Question

Specific heat, coefficient of viscosity, and thermal conductivity are related in the

• A. Prandtl number
• B. Reynolds number
• C. Froude number
• D. Biot number

Hint:

Match the three named properties to the defining formula of each dimensionless number listed.

Answer 1

The Correct Option is A

Step 1: Write the definition of the Prandtl number.
The Prandtl number is defined as \(Pr = \dfrac{c_p \mu}{k}\), where \(c_p\) is specific heat, \(\mu\) is the coefficient of viscosity, and \(k\) is thermal conductivity.
It compares how fast momentum diffuses through a fluid against how fast heat diffuses through it.

Step 2: Rule out the other dimensionless numbers.
Reynolds number, \(Re = \dfrac{\rho v D}{\mu}\), uses density, velocity, and a length scale, not specific heat or conductivity.
Froude number, \(Fr = \dfrac{v^2}{gL}\), only involves velocity, gravity, and length.
Biot number, \(Bi = \dfrac{h L}{k}\), uses a convective heat transfer coefficient and length, not viscosity or specific heat directly.

Final Answer:
Only the Prandtl number combines specific heat, viscosity, and thermal conductivity together. \[ \boxed{Pr = \frac{c_p \mu}{k}} \]