Physics 135A

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Physics 135A

• Physics 135A
• Lecture 18 Fluids Dynamics
• Dr. Z. Gong

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Physics 135A
Administrative Information

• Homework Set 8 is due today.
• 2nd Midterm will be in 2 weeks.

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Physics 135A
Review -1

• Common states of materials solid, liquid, gas,
  plasma
• Density mass per unit volume
• Specific gravity (SG) ratio of the density of
  the substance to the density of water _at_ 4oC

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Physics 135A
Review -2

• Pressure is defined as force per unit area
• in the unit of N/m2 Pascal
• Pressure in liquid
• The atmospheric pressure at sea level is
• 1 atm1.01325105 N/m2
• Pascals principle
• and hence

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Physics 135A
Physics 135A
Review -3

• Mercury barometer
• 1 torr 1 mm-Hg 133 N/m2
• When an object is in the fluid or gas, it
  experiences buoyant force exerted from the fluid
  or gas to it.
• Archimedess principle The buoyant force on a
  body immersed in a fluid is equal to the weight
  of the fluid displaced by that object ?F ?Fg?V
  WF

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Physics 135A
Physics 135A
Fluid dynamics

• Laminar flow each particle of the flow follows
  a smooth path, and the pass does not cross over
  one another
• Turbulent flow erratic flow that turns in small
  circles. Absorb a lot of energy. Has great
  viscosity.
• Viscosity comes from the friction between
  different layers of flow when there is speed
  difference.

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Physics 135A
Equation of continuity

• Flow rate determines how fast the fluid flow
  passing through a tube, where A
  is the cross section and v is the velocity of
  fluid
• Equation of continuity if the fluid is
  incompressible, and theres no fluid flow in or
  out the side, then the flow rate through A1 and
  A2 is the same

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Physics 135A
Example -1
Water comes into a tube at the rate of 1m3/s.
What should the radius of the spigot be so that
water will come out of it at 30m/s? Assume no
leakage of water from the tube and water is
incompressible, the equation of continuity holds.
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Physics 135A
Bernoullis principle

• Bernoullis principle when the velocity is high
  the pressure is low. When the velocity is low the
  pressure is high.
• Example when the train
• passes by at high speed
• the pressure around it
• is lower so that any objects
• might be pushed toward the train.

v
P
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Physics 135A
Bernoullis equation

• When fluid flows through the tube due to pressure
  difference, the pressure will do work on the
  fluid. Based on work energy principle
• We hence get the Bernoullis equation

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Physics 135A
Bernoullis equation special cases

• Torrecellis theorem when fluid comes out from
  the bottom of a big reservoir, the velocity of
  the fluid leaving the reservoir is the same as a
  freely falling object from the same height.
• Proof

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Physics 135A
Example -2
You need to siphon water from a clogged sink.
The sink has an area of 0.375m2 and is filled to
a height of 4.0cm. Your siphon raises 50cm above
the bottom of the sink and then descends 100cm to
a pail. The siphon has a diameter of 2.0cm.
Assuming water enters the siphon tube with zero
velocity, calculate the velocity when it enter
the pail. Estimate how long it will take to empty
the sink.
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Physics 135A
Example -2
Following Torrecellis theorem, and use the
average depth of water
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Physics 135A
Dynamic lift

• When theres no height difference, then the
  faster the flow, the smaller the pressure will
  be.
• For example, the airplane wings
• The same amount of air
• pass by. The longer the
• path, the faster the speed.

P smaller
v faster
P larger
v slower
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Physics 135A
Venturi tube

• When the speed of fluid flow is faster, the
  pressure is less.
• Applications
• Perfume atomizer
• Carburetor in the motor
• engine

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Physics 135A
Viscosity

• Viscosity Internal friction within fluid.
• The slower layer retards the
• faster layer next to it. The
• velocity varies gradually.
• The coefficient of viscosity ?
• is material dependent
• where v/l is velocity gradient.

Fluid flow
Stationary tube
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Physics 135A
Poiseuilles equation

• Because of viscosity, a pressure difference
  between the ends of the tube is necessary to keep
  the fluid from flowing.
• Poiseuilles equation describe the volume of rate
  of flow Q as
• where r is the radius of the tube, L is the
  length of the tube, and (P1 P0 ) is the
  pressure difference.
• Poiseuilles equation holds for laminar flow only!

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Physics 135A
Example -3
A patient is to be given a blood transfusion.
The blood is to flow through a tube from a raised
bottle to a needle inserted in the vein. The
inside diameter of the needle is 0.40mm and the
required flow rate is 4.0cm3 blood per minute.
How high should the bottle be placed above the
needle? The density of blood is 1.05103kg/m3,
the viscosity of blood is 410-3Pas. The blood
pressure is 18torr above atmosphere pressure.
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Physics 135A
Example -3
h
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Physics 135A
Surface tension

• There is tension force at the surface of fluid
  due to the attraction net force from the
  neighboring molecular at the surface.
• Surface tension
• The use of soap or detergent
• is to reduce the surface
• tension of water surfactant

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Physics 135A
Capillarity

• Surface tension come from the attraction force
  between molecular.
• If the cohesive force is stronger than the
  adhesive force, such as mercury in glass
  container, the surface will look like case 1.
• Otherwise, such as water in glass container, the
  surface will look like case 2.

Case 1
Case 2