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This next week we’ll finish up fluidswith the study of fluid flow

FridayFluid moving through things

andthings moving through fluids.

MondayObjects

travelingthrough

the airstream.

Wednesday

Liftand

flight.

Then jump toChapter 10

so we can coverelectricity, electronics,and light!

Beading is evidence that water

sticks to itself.

Droplets runslowing down

surfaces

& pull slowly away from surfaces

as they fall.evidence that water sticks to materials.

We describe this stickiness of a fluid (even water and air exhibit it)

by the term “viscosity”.

FLUID VISCOSITY ( )secm

kg

⋅

Air (20o C) 0.0000183Water (20o C) 0.00100Olive oil (20o C) 0.0840Honey (20o C) 1000

fast flow

Consider flow througha section of garden hose

of diameter, D

slow flow

slow flow

stationary/crawling

D

Without viscosity, flow rate would be simple:

In a time interval of 1 second (t = 1 sec)all water in the pipe would flow how far?

A. v / tB. v tC. v t 2

Flow rate: gallons/minuteliters/minutecc/secm3/sec

volumeper unit of time

At a constant flow rate, each and every seconda fixed volume of water

would flow past any given point.

v

12

Without viscosity, flow rate would be simple:

In a time interval of 1 second (t = 1 sec)what volume of water passes through A?

A. v t B. A v tC. A t D. A v

v

12

vt

So the flow rate would be

Volumesecond

=Avtt

= Av

How does the flow rate depend on the hose or pipe’s diameter?

A. rate D B. rate D2

C. rate 1/DD. The rate does not depend on D

Volumesecond

D2So simple geometryargues the flow ratedepends at least on

The other factor (other than cross section) was v.

What effects the speed of the fluid through a section of hose?

P1 P2

As the differential pressure P = P1 – P2

increases, the flowrate can be expected to

A. increaseB. stay the same.C. decrease.

Volumesecond

PD2So far we expect:

Viscous forces provide a friction which can keep fluids from accelerating continuously.

The greater a fluid’s viscosity,,

A. the greater the flowrate.B. the smaller the flowrate.C. has no effect on the flowrate.

Which relationship below best seems torepresent this dependence on viscosity?

A. B.

C. D.

∝

t

V 2∝tV

1

∝Δ

Δ

t

V ∝

t

V

Volumesecond

PD2So far we expect:

Viscous forces act everywhere the fluidneeds to slide past the inner hose wall.

The greater a length, L, of hose

A. the greater the flowrate through it.B. the smaller the flowrate through it.C. has no effect on the flowrate.

Which relationship below best seems torepresent this dependence on viscosity?

A. B.

C. D.

Lt

V ∝ 2L

t

V ∝

Lt

V 1∝ L

t

V ∝

fast flowslow flow

slow flowD

We’ve noted that fluid far from the inner walls of the hose travels the most freely.

In fact like blood in a capillary tube

or mercury in a thermometer

even water will not dribble freely from

a narrow enough straw.

fast flowslow flow

slow flowD

This makes the dependence on Deven stronger than the simple

geometry of the size of the opening.

Volumesecond

PD2

L4

Volumesecond

PD4

LOver the years mineral deposits have narrowed (mainly) the hot water pipes

throughout your folk’s home.

The hot water pipes must have aneffective inner diameter now ___

times the size of the cold water pipes.

A. B.

C. D.

E. F.

50.021 =

71.021 = 84.0

21 4 =

25.041 =

125.081 =06.016

1 =

City water pressure hasn’t really changed, but the hot water’s flowrate is

about half that of the cold water.

4

Volumesecond

PD4

L

You’re watering the backyard, but can’t reach the very back corners.

You attach a 2nd identical hose to increase your reach.

The flow rate

A. doubles.B. remains unchanged.C. is halved.D. is about ¼ what it was.

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!