Flow Conversion Device for obtaining Laminar Flow
using Reynolds Number Theory
Nikhil Ram Mittal, Panshul Raghav, Pallavi Arya, Pranav Chadha
UG students [Mechanical], Dept. of Mechanical Engineering, JSS Academy of Technical Education, Noida,
Uttar Pradesh, India
Abstract: This device is a flow conversion device which converts fluid flow into laminar
flow. Basically, this device works on the principle of breaking the fluid layers so that the
diameter of flow remains under the limit of boundary layer. This is achieved by using large
number of capillaries or small diameter tubes. A laminar flow is characterised by the parallel
flow of fluid layers. This parallel flow between layers can be achieved by reducing the
disruption between layers. To achieve parallel flowing layers the viscous forces should be
high enough to hold layers intact. But in case of fluids which have low viscosity, parallel
flowing layers can be obtained by reducing the flow velocity or by reducing the area of flow
so that fluid flows within the limits of boundary layer. Mathematically, a laminar flow has a
Reynolds number less than 2000. To achieve laminar flow at high velocities, the diameter of
flow has to be reduced.
Introduction: As characterised by uniform velocity profile, this device converts turbulent
flow to laminar by dividing non-uniform flow velocity into uniform flow velocity, reducing
the turbulence of fluid. Thus, allowing laminar flow at higher flow rates. Laminar flow has
many essential uses be it industrial or for decoration in water fountains. Laminar can also be
used in fire brigade pumping system. Laminar flow does not draw air in the flow thus gives a
crystal clear tube like flow which even produces total internal reflection when a ray of light is
introduced at the total internal reflection angle.
To obtain a perfect streamlined flow, this device is installed with 6 circular perforated plates.
The plates are equidistant and aligned in such a manner that input flow is streamlined in the
form of thin parallel layers of small diameter and uniform flow velocity profile. The fluid
needs to be particle free to avoid turbulence, for this purpose we have installed a wire mesh
as first layer followed by a water filter at the inlet.
Laminar flow device: This device has a casing equipped with filters to avoid foreign dust
particles, a set of 6 perforated circular plates to generate a uniform flow velocity profile,
capillaries or small diameter cylindrical tubes which maintain the velocity profile uniformly.
The device includes an inlet port and outlet port, discharge nozzle body having a discharge
outlet passage. The discharge outlet passage has a gradually reducing flow area to further
reduce turbulence.
Working principle: The device works on the principle of breaking the fluid layers so that the
diameter of flow remains under the limit of boundary layer. This is achieved by using large
number of capillaries or small diameter tubes. A laminar flow is characterized by the parallel
flow of fluid layers. This parallel flow between layers is achieved by reducing the disruption
between layers.
CALCULATIONS FOR THE LAMINAR FLOW DEVICE:
TERMS USED:
1. LAMINAR FLOW:- The flow of a viscous fluid in which particles of the fluid moves
in parallel layers, each of which has a constant velocity but is in motion relative to its
neighboring layers.
2. TURBULENT FLOW:-The flow of a fluid past an object such that the velocity at any
fixed point in the fluid varies irregularly.
REYNOLDS NUMBER:-It is the ratio of inertial force to viscous force.
Re=(inertial force/viscous force)
FORMULAE USED:
1. AREA (A) = πr2 = πd2/4
2. BERNOUILLI’s EQUATION:
𝑃+
Where,
𝜌𝑉 2
+ 𝜌𝑔𝐻 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
2
P=pressure
H=elevation
ρ=density
g=gravitational acceleration
V=velocity
3. Q(discharge) = V*A
Q=discharge
V=velocity
A=area
4. Reynolds Number (Re) = ρVDH / μ
V= mean velocity of the fluid (SI unit : m/s)
Ρ= density of the fluid (kg/m3)
DH= hydraulic diameter of the pipe (m)
μ= dynamic viscosity of the fluid (Pa)
Table 1: For Reynolds number with diameter = 0.005m
S.
Inlet
Outlet
No.
Discharge
Velocity
Working
Diameter
Pressure
Outlet
(kg/m)
(m)
Curvature
Reynolds
number
Discharge Velocity
(Q1)(m3/s) V1 (m/s)
Q2
V2
1.
2.6842
0.5731
1.1917
0.4094
640028
0.005
Concave
2047.12
2.
2.8496
0.6084
2.0355
0.4346
679070
0.005
Convex
2173.17
3.
2.9268
0.6249
2.0908
0.4464
697405
0.005
Concave
2232.21
4.
3.0083
0.6423
2.1489
0.4588
716235
0.005
Convex
2294.32
Curvature
Reynolds
Table 2: For Reynolds no. with diameter = 0.01m
S.
Inlet
Outlet
No.
Discharge
Velocity
(Q1)(m3/s) V1 (m/s)
Discharge Velocity
Q2
V2
Working
Diameter
Pressure
Outlet
(kg/m)
(m)
number
1.
5.5418
0.2958
3.9587
0.2113
1102608
0.01
Concave
2113.06
2.
5.6748
0.3029
4.0542
0.2164
1129180
0.01
Convex
2164.81
3.
5.9829
0.3193
4.2734
0.2281
1190230
0.01
Concave
2281.63
4.
6.0720
0.3241
4.3371
0.2315
1207971
0.01
Convex
2315.42
Sample calculations:
Diameter of the outlet (d) = 0.05m
Cross sectional area of flow = πd2/4 = 1.96*10-5
Discharge at outlet (Q2) = 1.7917 m3/s
Velocity of flow (V2) = Q2/A = 1.7917/4.37 = 0.4094
Discharge at inlet (Q1) = 2.6842 m3/s
Velocity of flow (V1) = Q1/A = 26842/4.37 = 0.6142
By Bernoulli’s equation:
𝑃1 +
𝑉12
𝑉22
+ ℎ1 = 𝑃2 +
+ ℎ𝑒𝑎𝑑 𝑙𝑜𝑠𝑠
2𝑔
2𝑔
Putting, P2 = 1 atm and head loss = 0.013
We get, P1 = 640028 N/m2
Re =
𝑉2 𝐷
𝜈
So, Re =
, where ν = 10-6
0.4094∗0.005
10−6
= 2047.12
CONCLUSION:
Laminar flow conversion device is suitable for obtaining laminar flow. Based on the
calculations the Reynolds number obtained is suitable for the device to work as a laminar
flow device. The device can easily be used for converting the flow diameter=0.005m and
diameter=0.01m with velocities from 2m/s and 5m/s.
FUTURE SCOPE:
The nozzle, the flow obtained is turbulence free. In future the device can be used for testing
of air vessels, firefighting jets, fountains and water displays.
REFERENCES:
1. Rogers, D.F. (1992). Laminar flow analysis. Cambridge U. Press. ISBN 0-52141152-1.
2. M. D. Deshpande and R. N. Vaishnav. Submerged laminar jet impingement on a
plane. J. Fluid Mech., 114:213–236, 1982.
3. Christopher J. Bloch, Method and apparatus for water jet improved nozzle.
Publication number -‘US 5169065 A’
4. Mack LM.1984.”Boundary – layer linear stability theory”. AGARD Rep No. 709.
5. E. John Finnemore, Joseph Franzini "Fluid Mechanics with Engineering
Applications",McGraw-Hill,2002