1. L 15 Fluids [4] > Fluid flow and Bernoulli’s principle
> Airplanes and curveballs
> viscosity
> surface tension

2. Basic principles of fluid motion
I. Continuity equation: v  A = constant  v1A1 = v2A2
II. Bernoulli’s principle states that as the speed of a moving fluid increases, the pressure within the fluid decreases. A1 A2 v2 v1

3. Blowing air over the top of the tube lowers the
air pressure on that side allowing the fluid to rise

4. Bernoulli’s principle
fast flow  low pressure
slow flow  high pressure
Low
pressure
High pressure
Flow on top
No flow

5. Why does a roof blow off in high winds ?
Low Pressure
Normal
Pressure

6. Wind tunnel visualization of air flow
streamlines

7. Streamlines and fluid flow
The black lines are the paths that the fluid takes as it flows.
Wider spacing indicates low speed flow, narrow spacing indicates high speed flow
Color indicates pressure
High Low
pressure pressure

8. Bernoulli’s Principle
Fluid flow velocity = v
Fluid pressure = P
 where v is high, P is low
 where v is low, P is high

9. Frames of reference
From the perspective of the jet, the air moves relative to the jet
The jet moves through the air

10. Streamlines around a wing

11. Flow over an airplane wing

12. Control surfaces on a plane
By extending the slats, the wing area can be increased to generate more lift at low speeds for takeoff and landing

13. How does a plane turn?
Lift Force
Level Flight
Banked turn

14. Airflow around a baseball that is NOT spinning
The ball is moving but from the ball’s perspective the air moves relative to the ball
The streamlines are bunched at the top and bottom indicating higher flow speed
The pressure forces are balanced

15. Curveballs The ball is rotating clockwise.
The layer of air adjacent to the
ball is dragged along by the
rotation, causing the flow speed
to be higher on the top side. The
higher pressure on the bottom
causes the ball to curve upward.
High speed,
Low P
the lift on a rotating
body moving through
a fluid is called the
MAGNUS FORCE
low speed,
high P

16. Curveballs & Screwballs
the dimples on a golf ball are there to increase the air drag on the rotating ball (back spin) causing it to experience extra lift.

17. Viscosity
so far we have considered only “ideal” liquids  liquids that can flow without any resistance to the flow
“real” liquids (like ketchup) have a property called viscosity which is a tendency for the liquid to resist flowing

18. viscosity
for example – pancake syrup flows more slowly than water – we say that pancake syrup is more “viscous” than water.
Ketchup and molasses are also good examples
viscosity is sometimes referred to as the “thickness” of a liquid
viscosity is the most important property of motor oil

19. Seeing the effects of viscosity
Pancake
syrup
Substances with higher
viscosity take longer to
flow down the ramp.
viscosity is a measure of the resistance that one
layer of liquid experiences when flowing over another layer.

20. Viscosities of various substances
water has a viscosity of about 1 unit
pancake syrup has a viscosity of 2500
ketchup has a viscosity of 98,000
Lava- 100,000
peanut butter has a viscosity of 250,000
glass is a liquid with a very high viscosity of  it does flow, but very slowly!
viscosity depends on temperature  warm syrup flows faster than cold syrup

21. Motor Oil SAE – Society of American Engineers
the viscosity of oil tends to decrease as it heats up (oil breakdown)
what does W-30 mean?
viscosity index-
hot engine
viscosity index- cold engine
A higher viscosity index indicates the viscosity
changes less with temperature than a lower viscosity index.

22. Measuring viscosity ball bearings low viscosity high viscosity
Liquid (e. g. water)
high viscosity
Liquid (e.g. syrup)

23.  (eta) is the fluid’s viscosity
Flow through a pipe L D P2 P1
big
effect!
 (eta) is the fluid’s viscosity
A 10 % reduction in diameter reduces the flow by 34 %
If D  D/2, the flow is reduced by 94 %

24. Blood flow in arteries
A pipe clogged
With calcium
deposits

25. SURFACE TENSION
a surface tension force causes a fluid surface to behave like an
elastic sheet
Molecules at the surface
feel a net force
insect on water surface

26. Suspended by surface tension

27. soap films

28. measuring surface tension forces
soap film W