Fluid Dynamics

1

Physics 108
–

lecture 8: Fluid Dynamics

Fluid dynamics is the study of how flowing fluids behave
.




An ideal flowing fluid is

•
steady state (motion at any one location not changing)

•
irrotational (fluid not rotating around direction of flow)

•
nonviscous (no friction internally or on walls)

•
imcompressible (density is constant)



Mass flow rate
: relates to area, velocity, and density:






why:





The equation of continuity
:

mass going in equals mass coming out





why:





2

Example (continuity):
Your garden
hose is about 1.0cm in radius. If water
flows at 1.0m/s through the hose and
reaches a nozzle of radius 1.5mm, what is
the velocity coming out the nozzle?


Given


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Conversions/Equations

3

Bernoulli’s equation

energy is conserved for a flowing fluid

(see book derivation)






P
1,2

= pressure at pts 1,2

v
1,2

= speed at pts 1,2

y
1,2

= height at pts 1,2


= fluid density

g = gravity





Think Pair Share Task: what would happen above if someone:


squeezed the bag:



uncoiled the hose and put the bag higher:

4

Example (Bernoulli):
An IV bag on a
patient is located 0.7m above their hand.
The patient has a gauge blood pressure of
50mmHg. If the bag’s fluid level is
decreasing at a rate of 1.0mm/min under
atmospheric pressure, what is the velocity of
the fluid entering the patient’s arm?

Given


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Conversions/Equations

5

What is Viscosity?


•
Viscosity (

)
-

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.

Viscosity can be thought
of as a measure of the “thickness” of a fluid. Higher viscosity means higher
resistance to flow.



The units of viscosity are
Poiseuilles (Pl)

, or centipoise (cP):


[Pl] = [Pa][s]


and 1[cP] = 0.01[Pl]



•
Poiseuille’s law

•
Poieseuillés law relates how much
volume of fluid per amount of time

can be forced
through a tube. This is called a volume flow rate and is related to the:

•
viscosity of the fluid (higher viscosity


lower flow rate)

•
pressure difference on the tube ends (greater pressure


higher flow rate)

•
geometry of the tube (larger radius and shorter length


higher flow rate)




R = tube radius


P = pressure difference between tube ends



= viscosity

L = tube length

6

Example (viscosity):
Blood flows into a
dialysis machine through a 1.3mm diameter
tube of length 2m. The pressure driving the
flow equals the patient’s 50mmHg blood
pressure. What
volume

of blood is processed
in 1 hour by the machine?


Given


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Want


Conversions/Equations