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Flowmeter Discharge Coefficient Estimation
Elizabeth Bankston Team 1
Abstract
An Edibon FME18 Flow Meter demonstration system was used to obtain experimental
values for this experiment. The data obtained was used to calculate energy loss, volumetric flow
rate, the square root of pressure drop, and estimate the discharge coefficient for a venturi
flowmeter, orifice flowmeter and a rotameter. The energy loss for a rotameter remained constant
at around 0.0023 kJ/kg, no matter what the flow rate was. The venturi had a similar theme at
around 0.0001 kJ/kg. The orifice meter lost more energy as the flow rate increased, with the
maximum energy lost being 0.001 kJ/kg. For a rotameter, flow rate had no effect on the square
root of pressure drop; while increasing flow rate increased the square root of pressure drop for
both the venturi meter and the orifice meter. The estimated discharge coefficient for the venturi
meter and orifice meter were, respectively, 0.656 and 0.680. For the venturi meter, the estimated
discharge coefficient was off by 0.324, which indicated that the systemโs venturi meter was
operating at a lower efficiency than it should have. The large error could also be due to
technical errors or human errors. For the orifice meter, the estimated discharge coefficient was
off by 0.07, which indicated that the systemโs orifice meter was operating more efficiently than
was expected.
Introduction
In any piping system, a fluid will travel through an array of pipe fittings, valves, and
elbows. When a fluid flows through such components, a pressure drop occurs due to the
frictional effects caused by changing the pathway of the fluid. Obstruction flowmeters are
devices used to measure fluid flow rate, by obstructing the flow and using a differential pressure
transducer to record the pressure before and after the obstruction (Cengel & Cimbala, 2014).
Orifice, venturi and nozzle flowmeters are all common types of obstruction flowmeters.
An orifice meter is one of the most common flow meters used (Wilhelm et al., 2004) and
one of the cheapest obstruction flowmeters (Cengel & Cimbala, 2014). The orifice meter is a
plate with a hole, significantly smaller than the inside pipe diameter, which is then placed inside
a pipe (Wilhelm et al., 2004). One of the negatives to using an orifice meter is that it causes a
sudden change in flow area, which leads to significant head loss or permanent pressure loss
(Cengel & Cimbala, 2014). Figure 1 shows the typical orifice flow pattern where P 1
- P
2
indicates
significant head loss and P 1
- P
3
indicates the permanent head loss.
Figure 1: Pressure drop pattern caused by an orifice meter (Cengel & Cimbala, 2010).
A rotameter consists of a vertical tapered conical tube with a float inside that is free to
move. The float rises and falls as the fluid flows through the tapered tube, so that the float
weight, drag force, and buoyancy force balance each other and the net force acting on the float is
zero (Cengel & Cimbala, 2014). The flow rate is then determined by comparing the height of the
float to the scale on the side of the tube. Figure 2 shows how a rotameter balances out the forces
so that the net force equals zero and the scale to determine the flow rate. It is also of note that
rotameters have significantly more energy recovery than orifices, due to the more gradual
obstruction in a rotameter than in an orifice (Ramirez et al.). Although rotameters have more
energy recovery than orifices do, rotameters typically have an accuracy of + 5 percent; which
means that rotameters are not appropriate for applications that require precision measurements
(Cengel & Cimbala, 2014).
Figure 2: Typical operating system of a Rotameter (โFlow: The Basics of Rotametersโ,
The manometer heights were converted to meters before being used in equation (1),
which calculates pressure at the corresponding manometer location. After calculating the
pressure, energy loss was calculated for each flow meter in the system using equation (2); which
was derived from the energy equation when W turbine
and W pump
equal zero, V 1
and V 2
are equal,
and z 1
and z 2
are equal (equation (3)).
๐ฟ๐๐ ๐
โ๐
๐
๐๐ฝ
๐๐
๐ 1
๐
๐ 1
2
2
1
๐๐ข๐๐
๐ 2
๐
๐ 2
2
2
๐ก๐ข๐๐๐๐๐
๐๐๐ ๐
Where:
P = Pressure of the fluid at a certain point (Pa),
ฯ = density of water (kg/m
3
g = gravitational acceleration (m/s
2
h = manometer height (m)
E
Loss
= energy loss (kJ/kg),
โP = pressure drop and in this case permanent pressure loss (kPa),
ฮฑ = kinetic energy correction factor (unit less),
V = fluid velocity (m/s),
z = elevation (m),
W
turbine
= power required to run a turbine,
W
pump
= power required to run a pump.
It is important to take note of two things: 1) pressure should be converted to kilopascals
(kPa), so that conversion factor (i) can be used and result in kilojoules per kilogram (kJ/kg), and
- that the pressure drop (โP) is different for a venturi meter, an orifice meter and a rotameter.
Pressure drop for a venturi meter, an orifice meter, and a rotameter, when calculating energy
loss, can be found in table 1.
๐๐ฝ
๐๐
3
(i)
Table 1: Pressure drops used for calculating energy loss.
Venturi Orifice Rotameter
โP P
1
โ P
3
P
6
โ P
8
P
4
โ P
5
Energy losses for all three flowmeters was then plotted against the calculated flow rate.
Flow rate was calculated using equation (3) and the square root of pressure drop was calculated
using equation (4).
๐
๐ก
1 ๐
3
1000 ๐ฟ
๐
3
๐
๐๐๐ก๐๐
Where:
Q = volumetric flow rate (m
3
/s),
V = volume (L),
t = time (s),
Q
meter
= volumetric flow rate at the flow meter desired, also called square root of
pressure drop.
It is also important to note that the pressure drop for calculating the square root of
pressure drop is different than the pressure drop used to calculate energy loss for the venturi and
orifice meters (table 2).
meter showed similar energy losses; however, the orifice meter had the most energy loss as flow
rate increased (figure 3).
Figure 3: Energy losses (kJ/kg) versus flow rates for a Venturi, Rotameter, and Orifice flow
meter.
When calculating for energy loss, the pressure drops used were different than the pressure
drops used to calculate the flow rate at a specific flow meter. Calculating energy loss required
the permanent pressure loss; while calculating the flow rate at a specific flow meter required the
pressure drop across the flowmeter desired (figure 1). This is because just after the fluid moves
through the flowmeter, there is a large pressure drop, but as the fluid continues to travel through
the pipe some pressure is recovered. The difference between the inlet pressure and the pressure
downstream of the outlet is the permanent pressure loss; so when calculating energy loss, the
pressure recovered can be ignored, but the immediate pressure drop after an obstruction
determines the flow rate at that flowmeter.
When the calculated flow rate was plotted against the square root of pressure drop for the
rotameter, it was observed that the data created a vertical line (figure 4). This was suggests that
the pressure drop remains constant no matter what the flow rate is. Trend lines were created for
the venturi and orifice data to determine the slope of the line, which is used to calculate the
estimated discharge coefficient (figure 4). Equation (5) and table 2 were used to estimate the
y = 0.2925x
Rยฒ = 0.
y = 2.3135x
Rยฒ = 0.
0
0 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035 0.0004 0.
Energy losses (E) [kJ/kg]
Volumetic flow rate (Q) [m^3/s]
Venturi
Rotameter
Orifice
discharge coefficient for both the venturi meter and the orifice meter, which yielded 0.656 and
0.602 as the respective discharge coefficients (table 3).
Figure 4: Volumetric flow rate versus the square root of the pressure drop across either the
Venturi meter, the Orifice meter or the Rotameter.
Table 3: Data comparison of Theoretical and estimated Discharge Coefficients for Venturi
and Orifice Flowmeters.
Venturi Orifice
Discharge Coefficient (C d
) Discharge Coefficient (C d
Theoretical C d
0.95 9 Theoretical C d
Estimated C d
0.656 Estimated C d
In table 3 the theoretical discharge coefficient is shown for both the venturi and orifice
meters, which are calculated by using either equations (6), (7), and (8) or equations (9), (7), and
๐
- 1
8
71 โ๐ฝ
5
๐
๐
- 75
y = 1E-05x
Rยฒ = 0.
y = 9E-06x
Rยฒ = 0.
0
0 10 20 30 40 50 60
Volumeteric flow rate (Q) [m^3/s]
Square root of pressure drop [Pa]
Venturi
Orifice
Rotameter
Conclusion
Using the data collected from a FME18 Flow Meter demonstration system, it was
possible to calculate the energy losses and discharge coefficients for a venturi meter and an
orifice meter. As flow rate increases, energy loss tends to increase as well, for the orifice and
venturi meters; whereas the rotameter tends to have a stable level of energy loss, no matter the
flow rate. The estimated discharge coefficient for a venturi meter was much lower than the
theoretical discharge coefficient; while the estimated discharge coefficient for an orifice meter
was higher than the theoretical discharge coefficient. The lower than expected estimated
discharge coefficient indicates that the venturi meter was operating at a lower efficiency than it
should have, while the orifice was operating at a higher efficiency than it should have.
References
Cengel, Y. A., & J. M. Cimbala. Fluid Mechanics: Fundamentals and Applications. McGraw-
Hill Companies Inc., 201 0. Web. 1 November, 2015.
Cengel, Y. A., & J. M. Cimbala. Fluid Mechanics: Fundamentals and Applications. New York:
the McGraw-Hill Companies Inc., 2014. Book. 1 November, 2015.
โFlow: The Basics of Rotametersโ sensors ONLINE. 2002. Web. 1 November, 2015.
http://www.sensorsmag.com/sensors/flow/the-basics-rotameters- 1068
Ramirez, B. C., G. D. N. Maia, A. R. Green, D. W. Shike, L. F. Rodrรญguez, &R. S. Gates.
Technical note: DESIGN AND VALIDATION OF A PRECISION ORIFICE METER FOR
VENTILATION RATE CONTROL IN OPEN-CIRCUIT RESPIRATION CHAMBERS.
TRANSACTIONS OF THE ASABE. N.P. N.D. 57(6): 1865-1872. Web. 1 November
Wilhelm, L. R., D. A. Suter, & G. H. Brusewitz. Fluid flow. Chapter 4 in Food & Process
Engineering Technology. N.P. 2004: 65-110. St. Joseph Michigan: ASAE (Rev. Aug.
2005). Web. 1 November 2015.
