Q1: Power number is the ratio of

ANS:A - drag stress to inertial stress.

The power number (Np) is defined as the ratio of inertial stress to viscous stress in a fluid flow situation.

Explanation:

1. Power Number (Np):
   • The power number is a dimensionless quantity used to characterize the flow behavior of fluids in different geometries, such as in stirred tanks or impeller-driven flows.
   • It is defined as: Np=Pρ⋅N3⋅D5\text{Np} = \frac{P}{\rho \cdot N^3 \cdot D^5}Np=ρ⋅N3⋅D5P​ where:
     • PPP is the power input to the fluid (in watts),
     • ρ\rhoρ is the fluid density,
     • NNN is the rotational speed of the impeller (in revolutions per second),
     • DDD is the impeller diameter.
2. Relationship to Stresses:
   • In fluid dynamics, the power number represents the ratio of inertial forces to viscous forces in the flow. It indicates how the fluid responds to the rotational motion imparted by the impeller.
   • It is specifically the ratio of the inertial stress (due to the motion of the fluid) to the viscous stress (resistance to flow due to viscosity).
3. Options Given:
   • Drag stress is typically associated with fluid resistance in the direction of flow, which is more related to Reynolds number and flow resistance.
   • Inertial stress refers to forces related to the motion of the fluid particles.
   • Gravitational stress is the force exerted by gravity on the fluid.
4. Conclusion:
   • The power number (Np) is correctly described as the ratio of inertial stress to drag stress. It quantifies how the inertial forces (related to the impeller's motion) compare to the viscous forces (related to fluid resistance) in a given flow situation.