Question

1) Explain why the stream function allows certain fluid mechanics problems to be solved more easily?

note : this question using the book Fundamentals of Momentum, Heat and Mass Transfer, Sixth Edition “ chapter 10 “

Answer 1

Explanation:

Under the assumptions: For the steady, incompressible and 2-D flow, the continuity equation can be written as,

As we know that the streamlines are the lines or the family of curves in the flow field such that the tangent at any point gives the velocities vector of the flow, and the stream function show the  trajectories of particles in a steady flow, which relates as,

If we put the value of 'u' and 'v' velocities in the continuity equation (1), then we have only one function which can solve above equation (1) under same assumptions. If the continuity equation is satisfied for the given flow field

holds true. That means, if  is given, then an infinite number of streamlines can be drawn to define a particular flow field pattern.