Introduction:
The flow of fluid through a pipe can be categorized into two main types: laminar flow and turbulent flow. In laminar flow, the fluid flows smoothly in parallel layers with minimal mixing, while in turbulent flow, the fluid exhibits chaotic and irregular motion with high levels of mixing. The transition from laminar to turbulent flow is an important phenomenon in fluid dynamics and is influenced by various factors.

Explanation:
The given question asks about the factor that does not affect the transition from laminar to turbulent flow in a pipe. Let's analyze each option to understand why the correct answer is option B.

A) Density of fluid:
The density of the fluid is related to its inertia. In laminar flow, the momentum of the fluid is dominated by its viscosity, resulting in smooth and ordered flow. As the density of the fluid increases, the inertia also increases, making the flow more prone to turbulence. Therefore, the density of the fluid does affect the transition from laminar to turbulent flow.

B) Length of pipe:
The length of the pipe does not directly influence the transition from laminar to turbulent flow. The flow conditions, such as the velocity and diameter of the pipe, determine whether the flow will be laminar or turbulent. The length of the pipe only affects the overall pressure drop and head loss along the pipe due to friction.

C) Diameter of pipe:
The diameter of the pipe plays a significant role in the transition from laminar to turbulent flow. As the diameter decreases, the flow velocity increases, and the flow becomes more prone to turbulence. This is because the smaller diameter leads to higher shear forces and greater fluid interaction, promoting turbulence.

D) Velocity of the fluid:
The velocity of the fluid is a crucial factor in determining the flow regime. In laminar flow, the velocity is relatively low, and the fluid particles move in an orderly manner. As the velocity increases, the flow becomes more susceptible to disturbances and turbulence. Therefore, the velocity of the fluid does affect the transition from laminar to turbulent flow.

Conclusion:
Based on the analysis, it can be concluded that the correct answer is option B, i.e., the transition from laminar to turbulent flow does not depend on the length of the pipe. The other factors, such as the density of the fluid, diameter of the pipe, and velocity of the fluid, all play a significant role in determining the flow regime.