# Rate of flow from a bucket with a hole in it.

• jprockbelly
In summary, the question is asking about the rate of water flow from a bucket with a hole at its base, given the area of the hole, the height of the water in the bucket, and the equations for velocity head and rate of flow. There may be other methods for solving this problem, but the weight of the water above the hole is the most important factor in determining the pressure at the hole.
jprockbelly

## Homework Statement

Consider a bucket with a hole, area A, near the base. If the bucket is filled with water to a height h above the hole at what rate will water flow out of the hole?

## Homework Equations

I would guess that the relative equations are the velocity head, v2 = 2*h*g, and the rate of flow, Q = A*v. However I am not sure that this is the correct way to go, as I would have thought that the pressure difference between the water at the base of the bucket and the atmosphere would be important.

## The Attempt at a Solution

If I am correct this can then be solved as:

Q=A*(2*h*g)^0.5, as a volume per second

Can anyone tell me if there is another way to do this?

{sorry, just realized this should have been postd in the physics, not maths forum}

Last edited:
This is correct.

Although the air pressure is pushing down on the water at the top of the bucket, it is also pushing on the water coming out the hole in bottom. Sort of like it is trying to push the water back up into the bucket. The effect is that these two pressures from the atmosphere cancel out.

jprockbelly said:

## Homework Statement

Consider a bucket with a hole, area A, near the base. If the bucket is filled with water to a height h above the hole at what rate will water flow out of the hole?

## Homework Equations

I would guess that the relative equations are the velocity head, v2 = 2*h*g, and the rate of flow, Q = A*v. However I am not sure that this is the correct way to go, as I would have thought that the pressure difference between the water at the base of the bucket and the atmosphere would be important.

## The Attempt at a Solution

If I am correct this can then be solved as:

Q=A*(2*h*g)^0.5, as a volume per second

Can anyone tell me if there is another way to do this?

{sorry, just realized this should have been postd in the physics, not maths forum}
No, the "pressure difference between the water at the base of the bucket and the atmosphere" is NOT important. What is important is the pressure at the hole. The water in the bucket under the hole is irrelevant. Also the atmospheric pressure is not important because it is essentially the same at the top of the water and at the hole. On the pressure caused by the weight of the water above the hole is important. If the top of the water is h above the hole, then you have a column of water of volume hA above the hole. Its weight is $g\mu hA$ where $\mu$ is the density of water which, in g/cm3, you can take to be 1. The force at the hole is ghA so the pressure is gh.

Thanks to both of you for your replies.

HallsofIvy, I am somewhat confused by your reply. Are you saying that the pressure IS important, or are you simply elucidating for my benefit?

## 1. What affects the rate of flow from a bucket with a hole in it?

The rate of flow from a bucket with a hole in it is affected by several factors, including the size and shape of the hole, the size of the bucket, the height of the water level in the bucket, and the type and thickness of the material the bucket is made from.

## 2. How can I calculate the rate of flow from a bucket with a hole in it?

The rate of flow from a bucket with a hole in it can be calculated using the Bernoulli's equation, which takes into account the cross-sectional area of the hole, the velocity of the water, and the height of the water level in the bucket. Other methods such as the Torricelli's law or the Poiseuille's law can also be used depending on the specific conditions.

## 3. Does the shape of the hole affect the rate of flow from a bucket?

Yes, the shape of the hole can affect the rate of flow from a bucket. A circular hole will have a greater flow rate compared to a square or rectangular hole of the same area, as circular holes have a lower resistance to the flow of water.

## 4. What happens to the rate of flow as the water level in the bucket decreases?

The rate of flow from a bucket with a hole in it decreases as the water level in the bucket decreases. This is because the pressure at the bottom of the bucket decreases as the water level decreases, resulting in a lower flow rate. However, the rate of flow can also be affected by other factors such as the shape of the hole and the material of the bucket.

## 5. Can the rate of flow from a bucket with a hole in it be controlled?

Yes, the rate of flow from a bucket with a hole in it can be controlled by adjusting the size and shape of the hole, as well as the height of the water level in the bucket. Additionally, using different materials for the bucket or altering the temperature of the water can also affect the rate of flow. Controlling the rate of flow can be useful in various applications, such as in irrigation systems or for draining water from a container.

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