Question

If the Reynolds number is less than \(2000\), the flow in a pipe is

• A. Turbulent
• B. Laminar
• C. Transition
• D. None of the above

Hint:

For pipe flow: \[ Re<2000 \Rightarrow \text{Laminar} \] \[ 2000<Re<4000 \Rightarrow \text{Transition} \] \[ Re>4000 \Rightarrow \text{Turbulent} \]

Answer 1

The Correct Option is B

Concept:
Reynolds number is a dimensionless quantity used in fluid mechanics to determine the nature of flow of a fluid. It is given by: \[ Re=\frac{\rho vD}{\mu} \] where, \[ \rho = \text{density of fluid} \] \[ v = \text{velocity of fluid} \] \[ D = \text{diameter of pipe} \] \[ \mu = \text{coefficient of viscosity} \] The value of Reynolds number tells us whether flow is smooth or irregular.

Step 1: Understand the meaning of laminar flow.
Laminar flow means the fluid particles move in smooth parallel layers. There is no random mixing of fluid layers. This type of flow occurs when viscous forces are dominant.

Step 2: Recall the Reynolds number ranges.
For flow through a pipe: \[ Re<2000 \Rightarrow \text{Laminar flow} \] \[ 2000<Re<4000 \Rightarrow \text{Transition flow} \] \[ Re>4000 \Rightarrow \text{Turbulent flow} \]

Step 3: Apply the given condition.
The question says: \[ Re<2000 \] From the standard classification: \[ Re<2000 \Rightarrow \text{Laminar flow} \]

Step 4: Check the options.
Option (A) Turbulent is incorrect because turbulent flow occurs at high Reynolds number.
Option (B) Laminar is correct because \(Re<2000\).
Option (C) Transition is incorrect because transition flow occurs approximately between \(2000\) and \(4000\).
Option (D) None of the above is incorrect because option (B) is correct. Hence, the correct answer is: \[ \boxed{(B)\ \text{Laminar}} \]