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Fluid Mechanics

Q1: What is the ratio of the velocity at the axis of the pipe to the mean velocity of flow in case of pipe flow under viscous condition ?

A 0.5

B 0.67

C 1

D 2

ANS:D - 2

In pipe flow under viscous conditions, the ratio of the velocity at the axis of the pipe (centerline velocity) to the mean velocity of flow is approximately 0.5.

Explanation:

  1. Centerline Velocity (Maximum Velocity):
    • The velocity at the axis (centerline) of the pipe is the maximum velocity in the flow profile for laminar or turbulent flow.
  2. Mean Velocity (Average Velocity):
    • The mean velocity is the average velocity of the fluid flow across the cross-sectional area of the pipe.
  3. Ratio Calculation:
    • For fully developed laminar or turbulent flow in a circular pipe, the maximum velocity at the axis of the pipe is approximately twice the mean velocity due to the parabolic velocity profile.
    • Therefore, the ratio of centerline velocity to mean velocity is: Velocity at axisMean velocity≈24=0.5\frac{\text{Velocity at axis}}{\text{Mean velocity}} \approx \frac{2}{4} = 0.5Mean velocityVelocity at axis​≈42​=0.5

Conclusion:

Hence, the ratio of the velocity at the axis of the pipe to the mean velocity of flow in pipe flow under viscous conditions is 0.5. This ratio holds for both laminar and turbulent flows, where the flow profile is well-developed and symmetric.



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