# Fluid Dynamics

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24 Οκτ 2013 (πριν από 4 χρόνια και 8 μήνες)

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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):
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)

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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Conversions/Equations