Question

Which of the following expressions represent the Reynolds number of a fluid flowing through a uniform circular cross-section pipe?

• A. \( (\text{density of the fluid}) \times (\text{average velocity of the fluid}) \times (\text{internal diameter of the pipe}) / (\text{dynamic viscosity of the fluid}) \)
• B. \( (\text{average velocity of the fluid}) \times (\text{internal diameter of the pipe}) / (\text{kinematic viscosity of the fluid}) \)
• C. \( (\text{dynamic viscosity of the fluid}) \times (\text{average velocity of the fluid}) \times (\text{density of the fluid}) \times (\text{internal diameter of the pipe}) \)
• D. \( (\text{kinematic viscosity of the fluid}) \times (\text{average velocity of the fluid}) \times (\text{internal diameter of the pipe}) \)

Hint:

The Reynolds number is crucial for determining whether the flow of fluid in a pipe is laminar or turbulent. The standard formula involves the fluid's density, velocity, diameter, and dynamic viscosity.

Answer 1

The Correct Option is A, B

The Reynolds number (\( Re \)) is a dimensionless quantity used to predict the flow regime (laminar or turbulent) of a fluid. It is given by the equation: \[ Re = \frac{\rho v D}{\mu} \] Where:
- \( \rho \) is the density of the fluid (kg/m³),
- \( v \) is the average velocity of the fluid (m/s),
- \( D \) is the internal diameter of the pipe (m),
- \( \mu \) is the dynamic viscosity of the fluid (Pa·s).
This is the formula for calculating the Reynolds number when a fluid flows through a pipe with a uniform circular cross-section.

Step 1: Interpretation of Other Options
- Option (B) uses kinematic viscosity instead of dynamic viscosity, which leads to a different formulation. - Option (C) does not match the correct form of the Reynolds number. - Option (D) uses kinematic viscosity and does not represent the correct form.

Final Answer: \[ \boxed{\text{(A) } (\text{density of the fluid}) \times (\text{average velocity of the fluid}) \times (\text{internal diameter of the pipe}) / (\text{dynamic viscosity of the fluid})} \]