The mass diffusivity, the thermal diffusivity and the eddy momentum diffusivity are same for, N_Pr = N_Sc = __________

ANS:A - 1

The mass diffusivity, the thermal diffusivity, and the eddy momentum diffusivity are equal when the Prandtl number (Pr) is equal to the Schmidt number (Sc). Therefore, NPr = NSc = 1. Explanation:

1. Prandtl Number (Pr):
   • Prandtl number is the dimensionless ratio of momentum diffusivity to thermal diffusivity.
   • It represents the relative importance of momentum diffusion (viscous effects) to thermal diffusion (conductive effects) in a fluid flow.
   • Mathematically, Prandtl number is defined as Pr=Momentum DiffusivityThermal DiffusivityPr=Thermal DiffusivityMomentum Diffusivity​.
2. Schmidt Number (Sc):
   • Schmidt number is the dimensionless ratio of momentum diffusivity to mass diffusivity.
   • It represents the relative importance of momentum diffusion (viscous effects) to mass diffusion (diffusive effects) in a fluid flow.
   • Mathematically, Schmidt number is defined as Sc=Momentum DiffusivityMass DiffusivitySc=Mass DiffusivityMomentum Diffusivity​.
3. Equality of Diffusivities:
   • When the Prandtl number (Pr) is equal to the Schmidt number (Sc), it means that the momentum diffusivity, thermal diffusivity, and mass diffusivity are all equal in magnitude.
   • This condition typically occurs in certain fluid systems where the transport processes of momentum, heat, and mass are similar in nature and have comparable characteristic timescales.
   • The value of NPr (the ratio of Prandtl number to Schmidt number) is therefore equal to 1, indicating the equality of diffusivities.