Question

Match the following non-dimensional numbers with the corresponding definitions :

Non-dimensional

number

Definition

P

Reynolds number

1

(Buoyancy force)/ (Viscous force)

Q

Grashof number

2

(Momentum diffusivity)/

(Thermal diffusivity)

R

Nusselt number

3

(Inertia force)/ (Viscous force)

S

Prandtl number

4

(Convective heat transfer)/

Conduction heat transfer)

Options :

  1. P-1, Q-3, R-2, S-4

  2. P-3, Q-1, R-2, S-4

  3. P-4, Q-3, R-1, S-2

  4. P-4, Q-3, R-1, S-2

Show Answer

Answer :

P-4, Q-3, R-1, S-2

Solution :

Different dimensionless numbers:

  • WeberNumber=InertiaforceSurfacetensionforce
  • Reynoldsnumber=InertiaforceViscousforce
  • Machnumber=InertiaforceElasticforce
  • Eulersnumber=InertiaforcePressureforce
  • Froudenumber=InertiaforceGravityforce
  • Biot number  → Ratio of internal thermal resistance to boundary layer thermal resistance
  • Grashof number  → Ratio of buoyancy to viscous force
  • Prandtl number  → Ratio of momentum diffusivity (ν) and thermal diffusivity (α). Pr =ν/α 
  • Reynolds number  → Ratio of inertia force to viscous force
  • Nusselt number → Ratio of Convective heat transfer to Conduction heat transfer
  • Nu=hLck
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