This document defines and provides formulas for several dimensionless numbers that are used in engineering calculations involving fluid flow and heat transfer. It discusses the Reynolds number (Re), Prandtl number (Pr), Nusselt number (Nu), Grashof number, Biot number (Bi), Fourier number (Fo), Lewis number (Le), and Mach number (Ma). For each number, it provides the definition and explains what physical phenomenon or calculation the number relates to or can be used for.

1. DIMENSIONLESS
NUMBER

2. GROUP
MEMBERS:
MUHAMMAD FEROZ
2017-CH-720
IHTASHAM MEHMOOD
2017-CH-719
ADEEL AKRAM
2017-CH-718
MUHAMMAD AKMAL
2017-CH-722

3. DIMENSIONAL ANALYSIS:
• Dimensional analysis is a topic that deal with dimension.
• There are two types of dimensions.
• Fundamental dimension
• Derived dimension
• Dimensional analysis is use wo check the correction of given formula.
• Two terms are add when the dimensions of both quantities is same.

4. DIMENSIONAL ANALYSIS

5. 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.

6. 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 flowingfluids.
• 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

7. 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 pipediameter.
• At a Nusselt number of around one means that convection and conduction areabout
equal.
Where,
h = Heat transfer coefficient
l = Characteristic length
k = Thermal conductivity

8. Grashof Number:
• The Grashof number is used to determine the heat
transfer coefficient under free convection conditions.
It is basically a ratio between the buoyancy forces and
viscous forces.

9. Biot Number (Bi)
• It the ratio of the heat transfer resistances inside of and at the
surface of abody.
• 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 isused.
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 inthat
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

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