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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:
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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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Want
Conversions/Equations
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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:
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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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Want
Conversions/Equations
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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
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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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Conversions/Equations
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