Flow around Submerged Objects

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TOPIC 6

• Flow around Submerged Objects

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Framework

• Many practical situations involve flow past
  objects.
• Examples Flow of air around airplanes and
  automobiles, flow of water around submarines,
  design of road signs.
• Applications in chemical engineering Flow in
  packed beds, flow in fluidized beds, settling of
  solids in gases or liquids, flow over cylinders,
  flow through tube banks (important in heat
  exchanger design).

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Lift and Drag

• A body immersed in a flowing fluid will
  experience pressure and viscous forces from the
  flow.
• The sum of forces (due to pressure and shear
  stress) perpendicular to the direction of the
  flow is called LIFT

• The sum of forces (due to pressure and shear
  stress) acting in the direction of the flow is
  called DRAG.

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Determination of Drag Force

• Approaches
• Obtain detailed distribution of shear stresses
  and pressure along the surface of the object
• Use empirical approximations.

• It has been shown experimentally that the drag
  force acting on a body

(6.24)
where A is the projected area of the body normal
to the flow and Cd the drag coefficient
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Drag Coefficient

• The drag coefficient, Cd, depends on
• Shape
• Streamlined versus blunt bodies
• Smooth versus rough surfaces
• Particle Reynolds number
• The drag coefficient can be determined
  analytically for certain simple geometrical
  shapes at low Reynolds number flows, or
  experimentally, by placing the object in a wind
  or water tunnel and measuring the resistance as a
  function of Reynolds number.

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Drag Coefficient

• Values of drag coefficient for different shapes
  as a function of Reynolds number can be found in
  Figure 6.24 (6.22 2nd Ed.)of the textbook
• For low Reynolds numbers (Relt1) Cd24/Rep (Stokes
  law)

• In this case equation (6.24) becomes

(6.25)
Stokes flow
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Settling Under Gravity

• An important class of problems involves settling
  under gravity
• An object falling in air or in any other fluid,
  will attain a terminal velocity after an initial
  period of acceleration. At terminal velocity the
  sum of forces exerted on the object must be zero

Fweight-Fdrag-Fbuoyancy 0
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Example 1 Settling under gravity

• A small grain of sand, diameter Dp0.10 mm and
  specific gravity SG2.3, settles to the bottom
  of a lake after having been stirred up by a
  passing boat. Determine how fast it falls through
  in still water.

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Example 2 Settling under gravity

• A man jumps out of an airplane at high altitude.
  Determine the velocity of fall (terminal
  velocity)
• without having opened his parachute, assuming a
  drag coefficient of 1.1 and an area A0.5 m2.
• with a parachute open having a diameter of 6 m,
  assuming a drag coefficient of 1.2.
• The mass of man and parachute is 90 kg and rair
  0.909 kg/m3.

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