# Finding stream functions for a cylinder [fluid mechanics]

• Niles
In summary, a stream function is a mathematical function that describes the flow of a fluid and is important in fluid mechanics for visualizing and analyzing flow patterns. To find the stream function for a cylinder, the Laplace equation must be solved using potential flow theory. The boundary conditions include the no-slip condition and far-field boundary condition. The stream function can be used to calculate the pressure distribution around a cylinder by using Bernoulli's equation. Changing the radius of the cylinder will affect the stream function by altering the flow patterns and velocity.
The stream function satisfies Laplace's equation also. All you need to do is figure out what the boundary conditions are.

Chet

## 1. What is a stream function and why is it important in fluid mechanics?

A stream function in fluid mechanics is a mathematical function that describes the flow of a fluid. It is important because it allows us to visualize and analyze the flow patterns of a fluid, which can help us understand and predict its behavior.

## 2. How do you find the stream function for a cylinder?

To find the stream function for a cylinder, we can use the potential flow theory. This involves solving the Laplace equation, which is a partial differential equation, for a two-dimensional flow around a cylinder. The resulting stream function will depend on the velocity and position of the fluid particles around the cylinder.

## 3. What are the boundary conditions for finding the stream function of a cylinder?

The boundary conditions for finding the stream function of a cylinder include the no-slip condition, which states that the fluid particles at the surface of the cylinder have zero velocity, and the far-field boundary condition, which states that the fluid particles are unaffected by the cylinder at a far distance.

## 4. Can the stream function for a cylinder be used to calculate the pressure distribution?

Yes, the stream function can be used to calculate the pressure distribution around a cylinder. This is done by using Bernoulli's equation, which relates the pressure and velocity of a fluid. By combining this with the stream function, we can determine the pressure at any point around the cylinder.

## 5. How does changing the radius of the cylinder affect the stream function?

Changing the radius of the cylinder will affect the stream function by altering the flow patterns around the cylinder. As the radius increases, the streamlines will become wider and the velocity will decrease. Conversely, as the radius decreases, the streamlines will become narrower and the velocity will increase.

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