Topic: Heat Transfer
The Grashoff number, Gr is defined as (where g is gravitational acceleration, beta is volumetric thermal expansion coefficient, Delta T is temperature difference, L is characteristic length, mu is the viscosity and nu is kinematic viscosity.
- A. g * beta * Delta T * L³ / mu²
- B. rho² * g * beta * Delta T * L³ / mu²
- C. g * beta * Delta T * L³ / nu²
- D. g * beta * Delta T * L / nu²
Answer: C. g * beta * Delta T * L³ / nu²
Explanation: The Grashoff number (Gr) represents the ratio of buoyancy forces to viscous forces in a fluid. It is formally defined as Gr = (g * beta * Delta T * L³) / nu². Substituting kinematic viscosity nu = mu / rho also yields Gr = (rho² * g * beta * Delta T * L³) / mu². Options (b) and (c) represent identical mathematical expressions.