Question

For a liquid flowing in a circular cross section pipe, the transition from laminar to turbulent flow will NOT depend on which of the following factor(s)?

• A. The diameter of the pipe
• B. The length of the pipe
• C. The linear velocity of the liquid
• D. The viscosity of the liquid

Hint:

Write out the Reynolds number formula and check which of the four options is missing from it.

Answer 1

The Correct Option is B

Step 1: Recall the criterion for laminar to turbulent transition.
The flow regime in a pipe is set by the Reynolds number, \(Re\), a dimensionless group defined as
\[ Re = \frac{\rho v D}{\mu} \]
where \(\rho\) is the fluid density, \(v\) is the average linear velocity of the liquid, \(D\) is the pipe diameter, and \(\mu\) is the fluid viscosity.
Flow is laminar when \(Re\) is below about 2100, and turbulent when \(Re\) is above about 4000, with a transition zone in between.

Step 2: Check which listed quantities appear in \(Re\).
Pipe diameter \(D\) appears directly in \(Re\), so a change in diameter changes \(Re\) and can shift the flow regime. Option (A) does affect the transition.
Linear velocity \(v\) appears directly in \(Re\), so a change in velocity changes \(Re\). Option (C) does affect the transition.
Viscosity \(\mu\) appears directly, in the denominator, in \(Re\), so a change in viscosity changes \(Re\). Option (D) does affect the transition.

Step 3: Check pipe length.
The Reynolds number formula has no length term in it at all, only density, velocity, diameter and viscosity.
Physically, once flow is fully developed, whether it is laminar or turbulent is set locally by the same balance of inertial to viscous forces, no matter how long the pipe is; a longer pipe does not by itself push the flow from laminar to turbulent or back. Pipe length instead affects things like total pressure drop and entrance length, not the transition criterion.
So option (B), the length of the pipe, is the one factor the transition does NOT depend on.

Final Answer:
Since \(Re = \rho v D / \mu\) contains diameter, velocity and viscosity but not length, the laminar to turbulent transition does not depend on pipe length.
\[ \boxed{\text{(B) The length of the pipe}} \]