# Stream function find radial tangential velocity components

• xzi86
In summary, a stream function is a mathematical function used in fluid mechanics to describe the flow of a fluid in two dimensions. It is a scalar function that maps every point in a fluid to a value, and the contours of the stream function represent the streamlines of the fluid flow. The stream function can be used to find the radial and tangential velocity components by taking the partial derivatives of the stream function with respect to the radial and tangential directions, respectively. These derivatives give the velocity components in terms of the stream function. This information is significant as it provides valuable insights into the flow of the fluid, such as flow rate and direction. The stream function has various applications in fluid mechanics, including aerodynamics, hydrodynamics, and ocean
xzi86

## Homework Statement

Given the following stream function:

ψ=C(sin(theta)/r)

Find the radial and tangential velocity components.

? Don't know any

## The Attempt at a Solution

Absolutely no idea how to even begin. Do I take the integral or something? Any help appreciated

xzi86 said:
Find the radial and tangential velocity components.

## Homework Equations

? Don't know any

From wikipedia page on http://en.wikipedia.org/wiki/Stream_function" , the two relevant formulas would be

$$v_r = \frac{1}{r}\frac{\partial \psi}{\partial \theta}$$

$$v_{\theta} = - \frac{\partial \psi}{\partial r}$$

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## 1. What is a stream function?

A stream function is a mathematical function used in fluid mechanics to describe the flow of a fluid in two dimensions. It is a scalar function that maps every point in a fluid to a value, and the contours of the stream function represent the streamlines of the fluid flow.

## 2. How is the stream function used to find radial and tangential velocity components?

The stream function can be used to find the radial and tangential velocity components by taking the partial derivatives of the stream function with respect to the radial and tangential directions, respectively. These derivatives give the velocity components in terms of the stream function.

## 3. What is the significance of finding the radial and tangential velocity components using the stream function?

The radial and tangential velocity components provide valuable information about the flow of a fluid. The radial velocity component gives the flow rate per unit area at a certain point in the fluid, while the tangential velocity component gives the direction of the fluid flow. By finding these components using the stream function, we can better understand the behavior of the fluid.

## 4. What are some applications of using the stream function to find radial and tangential velocity components?

The stream function is commonly used in fluid mechanics to study the flow of fluids in various applications such as aerodynamics, hydrodynamics, and oceanography. It is also used in the design and analysis of pumps, turbines, and other fluid control devices.

## 5. Are there any limitations to using the stream function to find radial and tangential velocity components?

While the stream function is a useful tool in fluid mechanics, it has some limitations. It can only be used for two-dimensional flows and does not account for viscosity or turbulence in the fluid. It also assumes that the fluid is incompressible and irrotational, which may not always be the case in real-world applications.

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