Conservation of X

Question 1

What the two ways of analysing fluid motion?

Answer 1

The Lagrangian (moving particle) approach - small elements of fluid within the flow are followed all the time

Eulerian (control volume) approach - provides bulk description of the flow

Question 2

What are the advantages of the Lagrangian approach?

Answer 2

Approach is useful when:

• one particle is sufficient to describe entire flow field
• all particles move together e.g. rigid body motion
• when particles are few in number (non-continuum)

Question 3

What are the disadvantages of the Lagrangian approach?

Answer 3

• Usually need to follow many particles
• Motion of each is described by a different differential equation

Hence not widely used

Question 4

What is the general form of the conservation equation?

Answer 4

Storage = flux in - flux out + source - sink

Question 5

What is usually required for an unsteady volume/mass continuity equation?

Answer 5

A fluid with a free surface

Question 6

What is Newton’s Second Law of motion? (without assumption of constant mass)

Answer 6

The time rate of change of moment is equal to the net force

Question 7

What is X in the conservation equation integrals?

Answer 7

The amount of ‘stuff’ per unit volume (since we are integrating wrt to V with dV)

By separating it out from dV, we are assuming that X is constant across the cross-section which is a reasonable assumption since turbulent flow is an efficient mixer (hence added to other existing uncertainties, the usual 10% error is acceptable)

Question 8

What are the common forces that act on a fluid?

Answer 8

• Pressure differences e.g. weather
• Gravity e.g. open channel flows
• Density differences (against gravity) - warm air rises
• Friction/Viscosity e.g. shear stress at the boundary layer
• Forces exerted by a solid surface - by Newton’s III Law
• Others e.g. if fluid is electrically charged & passes through a magnetic field

Question 9

What are surface forces?

Answer 9

Forces due to stress (pressure, shear) as they are proportional to the total surface area over which they act

Question 10

What are body forces?

Answer 10

Forces acting on a fluid mass

Question 11

In which cases can a hydrostatic pressure distribution be used?

Answer 11

The hydrostatic equation comes from the vertical force balance and can hence only be used when the vertical acceleration is negligibly small