Question

For turbulent flow, the value of Reynolds number is

1. Re <2000
2. Re >2000
3. 1000< Re <2000
4. Re=1000

Answer 1

There are six different types of fluid flow namely: steady and unsteady, rotational and ir-rotational, laminar and turbulent, uniform and non-uniform, compressible and incompressible, one, two and three dimensional fluid flow. To differentiate these fluid flows from one another Reynold number is used.

Complete step by step answer:
The Reynold number is a ratio and it has no dimension. It is a ratio between the inertial forces and viscous forces. It is a system used to distinguish between various types of fluids. The formula for Reynold number is
${N_{\operatorname{Re} }} = \dfrac{{\rho vd}}{\mu }$
Where,
${N_{\operatorname{Re} }}$= Reynolds Number
$\rho$= density
V= velocity
D= diameter
$\mu$= viscosity
Reynolds number is used for distinguishing between Laminar flow and Turbulent flow and various other fluid flows. It is described as inertial force upon viscous force. Here inertial force is defined as any force which is solicited by an observer to maintain Newton's second law of motion (F = ma; F=force; m=mass; a= acceleration) and viscous force is defined by the force between a body and a fluid moving past it. It is directly proportional to inertial force and inversely proportional to the viscous force. Now, Laminar flow is a flow in which fluids travel smoothly or in regular paths. The flow of the fluid has no disturbance. Reynolds number for laminar flow is < 2000. Laminar flow example is the flow of honey from the bottle. Turbulent flow is opposite to laminar flow, in turbulent flow the flow of the liquid is not smooth and it is irregular. In turbulent flow the magnitude and direction of the liquid keeps on changing. Most of the fluid flow is turbulent. The most common example of turbulent flow is the flow of blood in arteries. The Reynold Number of turbulent flow is > 4000.
$\therefore$ For turbulent flow, the value of Reynolds number is Re > 2000.

Note: Mention the type of fluid flows and describe how Reynold number is useful in distinguishing between all of them. Write the formula of Reynolds number and explain each of its variables. Then define the Reynolds number for laminar and turbulent flow.