1. Ch 9: EXTERNAL INCOMPRESSIBLE VISCOUS FLOW
(can’t have fully developed flow)

2. Ch 9: EXTERNAL INCOMPRESSIBLE VISCOUS FLOW
(can’t have fully developed flow)
Re = UD/
CD = D/( ½ U2A)
Flow patterns around smooth
cylinder for different Re

3. Paradoxes Pipe Flow - hydraulic engineers knew p ~ Uavg2
- theory and capillary tube sowed p ~ Uavg2
Drag - theory predict no drag (1744 –d’Alembert)
Newton (1642 – 1727) in 1687 wrote Principia, entire second book devoted to fluid mechanics.
- several other paradoxes for external flows as well

4. Shape and Flow – Irvin Shapiro
Fluid Dynamics of drag
Parts I - IV
Newton (1642 – 1727) in 1687 wrote Principia, entire second book devoted to fluid mechanics.

5. EXPERIMENTAL SET UP
Air speeds up to 230 mph, drag forces object in jet upwards,
causing spring to extend downwards
Pressurized settling chamber underneath desk

6. Can measure U and Drag
Tubing leads air from settling chamber to U-tube manometer
which is calibrated in mph, so can measure drag force and speed.

7. PARADOX #1 Question #1: sketch the graph of drag vs velocity D R A G

8. Plot Drag (lbs) vs Velocity (mph)
from 0 – 250mh

9. D ~ U2
125 mph
250 mph
D ~ U
D = 6RU
Drag lower at
higher speed!

10. ASIDE: do you find it odd that viscous drag
D ~ U2
D ~ U
D = 6RU
ASIDE: do you find it odd that viscous drag
does not depend on density or pressure (p = RT)?

11. “The new law that he {Maxwell ~1862}
predicted seemed to defy common sense. It was that the viscosity of a gas – the internal friction that causes drag on a body that moves through it – is independent of pressure. One might expect that a more compressed gas to exert a greater drag.”
Turns out that the effect of being surrounded by more molecules is exactly cancelled out by the fact that their mean free path is less.
The Man Who Changed Everything – Basil Mahon

12. When very small dust particles fall through one column
of air at 1 atmospheric, they fall at the same terminal
velocity as if it was 0.01 atmosphere.

13. Question #2: if sphere is roughened,
PARADOX #2
Question #2: if sphere is roughened,
what happens to drag?

14. If pipe walls are roughened, what happens to pressure drop?

15. S R S R
Low Speeds
High Speeds

16. PARADOX #3
Question #3: What has more drag at
“high speeds”, a sphere or streamlined body
with the same diameter?
PARADOX #4
Question #4: What has more drag at
“low speeds”, a sphere or streamlined body
with the same diameter?

17. Equal weights in air and water, in air at “high speeds”
more drag on sphere, but in glycerin at “low speeds”
more drag on streamlined body

18. Summary of Paradoxes
(1) In the first experiment we found that sometimes an
increase of speed actually produces a decrease of drag.
(2) Sometime roughening increases drag and sometime
it decreases drag.
(3) Sometime streamlining increases drag and sometime

19. (1) In the first experiment we found that sometimes an increase of speed actually produces a decrease of drag.
Laminar Boundary Layer, bdy layer separates sooner on body, bigger wake
Turbulent Boundary Layer, bdy layer separates later on body, smaller wake

20. Components of pressure drag (P) and skin-friction
Viscous forces
in turbulent flow
greater than laminar,
but pressure forces
may be reduced
enough that total
drag goes down!
Components of pressure drag (P) and skin-friction
drag (V) for laminar and turbulent flows past an
unstreamlined body at high Reynolds number.

21. Most of the drag due
to skin friction, very
small wake.
Most of the drag due
to pressure drop, large
wake.

22. adverse pressure gradient
S e p a r a t i o n
adverse pressure gradient
Laminar bdy layer
Turbulent bdy layer
IDEAL FLOW LAMINAR FLOW TURBULENT FLOW

23. Momentum of fluid near surface is significantly greater in turbulent flow than laminar flow, hence turbulent flow is
more resistant to separation.

24. (2) Sometime roughening increases drag and sometime it decreases drag.
Turbulent flow allows
boundary layer to remain
attached longer.
Roughness makes skin
friction higher.

25. (2) Sometime roughening increases drag and sometime it decreases drag.
For U < A, both spheres
have laminar bdy
layer, as suspect greater
drag on rough surface
due to skin friction
For U < A, both spheres
have turbulent bdy
layer, as suspect greater
drag on rough surface
due to skin friction

26. Boundary layer becomes turbulent on roughened sphere sooner
50 yds
230 yds
Smooth
Dimpled
Boundary layer becomes turbulent on roughened sphere sooner
than it does for smooth sphere. Turbulent boundary layer better
at mixing high momentum outer flow with flow in boundary
layer. Thus energized by outer flow, turbulent boundary layer
separates further back on sphere, resulting in a smaller wake
and consequently less drag (1/5th as much at optimum speeds).

27. In the early days of golf , the balls
were smooth, and it was only
accidentally discovered that
scarred balls travel further than
smooth, unscarred ones. If today’s
balls are driven, say, 230 yds, a
smooth ball similarly struck
would travel only 50 yards.
Recently golf balls have been
designed with randomly spaced
hexagonals with the claim of an
additional 6 yards.

28. turbulent separation)
Trip
Flow over a sphere.
Bottom: Re = 15,000
(laminar separation)
Trip: Re = 30,000
(with trip wire
turbulent separation)
From Van Dyke,
Album of Fluid Motion
Parabolic Press, 1982
Original photographs by
Werle, ONERA, 1980
Smooth

29. Water: Glycerin: High Re Low Re
(3&4) Sometime streamlining increases drag and sometime it decreases drag.
Water:
High Re
Glycerin:
Low Re
At very low Reynolds numbers viscous effects extend far from body, really no boundary layer to speak of. At Higher Reynolds number there is form drag due to a pronounced wake. Streamlining will reduce the size of the wake at higher Reynolds numbers.

30. Viscous flow around sphere Viscous flow around stream- lined body
From Visualized Flow – Japanese Society of Mechanical Engineers
Viscous flow
around stream-
lined body
A 2-D model is installed between the small clearance between two glass plates. The flow of a viscous fluid in this narrow space has sreamlines which coincide with potential flow. [ referred to as Hele-Shaw flow; (h/L)2<<1]

31. Low Re – then friction drag important, want to decrease area
High Re – then pressure drag important,
want to decrease wake

33. Large wake
Small wake

34. First flight of a powered aircraft 12/17/03 120ft in 12 seconds
Same drag at 210 mph
Not until 1907 that a 0ne minute flight was accomplished in Europe ( Henri Farman). By 1905 the Wright brothers were making 30 minute flights.
First flight of a powered aircraft
12/17/03 120ft in 12 seconds
Orville Wright at the controls

35. The End
Cd of (a) is 2.0; Cd of (b) is 1.2