In this presentation, some dimensionless numbers are described which are mainly used.

1. DEPARTMENT OF CHEMICAL ENGINEERING
PRESENTED BY
AQIB JAH TEMURI (D-14-CH-33)

2. DIMENSIONLESS NUMBER

3. Reynold’s Number (Re)
It gives a measure of the ratio of inertial and viscous forces in fluid flow. It is often used to
determine if the flow is either laminar or turbulent:
• In laminar flow, viscous forces dominate. The flow paths are smooth, streamline and constant.
• In turbulent flow, inertial forces dominate. The flow regime is unstable, generating eddies and
vortices.
The Kind of flow depends on value of Re
• If Re < 2000 the flow is Laminar
• If Re > 4000 the flow is turbulent
• If 2000 < Re < 4000 it is called transition flow.

4. Prandtl Number (Pr)
• The Prandtl number, Pr, is the ratio of kinematic viscosity to the thermal diffusivity.
• It is used in many calculations involving heat transfer in flowing fluids.
• it gives a measure of the relative thickness of the thermal and momentum boundary
layers.
Where,
Cp = Fluid specific heat capacity
μ = Dynamic viscosity
k = Thermal conductivity

5. Nusselt Number (Nu)
• The Nusselt Number, Nu, is the ratio of convective to conductive heat transfer in a fluid
over a given length, l:
• For heat transfer in pipes, the characteristic length is the pipe diameter.
• At a Nusselt number of around one means that convection and conduction are about
equal.
Where,
h = Heat transfer coefficient
l = Characteristic length
k = Thermal conductivity

6. Sherwood Number (Sh)
The Sherwood Number, Sh, is a measure of the ratio of convective and diffusive mass
transfer in a fluid. It is analogous to the Nusselt Number in heat transfer:
Where,
hD = Mass transfer coefficient
l = Characteristic length
k = Molecular diffusivity

7. Froude Number (Fr)
• The Froude Number, Fr, is a measure of the ratio of the inertial and gravitational forces.
• It is often used to analyse fluid flow problems where there is a free surface. For example, in
agitated vessels, Fr governs the formation of free surface vortices.
Where,
v = Velocity
l = Characteristic length
g = Acceleration due to gravity

8. Schmidt Number (Sc)
• Schmidt Number, Sc, is the ratio of kinematic viscosity to the diffusivity. It can be expressed
as:
• It characterises mass transfer in a flowing fluid
Where,
D = Diffusivity
μ = Dynamic viscosity
p = Fluid density

9. Biot Number (Bi)
• It the ratio of the heat transfer resistances inside of and at the surface of a body.
• The Biot number (Bi) is used in heat transfer calculations.
Where,
h = Heat transfer coefficient
l = Characteristic length
kb = Thermal conductivity of the body

10. Fourier Number (Fo)
• Ratio of rate of heat conduction to the rate of heat storage.
• Used along with Biot number to solve transient state heat transfer problems.
• For mass transfer by diffusion, Fourier number for MT is used.
Where,
α = Thermal Diffusivity
t = Characteristic time
L = Length through which conduction occurs
D = Diffusivity

11. Lewis Number (Le)
• Ratio of thermal diffusivity to mass diffusivity.
• Fluid flow with simultaneous Heat & mass transfer by convection.
• It is also ratio of Schmidt number to Prandtl number.

12. Mach Number (Ma)
• The Mach Number, Ma, is the ratio of the fluid velocity to the velocity of sound in that
medium.
• In Chemical Engineering, the Mach Number is commonly used in calculations involving
high velocity gas flow.
Where,
u = Velocity of fluid
a = Speed of sound in fluid medium