Unsteady Fluid Flow: Incompressible and Stream Function Calculation

In summary, the conversation discusses an unsteady fluid flow with a velocity field of q= - 1/2 sin t (xe^-y, e^-y). It is shown that the flow is incompressible and a stream function is found. The method of finding the path of a fluid particle at (1,0) at t=0 is also mentioned. The concept of incompressibility is explained, stating that the sum of all six terms must be zero for the flow to be incompressible. The conversation also mentions the need to know the formula for calculating the divergence of a vector.
  • #1
ra_forever8
129
0
An unsteady fluid flow has velocity field q= - 1/2 sin t ( xe^-y, e^-y).
Show the flow is incompressible and find a stream function.
Find the path of the fluid particle which is at (1,0) at t=0.

I only know it has six faces and the sum of all six terms has to be zero in order to show the flow is incompressible.
Rest i really don't how to slove the problems
 
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  • #2
Were you taught that, if the flow is incompressible, then the divergence of the velocity vector must be equal to zero? Do you know the formula for calculating the divergence of a vector?
 

FAQ: Unsteady Fluid Flow: Incompressible and Stream Function Calculation

1. What is unsteady fluid flow?

Unsteady fluid flow is a type of fluid motion where the velocity and pressure of the fluid change over time. This can occur in various systems, such as pipes, channels, or rivers, and is often caused by external forces or changes in the flow conditions.

2. What does it mean for a fluid to be incompressible?

An incompressible fluid is one in which the density remains constant regardless of changes in pressure or temperature. This is a common assumption in fluid flow calculations and is often used to simplify the equations.

3. What is the role of stream function in unsteady flow calculations?

The stream function is a mathematical function that describes the flow of a fluid and is often used in unsteady flow calculations. It is a useful tool for visualizing the flow patterns and can help in solving the governing equations for fluid flow.

4. How is incompressible fluid flow calculated?

Incompressible fluid flow is typically calculated using the Navier-Stokes equations, which describe the motion of a fluid under the influence of various forces. These equations can be solved using numerical methods, such as finite difference or finite element methods.

5. What are some real-world applications of unsteady fluid flow calculations?

Unsteady fluid flow calculations have numerous applications in engineering and science. Some common examples include predicting the behavior of fluids in pipes and channels, designing efficient turbines and pumps, and studying the flow of blood in the human body.

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