Calculating Stream Function of Incompressible Fluid from Velocity

In summary, a stream function is a scalar function used to describe the motion of a fluid in two dimensions. It is related to the velocity of a fluid through the continuity equation and can be used to calculate the velocity at any point in the fluid. An incompressible fluid is a fluid with a constant density and the stream function can be calculated from its velocity using the equation: ψ = ∫v * dy. The stream function has practical applications in various fields, including fluid dynamics, meteorology, and oceanography, to analyze and predict the behavior of fluids. It can also be used to study turbulence and other complex fluid phenomena.
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Hi everybody, I have been looking for a way to calculate the stream function if I know the velocity [tex]\vec{v}[/tex]=(vx,vy,0) of a bidimentional flux.
From the formula given for [tex]\vec{v}[/tex], I know it is an incompressible fluid.
 
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Well, the derivatives of the stream function [itex]\phi[/itex] are generally related to the velocity components as...?
 

What is a stream function?

A stream function is a mathematical concept used to describe the motion of a fluid in two dimensions. It is a scalar function that maps out the streamlines of a fluid flow, which represent the path that a fluid particle follows over time.

How is the stream function related to the velocity of a fluid?

The stream function and the velocity of a fluid are related through the continuity equation, which states that the stream function is equal to the vertical component of the fluid's velocity multiplied by a constant. In other words, the stream function is a function of the velocity and can be used to calculate the velocity at any point in the fluid.

What is an incompressible fluid?

An incompressible fluid is a fluid that has a constant density and does not change volume under pressure. This means that the fluid's density remains the same regardless of the amount of pressure applied to it.

What is the equation for calculating the stream function of an incompressible fluid from its velocity?

The equation for calculating the stream function of an incompressible fluid from its velocity is: ψ = ∫v * dy, where ψ is the stream function, v is the vertical component of the fluid's velocity, and dy is the differential distance in the vertical direction.

What are some practical applications of calculating the stream function of incompressible fluids?

The stream function is used in various fields, such as fluid dynamics, meteorology, and oceanography, to describe and analyze the motion of fluids. It can also be used to model and predict the behavior of fluids in pipes, channels, and other systems. Additionally, the stream function can be used to study and understand turbulence and other complex fluid phenomena.

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