Navier Stokes

Question 1

Assumptions.

hint: 6!

Answer 1

1. steady flow ( d() /dt = 0)
2. incompressible fluid (p = constant)
3. gravity acting in y (g(x) = 0, g(z) = 0)
4. no change in velocity (u) in x direction
5. fluid flows in x (v=0, w=0)
6. viscous fluid (μ = 0)

Question 2

Steps

hint: 8

Answer 2

1. sketch - diagram and label
2. list - all assumptions (6)
3. con - apply continuity equation
4. mom - apply momentum equation
5. diff - differentiate eq 1
6. apply - boundary conditions BC1 & BC2
7. sub - in constant back to eq 1
8. calc - for required parameters

Question 3

What is the equation for shear stress?

Answer 3

tau = backwards y (du/dy)

Question 4

What is the equation for volumetric flow rate?

Answer 4

Q = integration A (u) • dA