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A flow is divided into two categories, which are known as laminar flow and turbulent flow. Whenever we design a fluid system, these two flows are considered. The amount of the energy of a system depends on the amount of friction. And we know that if friction is there, then heat loss will take place. Then this plays a major role, when the fluid flows.
Laminar flow – When a fluid flows layer by layer, then this type of flow is called laminar flow. Molecules in one layer do not mix with those in the other layer of the fluid. The flow is also called the streamline flow or viscous flow. In the flow, viscosity is significant.
Turbulent flow – When a layer of a fluid gets mixed with the other layer of the fluid, then this type of the flow is known as turbulent flow. In the flow, a particle of the fluid moves in an irregular manner.
Laminar flow
When there is no intermixing of the layer, then this type of flow is known as laminar flow. In the region, the velocity is varying with respect to the length that is known as the velocity gradient. When the particle enters into the system, the velocity of the particle is zero because of no slipping condition. And the molecule will resist the motion of the adjacent particle, and this adjacent particle will also resist the motion of its adjacent particle, and so on.
Reynold’s number for laminar flow
The Reynold’s number (Re) is a unitless number. By the Reynolds number, flow can be determined to be laminar or turbulent. The Reynolds number for the laminar flow is given as
Re=ρνl/ μ =ν l/v
Where
ν is kinematic viscosity (m2s-1)
ρ is the density of the fluid (kgm-3)
μ is the dynamic viscosity (kgm-1s-1)
v is the velocity of the fluid (ms-1)
l is the characteristic length (m)
Laminar flow through pipe
The characteristic length for the laminar flow through pipe is the diameter (D) of the pipe. Then the formula is given as
Re=ρνD/ μ=vD/ν
The flow is treated as a laminar flow if the Reynolds number is less than 2000. And the flow is treated as turbulent if the Reynolds number is greater than 2000.
If the velocity of the fluid rises, then the Reynolds number rises, and if the diameter of the pipe rises, then the Reynolds number rises, and flow tends to be turbulent.
As the dynamic viscosity of the fluid declines, the Reynolds number rises, and flow tends to be turbulent.
For example – Find the Reynolds number when the velocity of the fluid is 0.5 Ns/m2, velocity of fluid is 3 m/s, density of the fluid is 800 kg/m3, and diameter of the pipe is 20 mm. And if the velocity and viscosity become 60 m/s and 0.4 Ns/m2 respectively.
Solution:
Given
=800 (kgm-3)
=0.5 (kgm-1s-1)
v=3 (ms-1)
D=20 (mm)=0.02 (m)
We know that the Reynolds number if given by
Re=ρνD/ μ
Re=800×3×0.02 / 0.5
Re=96
The Reynolds number is less than 2000, then the flow is laminar.
If =0.4 (kgm-1s-1) and v=60 (ms-1), then the Reynolds number will be
Re=800600.020.4
Re=2400
If the velocity and viscosity become 60 m/s and 0.4 Ns/m2, then the flow becomes turbulent.
Laminar flow over a flat plate
The characteristic length for the laminar flow over a flat plate is the length (L) along the flow. Then the formula is given as
Re=ρνL/ μ =νL/v
If the Reynolds number is less than 5105, then the flow is treated as laminar flow. And if the Reynolds number is greater than 5105, then flow is treated as turbulent.
If the velocity of the fluid rises, then Reynolds number increases and the flow tends to be turbulent; if the length of the flat plate increases, then Reynolds number rises and the flow tends to be turbulent.
As the dynamic viscosity of the fluid declines, then Reynolds number rises and the flows tend to be turbulent.
Example – Find the critical length of the plate when the flow is laminar, if the kinematic viscosity is 5×10-4 m2/s, and the velocity of the fluid is 15 m/s.
Solution:
Given
Re = 5×105
v= 5×10-4 m2/s
ν=15 m/s
Then we know that the critical length of the plate is given as
L=νRe/v
L=5×10-4×5×105 / 15
L=16.67 m
The length of the plate, where laminar flow is present, is 16.67 m.
Conclusion
The Reynolds number helps us determine whether the flow is laminar or turbulent. By the Reynolds number, we can have the critical length of the flat plate before which the flow is laminar and after that length, the flow becomes turbulent.
