15. Fluid flow

Question 1

What is an ideal dynamic fluid?

Answer 1

• no turbulences occur during flow
• no sound waves develop in the flowing fluid, the fluid is incompressible (not valid for acoustic and ultrasound imaging)
• no friction - occurs with walls, or other objects adjacent to the flowing fluid (that move at different speed than the fluid) - this requires that the interaction of the fluid particles is limited to elastic collisions

Question 2

When is laminar fluid established for an ideal dynamic fluid?

Answer 2

i) flow lines in the fluid never cross each other

ii) flow tubes never penetrate each other

Question 3

What is the equation of continuity for fluids?

Answer 3

• an expression of the conservation of mass or the conservation of volume of an incompressible fluid
•states that the volume flow rate is constant along a tube - the fluid flows faster when it passes through a section of the tube with a smaller cross-section
A1V1 = A2V2

Question 4

If a tube widens from cross sectional area A to 3A - what happens to the speed of an ideal dynamic fluid?

Answer 4

If original velocity is v1, then the velocity changes to a v1/3 in the wider part of the tube
- ie speed of ideal fluid decreases

Question 5

What does Bernoulli’s law state about fluids?

Answer 5

Bernoulli’s law is an expression of the conservation of energy for a closed system
• it states that an increase in the speed of an ideal dynamic fluid in a tube is accompanied by a drop in its pressure

Question 6

For what type of fluid is the Bernoulli’s equation not sufficient?

Answer 6

• for a newtonian fluid
• the equation of continuity, however flow resistance leads to a pressure drop along a tube (bernoulli’s law insufficient)

Question 7

What is viscosity?

Answer 7

An interaction between neighbouring layers of a moving fluid in a direction parallel to the flow lines

Question 8

Viscosity in a Newtonian fluid

Answer 8

Viscosity replaces the assumption of elastic collisions required between the ideal dynamic fluid and its confining walls

Question 9

What does Poiseuille’s law state?

Answer 9

States that the volume flow rate of a Newtonian fluid through a cylindrical tube is proportional to the fourth power of the radius of the tube

Question 10

Describe the velocity distribution of a honey jar places upside down? What law is this?

Answer 10

•Poiseuille’s law
Viscous fluids:
• The velocity is maximum at the centre of the tube
•decreases away from the centre - the velocity is 0 on the walls of the tube

If a fluid has negligible resistance, the speed is the same all across the tube

Question 11

Formula for Reynold’s number

Answer 11

Re = (pvd)/n
p - fluid density
v - objects speed
d - diameter of object

n - viscosity

Question 12

What is reynold’s number used for?

Answer 12

Can determine whether the flow of a stationary fluid around a moving object is laminar, turbulent, or a combination
•Re > 10^6: Turbulent