Incompressible Flow 2 - Analytical Solution for a Simple Flow and Stream Functions

Question 1

For a uniform flow between two parallel plates, what is the velocity distribution observed?

Answer 1

Growing boundary layers around core flow
Boundary layers merge
Fully developed viscous flow
u = u(y), v = 0

Question 2

For a uniform flow between two parallel plates, what is the pressure distribution observed?

Answer 2

Exponential decrease
Linear pressure drop in fully developed flow region

Question 3

What does a streamline show?

Answer 3

The direction in which a fluid particle is moving in a flow field

Question 4

Mathematical definition of a streamline

Answer 4

A line everywhere tangential to the direction of the local fluid velocity vector

Question 5

Point about particles in streamline

Answer 5

As velocity of fluid particles is always tangent to its streamlines, the fluid particles can move along the streamline but cannot travel across it

Question 6

What is a stream tube?

Answer 6

Flow between two streamlines as particles cannot move across the streamlines and mass is conserved

Question 7

Example of streamline

Answer 7

Solid wall - satisfies conditions

Question 8

Change in Psi between two streamlines

Answer 8

Equal to volume flow rate Q between the two streamlines