Dimenssionless analysis

             Dimensionless analysis     

  1- Mach number

Mach number is used in momentum transfer in general and near/ultra sonic flow and throttling calculations in particular. It is normally defined in the following form :

Where:
V	=	Velocity
V_sound	=	Velocity of sound in fluid

.

2- Reynolds number

Reynolds number is proportional to { (inertial force) / (viscous force) } and is used in momentum, heat, and mass transfer to account for dynamic similarity. It is normally defined in one of the following forms

or

Where:
D	=	Characteristic length
G	=	Mass velocity
mu	=	Viscosity
rho	=	Density
V	=	Velocity

3-Froude Number

Froude number is proportional to { (inertial force) / (gravitational force) } and is used in momentum transfer in general and open channel flow and wave and surface behavior calculations in particular. It is normally defined in one of the following forms

or

Where:
a	=	Acceleration
g	=	Gravitational acceleration
L	=	Characteristic length
V	=	Velocity

4-Euler Number

Euler number is proportional to { (friction head) * (velocity head) } and is used in momentum transfer in general and fluid friction in conduits calculations in particular. It is equivalent to (N/2) where N is the number of velocity heads. It is normally defined in one of the following forms :

or

Where:
delta-P	=	Pressure drop
gc	=	Dimensional constant
G	=	Mass velocity
rho	=	Density
V	=	Velocity

5-Weber Number

Weber number is proportional to { (inertial force) / (surface tension force) } and is used in momentum transfer in general and bubble/droplet formation and breakage of liquid jets calculations in particular. It is normally defined in one of the following forms :

or

Where:
gc	=	Dimensional constant
G	=	Mass velocity
D	=	Characteristic length
rho	=	Density
sigma	=	Surface tension
V	=	Velocity

6-BIOT NUMBER

Biot number is proportional to { (thermal internal resistance) / (surface film resistance) } and is used in heat transfer in general and unsteady state calculations in particular. It is normally defined in the following form:

Where:
delta-x	=	Mid-plane distance
h_T	=	Heat transfer coefficient
k	=	Thermal Conductivity

7-Grätz Number

Grätz number is proportional to { (thermal capacity) / (convective heat transfer) } and is used in heat transfer in general and convection in laminar flow calculations in particular. It is equivalent to {(L/d) / (Re.Pr)} or {(L/d) / Pe}. It is normally defined in one of the following forms

or

Where:
alpha	=	Thermal diffusivity
Cp	=	Heat capacity
d	=	Diameter
G	=	Mass velocity
k	=	Thermal Conductivity
L	=	Length
m	=	Mass flowrate
rho	=	Density
V	=	Velocity

8-Power Number

Power number is proportional to { (drag force) / (inertial force) } and is used in momentum transfer in general and power consumption by agitators, fans, pumps, etc. calculations in particular. It is normally defined in the following form:

Where:
D	=	Characteristic length
gc	=	Dimensional constant
N	=	Rate of rotation
P	=	Power
rho	=	Density

9-Fourier Number

Fourier number is used in heat transfer in general and unsteady state heat transfer calculations in particular. It is normally defined in one of the following forms:

or

Where:
alpha	=	Thermal diffusivity
Cp	=	Heat capacity
k	=	Thermal Conductivity
L	=	Characteristic length
rho	=	Density
t	=	Time

Drag Coefficient

Drag coefficient is proportional to { (gravitational force) / (inertial force) } and is used in momentum transfer in general and free settling velocities and resistance to flow calculations in particular. It is normally defined in the following form:

 

Where:
g	=	Gravitational acceleration
L	=	Characteristic dimension of object
rho	=	Density of object
rho_f	=	Density of surrounding fluid
V	=	Velocity

Pressure Coefficient

The pressure coefficient is is the ratio of pressure forces to inertial forces and can be expressed as
C_p = dP/(ρ v² /2)
    = dh (ρ v² /2 g)          (1)
where
C_p = pressure coefficient
dp = pressure difference (N)
ρ = fluid density (kg/m³)
v = flow velocity (m/s)
dh = head (m)
g = acceleration of gravity (= 9.81 m/s²)
The pressure coefficient is important in most fluid flow applications.

Pressure Coefficient Comparison Between Calculation (lines) and Experiment Around an Airfoil
Lift coefficient

The lift coefficient ( or ) is a dimensionless coefficient that relates the lift generated by a lifting body, the dynamic pressure of the fluid flow around the body, and a reference area associated with the body. A lifting body is a foil or a complete foil-bearing body such as a fixed-wing aircraft.
Lift coefficient is also used to refer to the dynamic lift characteristics of a two-dimensional foil section, whereby the reference area is taken as the foil chord.^[1][2]
Lift coefficient may be described as the ratio of lift pressure to dynamic pressure where lift pressure is the ratio of lift to reference area.
Lift coefficient may be used to relate the total lift generated by a foil-equipped craft to the total area of the foil. In this application the lift coefficient is called the aircraft or planform lift coefficient
Watercraft and automobiles equipped with fixed foils can also be assigned a lift coefficient.
The lift coefficient is equal to:

where

• is the lift force,
• is fluid density,
• is true airspeed,
• is dynamic pressure, and
• is planform area.