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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.
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.
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!