# Polar to cartesian coordinates for stream function

• xzi86
In summary, the conversation is about obtaining the equations of the streamlines in a velocity field with radial and tangential components. The equations for x and y are provided, but there is confusion about translating from polar to cartesian coordinates and calculating the x and y components of the velocity.
xzi86

## Homework Statement

Consider a velocity field where the radial and tangenetial components of velocity are V_r=0 and V_theta=cr, respectively, where c is a constant. Obtain the equations of the streamlines.

x=rcos(theta)
y=rsin(theta)

## The Attempt at a Solution

I know how to obtain the equations of the streamlines. I don't know how to translate the polar coordinates into cartesian. Since V_r=0, wouldn't there be no x-component? But looking at the textbook solution, there is an x component. Any help would be appreciated. Thanks.

hi xzi86!

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Vr = 0 means there is no radial component …

in which (x,y) direction is the radial direction?

x=x(r,$\theta$)=rcos$\theta$
y=y(r,$\theta$=rsin$\theta$

You are given

V$_{r}$=$\frac{dr}{dt}$=0

V$_{\theta}$=$\frac{d\theta}{dt}$=cr

How do you calculate

V$_{x}$=$\frac{dx}{dt}$

and

V$_{y}$=$\frac{dy}{dt}$ ?

## 1. What is the purpose of converting from polar to cartesian coordinates for a stream function?

Converting from polar to cartesian coordinates allows for easier visualization and calculation of fluid flow in two-dimensional systems. It also simplifies the application of mathematical operations and equations.

## 2. How is the conversion from polar to cartesian coordinates for a stream function performed?

The conversion can be done using the following equations:
x = r * cos(theta)
y = r * sin(theta)
where r is the distance from the origin and theta is the angle from the positive x-axis.

## 3. Can a stream function be represented in both polar and cartesian coordinates?

Yes, a stream function can be represented in both polar and cartesian coordinates. However, the equations and calculations may differ depending on the coordinate system used.

## 4. How does the stream function change when converting from polar to cartesian coordinates?

The stream function remains unchanged when converting from polar to cartesian coordinates. It is a mathematical property of fluid flow and is independent of the coordinate system used.

## 5. Are there any limitations to using cartesian coordinates for a stream function?

Cartesian coordinates are suitable for analyzing fluid flow in two-dimensional systems. However, they may not be ideal for three-dimensional systems or systems with complex geometries. In such cases, other coordinate systems may be more appropriate.

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