Which statement best describes the Grashof number?

Which statement best describes the Grashof number?

• A. A pH indicator
• B. A unit of heat transfer coefficient
• C. A dimensionless number related to buoyancy-driven flow
• D. A variable for diffusion coefficient

Answer: (C)

The Grashof number is a dimensionless measure of the relative importance of buoyancy to viscous forces in a fluid, which governs buoyancy-driven (natural) convection. It is defined as Gr = g β ΔT L^3 / ν^2, where g is gravity, β is the thermal expansion coefficient, ΔT is the temperature difference driving the flow, L is a characteristic length, and ν is the kinematic viscosity. A large Gr means buoyancy forces easily overcome viscous damping, so natural convection is strong; a small Gr means viscous effects dominate and conduction prevails. Because Gr is dimensionless, it lets us compare different systems without units and, together with the Prandtl number, relates to the Rayleigh number that often predicts the onset and intensity of convection. The other statements don’t fit because Grashof number is not a pH indicator, not a unit of heat transfer coefficient, and not a diffusion coefficient.

The Grashof number is a dimensionless measure of the relative importance of buoyancy to viscous forces in a fluid, which governs buoyancy-driven (natural) convection. It is defined as Gr = g β ΔT L^3 / ν^2, where g is gravity, β is the thermal expansion coefficient, ΔT is the temperature difference driving the flow, L is a characteristic length, and ν is the kinematic viscosity. A large Gr means buoyancy forces easily overcome viscous damping, so natural convection is strong; a small Gr means viscous effects dominate and conduction prevails.

Because Gr is dimensionless, it lets us compare different systems without units and, together with the Prandtl number, relates to the Rayleigh number that often predicts the onset and intensity of convection. The other statements don’t fit because Grashof number is not a pH indicator, not a unit of heat transfer coefficient, and not a diffusion coefficient.