At the bend in a pipe, along the outside curve,the pressure

A. decreases.B. can’t change.C. increases.

At the bend in a pipe, along the outside curve,

the water’s speed

A. decreases.B. can’t change.C. increases.

Water slows downand backs upagainst the outside wall. The streamline

broadens to show this.

At the bend in a pipe, along the

inside curve,the pressure

A. decreases.B. can’t change.C. increases.

Viscosity may makethe fluid“cling” tothe insidewall of the pipe and try to follow the curve…

At the bend in a pipe, along the

inside curve,the water’s speed

A. decreases.B. can’t change.C. increases.

Water slows downand backs upagainst the outside wall. The streamline

broadens to show this.

Water speeds upand races

ahead alongthe inside

wall.

Streamlinesthin to

show this!

Stream-linesregain theirmore evendistri-butionalongstraightsections of pipe.

Water slows downand backs upagainst the outside wall.

Water speeds upand races

ahead alongthe inside

wall.

Constant“energy/volume”

Pv += 2

21 ρ

Bernoulli’s principle argues that the fluid pressure must be

A. greater along the inside of the curve.B. greater along the outside of the curve.C. exactly the same along inside and outside.

Inside curve

Outside curve

The pressure gradient points (from region of highest pressure toward region of lowest pressure)A. to the right. B. to the left.C. into the screen (away from you).D. toward the center of curvature.

Inside curve

Outside curve

Notice the pressure gradient forcesfluid toward the center of its curved

path…providing the centripetal force that ANY mass needs to turn a corner!

Consider an obstacle in an airstream:(or an object moving through the air)

If there air is traveling rapidly enoughIts easy to imagine an empty “airpocket”

created in the obstacle’s “shadow.”

On the windwardside of this obstacle weexpect thepressure to be:

A. high, and the air speed to slow down.B. high, where the air speed increases.C. low, with the air speed slowing down.D. low, where the air speed increases.

On the windwardside of the obstacle we expect the streamlineshere to

A. broaden.B. stay uniform in their spacing.C. thin.

Where doesthis air go?

Builds high pressuredeflecting air aside.

Air slows, bendsaway from thebarrier wall.

Like in a plumbing elbow, high pressure forms at the

outside of the bend.

As dry leaves that before the wild hurricane fly,When they meet with an obstacle, mount to the sky,

Currents curveover the cornersto rejoining the airstream.

The air pressure at these cornersmust be

A. even higher than felt by the side facing the wind.

B. equal to the surrounding atmospheric pressure.

C. lower than the surrounding atmospheric pressure.

D. zero.

On the leewardside we might expect currents to be pretty still.

…curve around the corner, spill over the sides.

Viscosity may force the closest layers to

creep along the surface to which they stick…

On the leewardside we might expect currents to be pretty still.

Viscosity may force closest layersto creep along the surface to which they stick and curve around the corner, spill over the sides.

Streamlines like this are also used to describe the flow

moving past & around objects moving through the fluid!

Expect high pressure againwhere rushing air currents meet.

If moves FAST ENOUGH punches an air pocket behind it…

air will rush in to fill this vacuum!

How rapidly this air closes in the space behind determines the size of the “wake”

of “dead air.”

If relative motion between fluid and object is SMALL

smooth laminar flow results:

Amazingly, there are no pressure differences retarding motion!

Only viscous drag slows things down(a friction-like effect).

But we ABSOLUTELY expect that at high speeds

a wake does indeed develop!

This leaves a wake outlined by “turbulence”.

Conservation of angular momentum

can force this airthat comes spinningaround the corners

to develop vortices!

Which air foil design do Indy race cars have fixed on the back to aid in cornering?

A B

C

Your hand stuck out the window into the airstream around a moving car

palm forward

builds high pressureon your windward palm

with a lower pressure trailing wake.

You experience a pressure drag thatdrives your hand BACKWARD.

A hand tipped slightly upward

may actually be pushed up!

(the faster rushingair across the bottom

surface produces lowerpressure!)

A hand tipped slightly downward

can actually bepushed down!

But how SLOWLY must flow be forthe streamlines to remain laminar?

At what speeds does turbulence develop?

Let’s try to imagine what factors mightinfluence the onset of turbulence…

What might enhance formation of air pockets?

What might enhance air filling in such pockets?

Speed: Faster objects should produce

A. larger wakes, more turbulence.B. smaller wakes, less turbulence.C. no noticeable difference in wake or turbulence.

Fluid density:

Denser fluids should produce

Viscosity:More viscous fluids should produce

Size of obstacle:Larger objects should produce

Osborne Reynolds(1842 – 1912)

Considering these same variables, Reynolds defined a predictor

(formed basically by just multiplying them all together):

Reynoldsnumber

density · obstacle size · speed=viscosity

< 2000 Laminar flow

> 2000 Turbulent flow

Low pressureHigh speed

Viscous drag (air friction) doesaffect this ball traveling withlaminar flow through the air.

But NO pressure drag!

Reynoldsnumber

density · obstacle size · speed=viscosity

ρair = 1.200 kg/m3 at sea level and 20oC

Dbasball = 2.9 inches = 0.07 m

air = 0.0000183 kg/(m·sec)

0000183.0

07.0200.12300

v××>v

vm/sec >50.0 v

Maximum v 50 cm/sec

Above that turbulence sets in.

to keep the closest layers riding the surface

At high speeds viscosity is not enough

especially considering the high pressure that has developed there!

down the back side of the ball.

The surface layers of air sheer away from the surface!

Now the ball definitely suffers aPRESSURE DRAG!

SOME ANSWERS

Question 1

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Question 12

C. increases.

A. decreases.

Water is being forced into a constricted space.

Higher pressure slows it as it enters the bend.

C. increases.

A. decreases. Water clinging to the inside surface of the pipeis forced away from the pipe’s center, givingsubsequent layers of water more room to flow.When water encounters a new region of lower pressure it rushes in…speeds up!

B. along the outside. Pv += 2

21 ρSince, constant , wherever the

speed is low, the pressure will be high.

D. toward the center. Providing the centripetal force that guides the water into a turn.

A. high, & air speed to slow. Air is blocked and flow backs up!

The lower pressure on the underside, creates a pressure force down, increasing the frictional force.B

A.

A.

A.

B.

Speed:

Density:

Viscosity:

Size:

Greater fluid speed or density, increases thefluid’s momentum…and inertia would tend to keeping it moving in as straight a path as possible. This would be more likely to create the “air pocket” or shadow behind. An increase in viscosity would make the fluid to stick more to surfaces, riding down the backside of the object, more effectively closing the gap otherwise left behind,