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Question

The velocity distribution for flow between two fixed parallel plates

A
is constant over the cross-section
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B
is zero at the plates and increases linearly to the mid-plane
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C
varies parabolically across the section
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D
is zero in middle and increases linearly towards the plates
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Solution

The correct option is C varies parabolically across the section
  • The expression for velocity of flow between two parallel plates is given by :
u=12μ(Px)(Byy2)

where,

B=Distance between the plates

y=Distance of point from one of the plate

μ=Dynamic viscosity of flowing fluid

(Px)=Pressure gradient along the flow
  • It is clear from the expression that the velocity distribution between two plates is parabolic with max. value at the centre and minimum (zero) at the boundary/plate surface.

Note:
  • umax(at y=B2)=18μ(Px)B2
  • uavg=23umax
  • If one of the plate is moving with velocity V and other is at rest, then expression for velocity is as following:
u=VyB+12μ(Px)(Byy2)


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