Chapter 13: Fluids

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Chapter 13 Fluids

• Goal of this chapter
• define a fluid and relevant variables (pressure
  and density)
• study fluid at rest and the buoyancy principle
  (aka Archimedes principle)
• study simplest fluid in motion (e.g. non viscous
  fluid in non turbulent flow)

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Barometer
Suppose a liquid of density ? and an atmosphere
P What is h?
h
At the top of the column Ptop0 (vaccum) At the
surface of the liquid but inside the column
Pbottom inside ?gh At the surface of the liquid
but outside of the column Pbottom
outsideP Pbottom insidePbottom outside gt
?ghP gt hP/?g
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Barometer
Suppose a liquid of density ? and an atmosphere
P What is h?
h

• hP/?g
• P 1atm 1.01 105 Pa
• g9.8 m/s2
• If fluid is mercury If fluid is water
• ??13.6 103 kg/m3 ??1.26 103 kg/m3
• h0.76 m h 8.2 m
• Also do exercise 13-3 page 400 in your book
  hydraulic press

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13-3 Buoyancy and Archimedes principle
Suppose a piece of matter of density ??and volume
VAh partly immersed in a fluid of density ?w and
of pressure P0 at the interface fluid-air.
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At rest (floating)
A bday helium balloon released rises. A pool
balloon released under water jumps out of the
water.
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Archimedes principle A body wholly or partially
submerged in a fluid is buoyed up By a force
equal to the weight of the displaced fluid
Apparent weight
wapp w - B Where wAgh? and BAgy?w
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• A rectangular tub made of a thin shell of poured
  cement has a length l1m, a width w80 cm, a
  depth d60cm and a mass M200 kg. The tub floats
  on a lake.
• How many people n of mass m80 kg each can stand
  in the tub before it sinks?

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13-4 Fluids in motion(our assumptions)

• Real fluid motion involves
• Compression (mechanical, thermal)
• Laminar or trubulent flow
• (v and P depends on time)
• Rotational flow
• (whirlpool, vortices)
• Internal friction
• (viscosity)

• What we will study
• Incompressible fluids at constant temperature
• Laminar flow and irotational flow
• Non viscous fluid

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Equation of continuity
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• A garden hose of inside diameter 2 cm passes a
  flow rate of 0.25 L/s. What is the speed of the
  water in the hose? The nozzle of the hose is a
  circular opening of a diameter 1.0 cm. What is
  the speed of the water when it emerges?

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• An air-filled air balloon of radius R0.1m is
  totally submersed in a tank of water. What is the
  thickness t of the lead skin of the balloon if
  the balloon neither rises nor sinks? The density
  of lead ?Pb11.3 103 kg/m3
• ( assume that the weight of air is negligible
  ?airltlt?water)

Suppose tltltR, the volume V of lead is 4?R2t,
therefore the weight of the balloon is 4?R2t
g?Pb. The weight of water is 4/3?R3?waterg Once
again we suppose tltltR such that RtR For the
balloon nor to rise or sink 4?R2t g?Pb
4/3?R3?waterg therefore t0.003m3mm BTW this
result agrees with the assumption Rgtgtt.