Chapter 5: Finite Control Volume Analysis

Question 1

What is the continuity equation?

Answer 1

An equation regarding the conservation of mass. The eulerian expression of continuity is the following:

(DM/Dt)_sys=partial/partial(t)int_cv(rho1)dv+int_cs(rho1v dot normal_cs)dA

In words:
Rate of change of the mass in the coincident system=
Rate of change of the mass in the coincident cv+
net rate of flow of mass through the control surface.

Question 2

What 3 physical laws does all fluid problems have to satsify?

Answer 2

• Mass conservation
• Newton’s 2nd law F=ma
• Energy conservation (1st and 2nd law of thermo)

Question 3

What is the momentum equation?

Answer 3

The momentum equation is an equation for newtons 2nd law. For a CV it can be written as follows:

(D(mV)/DT)_sys=partial/partial(t)int_cv(rhoV)dv+int_cs(rho*V(v dot normal_cs))dA

Rate of change of linear momentumin the coincident system=
Rate of change of momentum inside CV+
Flux of linear momentum through the control surface.

Question 4

What is a flux?

Answer 4

It is the flow of a property per unit area and time.

[quantity]/([area]*[time])

Question 5

How do we treat a deforming CV?

Answer 5

CV becomes time dependent eventhough the flow might be time independent.