# Solve Fluid Flow Problem: Find Water Rise in Cylindrical Bucket

• joe007
In summary, a cylindrical bucket with a height of 30.0 cm and diameter of 14.0 cm has a circular hole with a cross-sectional area of 1.72 cm^2 at the bottom. Water is poured into the bucket at a rate of 2.00×10^−4 m^3/s from a tube above it. The question is how high will the water rise? To solve this, we can use the equation q=v/t and the fact that the rate at which water exits the hole is a function of the height of water in the bucket. The water level will rise until the rate of water running out of the hole equals the rate of water being poured in. Using this relationship, we can
joe007

## Homework Statement

A cylindrical bucket, open at the top, is 30.0 cm high and 14.0 cm in diameter. A circular hole with a cross-sectional area 1.72 cm^2 is cut in the center of the bottom of the bucket. Water flows into the bucket from a tube above it at the rate of 2.00×10^−4 m^3/s ...the question is how high will the water rise??

A v = A v

q=v/t

## The Attempt at a Solution

well so far i know that Av = 2*10^-4

but i am not sure how to approach this problem. do i use Bernoullis principle but how

this is my working out

2*10^-4=1.72*10^-4 *v

v=1.163m/s

help me here cheers

Last edited:
oops the question is how high will the water rise??

The rate at which water exits the hole is a function of the height of water in the bucket. The water level will rise until the rate of water running out of the hole exactly equals the rate at which water is being poured into the top. Do you have a relationship for volume/sec exiting a hole related to the water pressure above the hole?

yes it is 2*10^-4 m^3/sec

I would approach this problem by first understanding the concept of fluid flow and the factors that affect it. In this case, we have a cylindrical bucket with a hole at the bottom, and water is being poured into it from a tube at a constant rate. This means that the volume of water inside the bucket is increasing, and as a result, the water level will also rise.

To solve this problem, we can use the equation for continuity, which states that the volume flow rate (Q) remains constant at any point in a system. In other words, the volume of water entering the bucket from the tube (Q) must be equal to the volume of water exiting the bucket through the hole (Av), where A is the cross-sectional area of the hole and v is the velocity of the water.

So, we can set up the equation as follows:

Q = Av

Substituting the given values, we get:

2.00×10^−4 m^3/s = 1.72 cm^2 * v

Note that we need to convert the cross-sectional area from cm^2 to m^2, which gives us 1.72*10^-4 m^2.

Now, we can solve for v:

v = (2.00×10^−4 m^3/s) / (1.72*10^-4 m^2) = 1.163 m/s

This means that the water is flowing out of the hole at a velocity of 1.163 m/s. To find the height of the water level, we can use the equation for Bernoulli's principle, which states that the total energy of a fluid remains constant at any point in a system. In other words, the sum of the kinetic energy (1/2mv^2) and potential energy (mgh) of the water at the top of the bucket must be equal to the sum of the kinetic and potential energy of the water at the hole.

So, we can set up the equation as follows:

1/2mv^2 + mgh = 1/2mv^2 + mgh

We can cancel out the kinetic energy terms, as they are equal on both sides. Also, we can assume that the water level at the top of the bucket is at a height of 30 cm (since the bucket is 30 cm high).

Therefore, we get:

mgh = mgh

## 1. What is a fluid flow problem?

A fluid flow problem is a mathematical or engineering problem that involves understanding and predicting the movement of fluids, such as water or air. This can involve calculating the velocity, pressure, and other properties of the fluid in different scenarios.

## 2. How do you solve a fluid flow problem?

To solve a fluid flow problem, you need to first define the problem and the properties of the fluid, such as viscosity and density. Then, you can apply principles of fluid mechanics, such as Bernoulli's equation and conservation of mass, to create a mathematical model. Finally, you can use numerical methods or experimental data to solve the equations and find the desired solution.

## 3. What is the cylindrical bucket problem?

The cylindrical bucket problem is a specific type of fluid flow problem that involves finding the rise of water in a cylindrical bucket as it is filled. This problem is often used in introductory fluid mechanics courses to demonstrate concepts such as hydrostatic pressure and continuity.

## 4. How do you find the water rise in a cylindrical bucket?

To find the water rise in a cylindrical bucket, you can use the equation for hydrostatic pressure, which states that the pressure at any point in a fluid at rest is equal to the weight of the fluid above that point. By setting the pressure at the bottom of the bucket equal to atmospheric pressure and solving for the height of the water, you can find the rise of the water in the bucket.

## 5. What factors affect the water rise in a cylindrical bucket?

The water rise in a cylindrical bucket is affected by several factors, including the diameter and height of the bucket, the density of the fluid, and the acceleration due to gravity. It is also affected by any external forces acting on the fluid, such as air pressure or temperature changes. Additionally, the shape and surface properties of the bucket itself can affect the fluid flow and the resulting water rise.

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