Question

What is the generally accepted value of the Reynolds number above which the flow in smooth pipes is turbulent?

Short answer

Answer: The generally accepted threshold value of the Reynolds number for turbulent flow in smooth pipes is Re > 4,000. It is important to note that this value is an approximation and may vary depending on factors such as pipe roughness and the presence of disturbances in the flow.

Step-by-step solution

Definition of Reynolds Number

The Reynolds number is a dimensionless quantity that describes the behavior of fluid flows. It is an important parameter in fluid dynamics, as it helps predict when a smooth laminar flow becomes turbulent. The Reynolds number is denoted by Re and is given by the following formula: Re = (ρ*u*L) / μ where: - ρ is the fluid density - u is the fluid velocity - L is the characteristic length (typically the diameter for a pipe) - μ is the dynamic viscosity of the fluid

Laminar and Turbulent Flow

Laminar flow is a type of fluid flow where the fluid particles move in parallel layers without much mixing, and it occurs at low Reynolds numbers. On the other hand, turbulent flow is characterized by a chaotic and disordered motion of fluid particles, with a higher degree of mixing and energy dissipation. Turbulent flow occurs at high Reynolds numbers.

Threshold Reynolds Number for Turbulent Flow

For flow in a smooth pipe, the Reynolds number is generally considered to mark the transition between laminar and turbulent flow. In fluid dynamics, it is widely accepted that a flow becomes turbulent when the Reynolds number exceeds a value of approximately 2,000 to 4,000. So the generally accepted value of the Reynolds number above which the flow in smooth pipes is considered turbulent is Re > 4,000. It is crucial to remember, however, that this value is an approximation, and the exact threshold may vary depending on factors such as pipe roughness and the presence of disturbances in the flow.