2. Table of Contents:
1
• Dimensionless Number
• Uses of dimensionless number
2
• Reynold Number
• Significance of Reynold Number
3
• Grashof Number
• Significance of Grashof number
3. Dimensionless Number:
A dimensionless number is a mathematical ratio or parameter that is
used to describe a physical system without any units of measurement.
Why we use dimensionless number?
Reduce the number of variables that describe a system.
Reducing the amount of experimental data required to make
correlations of physical phenomena to scalable systems.
4. Types of Dimensionless Number:
Reynold Number
Nusselt Number
Lewis Number
Grashof number
Prandtl number
Rayleigh Number
Power Number
Fourier Number
5. 1.Reynolds Number
It is named after Osborne Reynolds, a British physicist who
studied fluid dynamics in the 1883s.
Reynolds Number are obtained by dividing a inertial forces by a
viscous forces.
At low Reynolds numbers, flows tend to be dominated by
laminar flow, while at high Reynolds numbers, flows tend to be
turbulent.
Reynolds Number tells us either the fluid flow is laminar or
turbulent.
8. Reynolds Experiments
Reynolds used a glass tube, filled with
a dye solution, to simulate the flow of
fluid through a pipe. The tube had a
diameter of 1.8 cm and was more than
5 meters long.
Reynolds observed that as the flow
rate increased, the flow pattern
changed from smooth and predictable
(laminar flow) to irregular (turbulent
flow).
Reynolds studied the condition under
which one type of flow changes into
the other type of flow.
9. Significance of Reynolds Number
The Reynolds number tells us whether the flow is
laminar as well as turbulent.
Analysis of the flow of a fluid in a cross-sectional
area.
It helps determine the velocity at which the flow
transits from laminar to turbulent.
The Reynolds Number is applied in determining the
behaviours of different liquids.
10. 2.Grashof Number:
The Grashof number is a dimensionless number used in fluid mechanics to describe the
relationship between buoyancy and viscosity in a fluid.
Definition:
Grashof number is defined as the ratio of the product of inertia force and buoyant force and
the square of viscous force present in the fluid.
It frequently arises in the study of situations involving natural convection and is analogous to
the Reynolds number.
The transition to turbulent flow occurs in the range 108 < GrL < 109 for natural
convection from vertical flat plates.
At higher Grashof numbers, the boundary layer is turbulent.
At lower Grashof numbers, the boundary layer is laminar, that is, in the range 103 < GrL < 106.
11. Buoyancy Force :
Buoyancy force is a force that acts on an object when it is
immersed in a fluid.
The buoyancy force is exerted in the opposite direction to
the force of gravity and is equal to the weight of the fluid
displaced by the object.
This upward force is also called Upthrust.
Due to the buoyant force, a body submerged partially or
fully in a fluid appears to lose its weight, i.e. appears to be
lighter.
12.
13. Mathematical Expression of Grashof Number:
Gr =
𝜌2𝑔𝐿3𝛽Δ𝑇
𝑣2
𝜌=Density of fluid
𝛽= Coefficient of expansion
ΔT= Temperature difference
v=Dynamic viscosity
a) where β is the coefficient of volume
expansion and β ≈ 3α is the change
in volume due to thermal
expansion.
b) When the thermal expansion is
restricted, thermal stress is
produced.
c) The coefficient of thermal expansion
formula explains how an object's size
increases as the temperature
changes.
14. Significance of Grashofs number in heat transfer:
The physical significance of grashof number are
as follows:-
2) This dimensionless number is used in the
analysis of free convection heat transfer.
3) The grashof number has the same importance
in free convection as the Reynolds number has
in forced convection.
4) Grashof number helps to find the type of flow
(laminar, transition, turbulent) in free
convection.
