Ratio of maximum velocity to average velocity for laminar fluid flow through a pipe - Fluid Mechanics

Discussion

• nabeel   -Posted on 18 Jun 18
  not 2 .is it 0.5
• bhanu   -Posted on 06 Feb 17
  i want to relation between kinematic viscosity and velocity of laminar flow
• garala brijesh   -Posted on 25 Apr 16
  Good
• Pankaj   -Posted on 29 Sep 15
  • The equation of velocity distribution of laminar fluid flow through a pipe having radius R is given by,
  
  u = – (1 / (4 μ)) (∂p/∂x) [R² – r²]
  
  where,
  u = velocity of fluid
  R = radius of pipe
  r = distance from the centre of the pipe
  
  • Maximum velocity occurs at the centre where r = 0. Putting this in above equation,
  
  U_max = – (1 / (4 μ)) (∂p/∂x) [R²]
  
  • Average velocity obtained by dividing discharge of the fluid across the cross sectional area of pipe (πR²)
  
  dQ = Velocity at radus r x Area of ring element
  
  = u x 2πr dr
  
  = – (1 / (4 μ)) (∂p/∂x) [R²] x 2πr dr
  
  • Therefore,
  
  Q = ₀∫^R – (1 / (4 μ)) (∂p/∂x) [R²] x 2πr dr
  
  = (π/8μ) (- ∂p/∂x) R⁴
  
  • Therefore, Average velocity,
  
  u = Q/A
  
  u = (1/8μ) (- ∂p/∂x) R²
  
  • Ratio of maximum and average velocity
  
  U_max / u = 2
  

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