Lecture 4 - Equations of fluid motion

Question 1

What do the navier stokes equations describe?

Answer 1

The motion of viscous fluids.

Question 2

Navier stokes equation?

Answer 2

rho(del_v/del_t + v * delta_v) = -delta_p = mu delta v + f

Question 3

Derive Bernoulli equation

Answer 3

see sheet

Question 4

Summarise Bernoulli equation

Answer 4

1. Applied to incompressible inviscid flows only
2. Holds along a streamline for a rotational flow
3. Holds at every point through an irrotational flow

Question 5

Assumptions about 1/2*v^2 + p/rho = constant ??

Answer 5

Assumes no body forces (such as gravity) and steady flow

Question 6

Reynolds number equation

Answer 6

Re = (rhoVL)/mu = VL/v

Question 7

For Reynolds number:

L - ?
v - ?
mu - ?
V - ?

Answer 7

L - characteristic length (blood vessel radius)
v - kinematic viscosity
mu - dynamic viscosity of the fluid
V - flow velocity

Question 8

what happens as Re -> inf ?

Answer 8

Diffusion terms vanish, thus flows with high reynolds numbers are approximately inviscid in the free stream

Question 9

DNS ?

Answer 9

Direct Numerical Simulation

Question 10

For a DNS, what doe increasing Reynolds number by 10 indicate?

Answer 10

CPU time will be increased by 1000 and storage requirement by 177.