ANS:B - buoyancy to viscous forces.

a) Buoyancy to inertial forces:

• This ratio is not typically represented by the Grashof number. Instead, it's the ratio represented by the Richardson number (Ri), which compares the buoyancy force to the inertial (or kinetic) forces in a fluid flow. It's commonly used to characterize the stability of stratified fluids.

• The Grashof number (Gr) is indeed defined as the ratio of buoyancy forces to viscous forces. It quantifies the relative importance of buoyancy-driven (or natural) convection compared to viscous forces within a fluid. A high Grashof number indicates that buoyancy forces dominate, while a low Grashof number indicates that viscous forces dominate.

• The ratio of inertial forces to viscous forces is represented by the Reynolds number (Re). It's one of the most fundamental dimensionless numbers in fluid mechanics and represents the balance between inertial (or kinetic) forces and viscous forces. A high Reynolds number indicates that inertial forces dominate, leading to turbulent flow, while a low Reynolds number indicates that viscous forces dominate, leading to laminar flow.

• This ratio is not commonly represented by a dimensionless number. Buoyancy and surface tension forces are typically analyzed separately in fluid mechanics and heat transfer. The role of surface tension forces is often quantified by the Capillary number (Ca), which compares the viscous forces to surface tension forces and is relevant in capillary flow and wetting phenomena.