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

Q.  Below diagram shows the velocity distribution of fluid flow through a pipe. Flow is laminar.
What is the ratio of maximum velocity to average velocity?

- Published on 04 Aug 15

a. 1
b. 2
c. 4
d. 3.14

#### 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 = distance from the centre of the pipe

• Maximum velocity occurs at the centre where r = 0. Putting this in above equation,

Umax = – (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 = 0R – (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

Umax / u = 2

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