be more complex, of course, but I doubt you'll have precision in the experiment to warrant a more complicated fit.

THANKYOU VERY MUCH! lol, big help

## 1. How do you set up the experiment to investigate the rate of discharge of water from a hole in a bucket?

The experiment can be set up by filling the bucket with a known amount of water and making a small hole near the bottom of the bucket. Place a container underneath the hole to catch the water and use a stopwatch to measure the time it takes for the water to completely drain from the bucket.

## 2. What factors can affect the rate of discharge in this experiment?

The size of the hole, the height of the water column, the temperature of the water, and the material of the bucket can all affect the rate of discharge. Other factors such as air resistance and surface tension may also play a role.

## 3. How can you ensure accurate and consistent results in this experiment?

To ensure accuracy and consistency, the experiment should be repeated multiple times and an average rate of discharge should be calculated. The same size hole and same amount of water should be used for each trial, and the experiment should be conducted in a controlled environment.

## 4. What is the relationship between the height of the water column and the rate of discharge?

The height of the water column above the hole has a direct effect on the rate of discharge. As the height increases, so does the pressure, resulting in a faster rate of discharge. This relationship is known as Torricelli's law.

## 5. How can the results of this experiment be applied in real-world situations?

Understanding the rate of discharge of water from a hole in a bucket can be useful in various real-world situations, such as designing water systems, predicting flood levels, and studying the flow of liquids in pipes. It can also be used to determine the efficiency of different drainage systems and help in making informed decisions about water usage.

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