Abstract: The experiment concentrates on various methods of measuring flow rates using a Venturi meter, Orifice meter, Turbine meter, Rota meter and actual flow rate using difference of weight of a tank. The main objectives of this lab are to study flow pattern analysis, Flow velocity profile measurement with Pitot tube. System Uncertainty Analysis of Flow rate (Orifice Plate). A velocity profile of air jet will be sketched using measurements from the Pitot tube. Furthermore, a velocity profile and turbulent flow across a cylinder will be studied using a laser Doppler Velocimetry and a vortices counter experiment. With the help of results, orifice meter and turbine meter will be calibrated using plots.
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Abstract:
The experiment concentrates on various methods of measuring flow rates using a Venturi meter,
Orifice meter, Turbine meter, Rota meter and actual flow rate using difference of weight of a
tank. The main objectives of this lab are to study flow pattern analysis, Flow velocity profile
measurement with Pitot tube. System Uncertainty Analysis of Flow rate (Orifice Plate). A
velocity profile of air jet will be sketched using measurements from the Pitot tube. Furthermore,
a velocity profile and turbulent flow across a cylinder will be studied using a laser Doppler
Velocimetry and a vortices counter experiment. With the help of results, orifice meter and
turbine meter will be calibrated using plots.
1
Table of Content:
Topic Page No.
Introduction 2
Theoretical Principles 3
Experimental System 9
Results and Discussions with Sample calculations 12
Conclusions 27
References 28
Nomenclature 29
Appendix
Data Sets 30
2
Introduction:
The experiments performed in this Lab gives an overview of flow measurement. The
flow measurement was calculated using different flow measuring devices such as a Venturi
meter, Orifice plate, Turbine and Rota meter. An air jet velocity was calculated and its profile
was studied using a Pitot tube. A velocity profile of a turbulent and laminar flow was studied
using a Laser Doppler Velociemetry.
The flow measurement using a Venturi, Orifice and a Turbine is an important
method. The flow measurement using a venture is the most precise method. This is because the
pipe loss due to turbulent flow is minimum in the Venturi. However, it is the most expensive
method of measuring flow rate because it is very expensive to manufacture a venture (its inner
surface needs a certain quality of surface roughness/ smoothness).
Moreover, a flow measurement using an orifice is relatively cheap method but, the
loss due to turbulent flow and disturbances in flow causes error in measuring a flow rate. A
calibration is required to measure the exact value of flow through the orifice. This technique is
important to use where the accuracy of flow measurement is not an important factor. This
method gives an approximate estimate of the flow rate.
Furthermore, a flow measurement using a turbine is another important flow
measurement method. In this method a turbine rotates with rotational speed ω, as the fluid flows
into the turbine. It can be shown that the rotational speed is proportional to the flow rate. The
relation between rotational speed and flow rate can be calibrated to find the flow rate for
consecutive flow rates.
A pitot tube is a common method of measuring an air jet velocity. It is often used to
measure the velocity of an air plane. This method takes into account the use of Bernoulli’s
equation and compares two points. One at a point far away from the pitot tube and other at the
position of the pitot tube (Stagnation pressure).
A flow past a cylinder can be studied using a water tunnel. A pattern of turbulence/
Vortex can be studied by injecting ink into the tunnel. This will give a good estimate of the flow
visualization. A laser Doppler Velocimetry can also be used to determine the velocity profile
across a cylinder.
In general, all the methods of flow measurements have different application. The
design (quality) and usage of flow measuring device depends on the required accuracy of the
application.
3
Theoretical Principles:
The Flow measurement can be calculated using different methods as mentioned
previously. The theoretical principles used to derive equation of flow rate are mentioned in this
section. Reynolds’s number and Bernoulli’s Equation are important criterion to study the flow
rate. They are described as follows:
Bernoulli’s Equation:
Bernoulli’s equation states that he sum of pressure, Kinetic energy and potential energy across
any two arbitrary points across a stream line is constant. This is shown in equation form as
follows:
𝑃1 + 𝜌𝑣1
2
2+ 𝑔𝑧1 = 𝑃2 +
𝜌𝑣22
2+ 𝑔𝑧2
Often, in many cases the potential energy change is negligible in flow measurement using these
devices. Thus, the equation reduces to the following:
𝑃1 + 𝜌𝑣1
2
2= 𝑃2 +
𝜌𝑣22
2
Reynolds’s Number:
The Reynolds’s number is described as the ratio of inertial force to the frictional/ viscous force.
This is defined in equation form as follows;
𝑅𝑒 = 𝐼𝑛𝑒𝑟𝑡𝑖𝑎𝑙 𝐹𝑜𝑟𝑐𝑒
𝐹𝑟𝑖𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝐹𝑜𝑟𝑐𝑒=
𝜌𝑣𝐷
𝜇=
𝑣𝐷
𝜗
Where
µ = dynamic viscosity
𝜗 = the kinematic viscosity
D = Diameter of pipe
v = velocity of the fluid
When,
𝑅𝑒 ≫ 1, inertial force is dominant
𝑅𝑒 << 1, viscous force is dominant
4
Venturi Meter:
A schematic of a venturi meter is shown as follows:
1
From the schematic, it is apparent that the change in potential energy across the flow is almost
negligible (0). Thus, the modified version of Bernoulli’s equation can be applied to ventuari as
follows:
𝑃1 + 𝜌𝑣1
2
2= 𝑃2 +
𝜌𝑣22
2
From equation of continuity, we equate the flow rate at the point in stream line at point 1 and at
that of point 2. Then, the Bernoulli’s equation can be manipulated using these two equations.
Thus, the equation of continuity becomes:
A1v1 = A2v2
𝑣1 = 𝐴2
𝐴1𝑣2
𝑃1 + 𝜌(
𝐴2
𝐴1𝑣2)2
2= 𝑃2 +
𝜌𝑣22
2
𝑣2 = √2(𝑃1 − 𝑃2)
𝜌(1 − (𝐴2
𝐴1)2)
Thus, Flow rate becomes:𝑄2 = 𝐴2𝑣2 = 𝐴2√2(𝑃1−𝑃2)
𝜌(1−(𝐴2𝐴1
)2)
1 www.ustudy.in
5
Orifice Meter:
The schematic of an Orifice meter is shown as follows:
2
From the schematic, it is apparent that the change in potential energy across the flow is almost
negligible (0). Thus, the modified version of Bernoulli’s equation can be applied to Orifice
similarly as in venturi case. From equation of continuity, we equate the flow rate at the point in
stream line at point 1 and at that of point 2. Then, the Bernoulli’s equation can be manipulated
using these two equations. The equation obtained for an orifice is similar to that of the venturi
meter. The only difference is that the equation of flow rate for orifice is calibrated by a factor c.
𝑣2 = 𝑐 √2(𝑃1 − 𝑃2)
𝜌(1 − (𝐴2
𝐴1)2)
Thus, Flow rate becomes:𝑄2 = 𝑐𝐴2√2(𝑃1−𝑃2)
𝜌(1−(𝐴2𝐴1
)2)
Where, 𝑐 = 𝑄𝐴𝑐𝑡𝑢𝑎𝑙
𝑄𝐼𝑑𝑒𝑎𝑙
The values of c are summarized in the following table:
Meter c
Venturi meter 0.95<c<0.98 ~1
Orifice meter 0.6<c<0.7
A plot of flow rate and Reynolds number can be made to find calibration.
2 www.engineeringexcelspreadsheets.com
6
Turbine Meter:
A turbine rotates as the fluid flows into the turbine. Ideally, the rotational speed of the turbine is
proportional to that of the flow rate through the turbine. The schematic of a turbine meter is
shown as follows:
The Roto meter frequency can be measured and a relation between the flow rate and rotational
speed can be measured.
𝜔 ∝ 𝑄
The loss due to friction is calculated as shown: 𝑄 = −2𝜋
16
𝑎4
𝜇
𝑑𝑃
𝑑𝑥
Actual flow rate measurement:
An actual flow rate measurement in the experiment can be done using a weight measurement.
The weight of fluid entering a tank can be measured for a given time. The difference between
initial and final weight can be calculated. Tis difference can be divided by time. This will yield
the actual flow rate.The equation for this measurement is as follows:
𝑄 = 𝑊2 − 𝑊1
𝜌𝑡
Where
W1 = initial mass
W2 = final mass
t = time taken during mass change
𝜌 = density of the fluid
Thus, actual flow rate can be calculated using this method.
7
Pitot Tube:
A Pitot tube again works on the principle of Bernoulli’s equation. The schematic of a Pitot tube
is shown as follows:
The equation of velocity using a Pitot tube can be derived with the help of modified Bernoulli’s
equation. In this case, the velocity at point 1 is zero because of stagnation pressure. Velocity at
point 2 is assumed to be velocity of the air jet.
𝑃0 + 𝜌(0)2
2= 𝑃1 +
𝜌𝑈2
2
𝑈 = √2(𝑃0 − 𝑃1
𝜌= √
2𝜌𝑙ℎ𝑔
𝜌
𝑈 = √4𝜌𝑙𝑔ℎ
𝜌
Where,
U = Velocity of Air Jet
h = difference in height in manometer
𝜌𝑙 = density of liquid
𝜌 = density of air
Note: A factor of 4 is introduced in the equation. This is because the experiment was set up in
such a way that the height of the manometer column was supposed to be multiplied by 2.
8
Laser Doppler Velocimetry:
Laser Doppler Velocimetry (LDV) is also known as Laser Doppler Anemometry (LDA). Flow
past a cylinder can be studied using this method. The observations on stream lines, Reynolds
number computation and vortex shedding can be studied using a flow tunnel.
A velocity along a vertical line can be measured using LDV.
Strouhal number can be calculated as:
𝑠𝑡 = 𝑓𝑑
𝑈~0.2
9
Experimental System:
The instruments and equipment used in this experiment are shown as follows: