1. Physics 2
Chapter 9
Section 4

2. Characteristics of Fluid Flow
Steady vs unsteady
steady – velocity of fluid particles at any
point is constant as time passes
velocity at 2 different points can be different but every particle that passes the same point is the same
unsteady – velocity at a point in the fluid
changes with time
extreme case is turbulent flow
Turbulent flow – occurs when there are sharp turns or obstacles
Velocity at any point changes erratically

3. Characteristics cont’d.
Compressible vs incompressible
incompressible – density stays nearly
constant as pressure
changes
most liquids are incompressible
most gases are compressible

4. Characteristics cont’d.
Viscous vs non-viscous
viscous – doesn’t flow readily
ex – honey
flow of viscous fluid is energy-dissipating
No fluid is truly non-viscous but some come close
More viscous the more energy lost

5. Characteristics cont’d.
Rotational vs irrotational
rotational – part of the fluid has rotational
and translational motion
Irrotational – all of the fluid has
translational motion only ▲
If rotational, a paddle wheel will turn since speed changes with depth

6. Streamline
When fluid flow is steady we use streamlines to represent the trajectories of the fluid particles
Streamline – line drawn such that a tangent to the streamline at any point is parallel to the fluid velocity at that point
For steady flow streamlines don’t cross

8. Equation of Continuity
The mass flow rate has the same value at every position along a tube that has a single entry and a single exit
For any 2 points along the tube
ρ1A1v1 = ρ2A2v2
where ρAv = mass flow rate
Put finger across garden hose and water comes out faster
Explain using equation of continuity

9. Equation of Continuity cont’d.
Mass Flow Rate= mass flow rate is the mass of a substance which passes per unit of time
[ρAv] = kg/s
where ρ – density of fluid
A – cross sectional area of tube
v – speed of fluid

10. Equation of Continuity cont’d.
If fluid is incompressible ρ1 = ρ2
so A1v1 = A2v2
where Av is volume flow rate
Volume flow rate – amount of volume passing a point per second
Q = Av and [Q] = m3/s
If cross sectional area of tube gets smaller, speed gets faster
Ex – river gets faster as it narrows

11. In the condition known as atherosclerosis, a deposit forms on the arterial wall and reduced the opening through which blood can flow. In the carotid artery in the neck, the radius of the opening is 3.5 mm at an unobstructed point but is only 2mm where a deposit forms. Determine the ratio of speeds of the blood at these two locations.

12. The water flowing from a gharden hose fills a 2 gallon bucket (231 in3) in 30s. Find the speed of the water that leaves the hose when the hose
(a) has an unobstructed opening whose radius is in
(b) has an obstructed opening reducing the area by a factor of 2 of the initial.

13. Volume and mass flow rates are constant for an incompressible fluid
Because V2 is greater than V1 there is acceleration from the large tube to the small tube. This can only be possible with an unbalanced force which is greater in the wide tube than the narrow tube.

14. V2 >V1; there is acceleration from wide to narrow
V2 >V1; there is acceleration from wide to narrow. Fwide > Fnarrow
P= F/A; (Fn <<Fw)/(An<Aw)
Pressure decreases with decreased Area.

16. Steady, irrotational, incompressible, non-viscous fluid
Can be described at any point along its path by specifying speed, pressure, and elevation
Observations –
1) if cross-sectional area drops, pressure drops, remember P= F/A
2) if rise in elevation the pressure decreases if the area stays the same

17. Bernoulli’s Equation P1 + 1/2 ρv12 + ρgy1 = P2 + 1/2 ρv22 + ρgy2
can be used to explain cases where fluids aren’t flowing through actual pipes
ex –
airplane wings are curved more on upper
surface
curve balls
drag zone in racing
Hurricanes – air rotates around an area of low pressure with speeds exceeding 180 mph and pressure drop below 950 millibars (1013 millibars is normal)
Coke cans suck together
Airplane wings are curved more on upper surface so air travels faster and pressure is reduced
Curve balls – when given a spin air close to ball is dragged around the ball so on ½ the speed is greater and pressure is less so gets deflected that way
Drag zone in racing – leader creates a partial vacuum due to air flow that follower gets pulled in t0

18. An aneurysm is an abnormal enlargement of a blood vessel
An aneurysm is an abnormal enlargement of a blood vessel. Suppose that, because of an aneurysm, the cross-sectional area of the aorta increases to 1.7 A1. The speed of the blood (ρ= 1060 kg/m3) through a normal portion of the aorta is 0.4m/s. Assuming the aorta is horizontal, determine the amount by which the pressure in the enlarge region exceeds the normal region.