Question

A flat plate is placed in an air stream at 20°C. The free stream velocity is 2 m/s. If the kinematic viscosity of air is \( 1.5 \times 10^{-5} \, {m}^2/{s} \), what is the Reynolds number at a distance of 1 m from the leading edge?

• A. \( 1.33 \times 10^5 \)
• B. \( 1.00 \times 10^5 \)
• C. \( 2.00 \times 10^5 \)
• D. \( 2.67 \times 10^5 \)

Hint:

The Reynolds number is essential for determining whether the flow is laminar or turbulent. In this case, a Reynolds number of \( 1.33 \times 10^5 \) indicates a transition from laminar to turbulent flow for flow over a flat plate.

Answer 1

The Correct Option is A

The Reynolds number (Re) is a dimensionless quantity used to predict the flow regime (laminar, transitional, or turbulent) in fluid dynamics. The Reynolds number for flow over a flat plate is given by: \[ Re = \frac{U L}{\nu} \] Where:
- \( U \) is the free stream velocity (2 m/s),
- \( L \) is the characteristic length (1 m),
- \( \nu \) is the kinematic viscosity of the fluid (\( 1.5 \times 10^{-5} \, {m}^2/{s} \)).
Substituting the given values: \[ Re = \frac{2 \times 1}{1.5 \times 10^{-5}} = \frac{2}{1.5 \times 10^{-5}} = 1.33 \times 10^5 \] Thus, the Reynolds number at a distance of 1 m from the leading edge is \( 1.33 \times 10^5 \).