Lecture 7: Down To Earth

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• Do you know
• You have 80,000km of blood vessels
• B747 Nonstop flight for 100 hrs

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Fluids in Motion
Flow the movement of fluid particles. At
different locations in the stream the particle
velocities may be different, as indicated by v1
and v2.
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Steady or unsteady flow
Steady flow the velocity of fluid particles at
any point is constant as time passes. In steady
flow, the pattern of streamlines is steady in
time, and no two streamlines cross one another.
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Unsteady flow the velocity of fluid particles at
any point of the fluid changes as time passes.
Unsteady flow - Turbulent flow is an extreme kind
of unsteady flow and occurs when there are sharp
obstacles or bends in the path of a fast-moving
fluid
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Compressible or incompressible flow Compressible
flow the density of a fluid varies as the
pressure changes -gases are highly compressible.
Incompressible flow the density of a fluid
remains constant as the pressure changes -
liquids flow in an incompressible manner.
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The Equation of Continuity
Why?
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• The mass of fluid per second (e.g., 5 kg/s) that
  flows through a tube is called the mass flow
  rate.
• Conservation of mass flow If a fluid enters one
  end of a pipe at a certain rate (e.g., 5
  kilograms per second), then fluid must also leave
  at the same rate, assuming that there are no
  places between the entry and exit points to add
  or remove fluid.

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EQUATION OF CONTINUITY The mass flow rate (rAv)
has the same value at every position along a tube
that has a single entry and a single exit point
for fluid flow. For two positions along such a
tube r1A1v1 r2A2v2 r fluid density (kg/m3) A
cross-sectional area of tube (m2) v fluid
speed (m/s) SI Unit of Mass Flow Rate kg/s
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r1A1v1 ?riAivi
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Cholesterol and Plugged Arteries
A clogged artery In the condition known as
atherosclerosis, a deposit or atheroma forms on
the arterial wall and reduces the opening through
which blood can flow.
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In the carotid artery in the neck, blood flows
three times faster through a partially blocked
region than it does through an unobstructed
region.
Doppler flow meter to measure the speed of red
blood cells. To locate regions where blood
vessels have narrowed.
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A1v1 A2v2, (r1 r2)
The ratio of the radii is
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The Equation of Continuity
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Circulation
Circulation
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Honey drop (viscous flow)
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• Water drop - nonviscous flow-all fluid particles
  across the pipe have the same velocity
• Honey (or blood) drop-A viscous - does not flow
  readily-different layers have different velocity.

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Why do we have viscosity?
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With friction or air resistance
PE? KE?PEHeat
Stop here
A roller coaster track
Energy form A ? Energy form B thermal energy
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• The flow of a viscous fluid (blood, honey) is an
  energy-dissipating process. The viscosity hinders
  neighboring layers of fluid from sliding freely
  past one another.
• A fluid with zero viscosity flows in an
  unhindered manner with no dissipation of energy.
• An incompressible, nonviscous fluid is called an
  ideal fluid (water).

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Laminar flow
The viscosity of a fluid is described by the
coefficient of viscosity ? SI Unit of Viscosity
Pa s
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POISEUILLE'S LAW
The viscosity h   of the fluid
Due to the viscosity, P2 gt P1
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In order to maintain a constant velocity, a force
F should be applied.
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• The volume flow rate Q (in m3/s) of the viscous
  fluid
• a difference in pressures P2 - P1 must be
  maintained between any two locations along the
  pipe in order for the fluid to flow. And Q P2
  - P1
• a long pipe offers greater resistance to the flow
  than a short pipe does- Q is inversely
  proportional to the length L.
• Q is inversely proportional to the viscosity h.
• Q being proportional to the fourth power of the
  radius, or R4.

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POISEUILLE'S LAW A fluid whose viscosity is ? ,
flowing through a pipe of radius R and length L,
has a volume flow rate Q given by
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Blood pressure circulation
Graph of blood pressure vs time in a major artery
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Key Concepts

• Viscous and non-viscous flow
• Physics of viscosity
• POISEUILLE'S LAW
• Blood pressure and circulation