Easy Fluid Problem: Find Stream Function & Pressure

[600burger]

Homework Statement

a. Given potential flow, find stream function and velocity components.
b. Compute pressure along the x-axis and plot it.

Homework Equations

Psi = 2axy

The Attempt at a Solution

So, I got the psi from phi (above) but i don't understand how I am to go from stream function Psi to the pressure distrobution...

 

[lalbatros]

From the stream function you can calcualte the velocity field.
You can guess that it is possible to get the pressure, just think to Bernouilli.
Anyway, plug the velocity field into the Navier-Stokes equations and you will get the pressure (gradient).

 

[piercas]

I would approach this problem by first understanding the concept of stream function and its relationship to potential flow. The stream function is a mathematical function used to describe the flow of a fluid in two-dimensional space. It is defined as the flow rate per unit width perpendicular to the flow direction. In potential flow, the stream function is related to the velocity components through the continuity equation.

To find the stream function in this problem, I would use the given equation for potential flow and apply it to the definition of stream function. This would give me the stream function as a function of x and y.

Once I have the stream function, I can use it to find the velocity components along the x-axis by taking the partial derivative of the stream function with respect to x. This would give me the u component of velocity, while the v component would be zero since there is no flow in the y-direction.

To compute the pressure along the x-axis, I would use the Bernoulli's equation, which relates the pressure to the velocity and stream function. By substituting the velocity components and the stream function into the equation, I can solve for the pressure at any given point along the x-axis.

After computing the pressure at different points along the x-axis, I can plot it to visualize the pressure distribution. This can help me understand the behavior of the fluid in the given potential flow and identify any areas of high or low pressure.

In summary, to solve this easy fluid problem, I would use the given equation for potential flow to find the stream function, and then use it to calculate the velocity components and pressure along the x-axis. Finally, I would plot the pressure distribution to gain a better understanding of the fluid flow.