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Fluid Mechanics and Hydraulic Machinery Miscellaneous

Fluid Mechanics and Hydraulic Machinery

  1. The velocity profile of a fully developed laminar flow in a straight circular pipe, as shown in the figure, is given by the expression
    u(r) = −
    R²
    ∂p
    1 −
    r²
    4μ∂xR²

    where ∂p/∂x is a constant
    The average velocity of fluid in the pipe is
    1. −
      R²
      ∂p
      8μ∂x
    2. −
      R²
      ∂p
      4μ∂x
    3. −
      R²
      ∂p
      2μ∂x
    4. −
      R²
      ∂p
      μ∂x
Correct Option: A


u = −
R²
−
dp
1 −
r²
4μdxR

dQ =u (2πrdr)

Solving, we get
Q = −
πR²
−
dp
8μdx

Now Q = Area ´ average velocity
∴  uav =
Q
=
Q
Area πR2

or   uav =
R²
dp
8μdx



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