Venturi & Orifice Meter
INTRODUCTION
As we learned in the Impact Jet lab, the speed of a moving jet of water is proportional to the water’s velocity. This is evident in a turbine flow meter, where the impact force of the water on the blades sets the rotor in motion. Once there is a steady rotational speed, we can say the speed is proportional to the velocity of the fluid. Measuring the flow rate of a system would be also be important for doctors who want to understand a patients’ blood flow in their circulatory system. For the purposes of this lab, we will study the flow rate within a pipe where the volume is the amount of fluid each second that passes through a cross-sectional area of that pipe. It will be necessary to assume uniform flow of the fluid within the pipe, the flow rate, which is known as Q. The flow rate is proportional to the velocity of the moving fluid, V and the formula is:
Q=V1A1=V2A2 (1)
Where 1 and 2 are varying locations within the system.
This lab will investigate the venturi meter and orifice meter, both of which indirectly measure flow rate. They measure the flow rate by means of a pressure change. The venturi meter has a converging section of pipe that causes the fluid’s velocity to increase, which creates a drop in the pressure. The orifice meter utilizes an orifice plate that contains a small hole, which also increases the fluids velocity. We will also take readings from a rotameter, which directly measures flow rate using a floatation device and that has a scale for pressure printed on it.
Since we will be only recording the pressure for the three devices, we will need to relate the pressure to velocity. We will employ the Bernoulli equation, which is for steady, incompressible flow, without viscous effects, in the control volume.
P1ρ+ V122+gz1=P2ρ+ V222+gz2
(2)
Where g equals the force of gravity, z equals the height, P equals the pressure, and
ρ equals the density of water.
We are interested in the actual flow rate and ideal flow rate. We will need the discharge coefficient to account for the viscous losses that we assumed were negligible. The discharge coefficient is the ratio of actual to theoretical. The discharge coefficient for a venturi meter is around 0.9 and the orifice meter is around 0.6. The venturi meter has a larger discharge coefficient because it contains a gradual change in pipe diameter whereas the orifice plate contains a sudden and drastic change in diameter where the fluid is flowing.
THEORY
The Venturi effect illustrates a reduction in fluid pressure as the fluid flows through the convergence of the pipe. As the fluid flow through the pipe, the fluid’s velocity will increase to satisfy the equation of continuity. The pressure will simultaneously decrease to satisfy the conservation of energy equation. The equation for the pressure drop caused by the Venturi effect is Bernoulli’s principle and the equation of continuity. The orifice meter has a similar pressure drop. We will measure how long it takes the bucket system to fill with 30 lbs of water. The time it takes to accumulate the known mass is known as the mass flow rate that is calculated as follows:
ṁ=∆m∆t
(3)
We are also interested in the volumetric flow rate so that we can compare this value to the theoretical flow rate to verify our results. The volumetric flow rate is calculated by dividing the mass flow rate by the density of water. The actual flow rate is shown:
Qactual=∆mρ∆t
(4)
Since we will be recording the height difference from the manometers, we can relate the height difference to the pressure drop as follows:
P1–P2 = ρwg (h1–h2)
(5)
Where h is the height of the manometer at the varying sections of the pipe, P1 and P2 are the pressure difference, g is the acceleration of gravity, and
ρ
is the density of water. The ideal flow rate is found using Bernoulli’s equation (Eq 2) and by using the fact that the pipe is horizontal. Therefore, we can neglect the forces of gravity and the height:
V122+P1ρ=V222+P2ρ
(6)
The ideal flow rate considers the ratio of the different sections of the pipe and we can substitute this value into equation 6:
Qideal=V2A2=A22(P1–P2)ρ(1–d4D4)
(7)
The discharge coefficient is the ratio of the actual flow rate to the ideal flow rate:
Cd=QactualQideal
(8)
The discharge coefficient is a dimensionless number that we use to identify the pressure loss behavior of different nozzles or orifices in the types of fluid systems under investigation. As mentioned earlier, the discharge coefficient accounts for the frictional losses that we assumed were negligible. We will need the discharge coefficient, Cd, to compare it to the calculated Reynolds number:
Re=ρVDμ
(9)
Where ρ is the density of the fluid, V is the velocity, D is the diameter, and µ is the viscosity. We can expect a Re> 4000 because the flow is turbulent. The velocity of the fluid for both the orifice and venturi meters and can be seen in the Appendix section of this report.
EXPERIMENTAL APPARATUS AND PROCEDURE
(4)
(3)
(2)
(1)
Figure 1 Venturi and Orifice Meter Experimental Setup
Description of numbers from Figure 1:
(1) Venturi Meter
(2) Orifice meter/plate
(3) Rotameter
(4) Manometers
Figure 2 Schematic of Venturi Meter
Figure 3 Schematic of orifice meter
We recorded the room temperature as 22 C and the atmospheric pressure around 101 kPA to allow for determining accurate fluid properties at the time of the experiment. The apparatus for this experiment contained an orifice meter and plate, a venturi flow meter, a rotameter, a weighing bucket with a scale, a stopwatch, and manometers that corresponded to the different meters used. A picture showing the different flow meters is in Figure 1. The manometer tubes 1 and 2 corresponded to the venturi meter. Tubes 3 and 4 corresponded to the venture expansion. Tubes 5 and 6 were for the orifice flow meter. The rotameter height is located at the top of the float of the rotameter. The rotameter height was set at 180 mm to begin the experiment. We turned on the water and allowed it to flow through the flow meters. The manometers allow us to read the pressures at the entrance and exit points of each meter. The rotameter simply provided a reading based on where the top of the float is. We changed the flow rate to correspond to the rotameter height reading of 160, 140, 120, and 100 mm. We filled the apparatus’ bucket system with first 8 kg then 13.6 kg of water and we recorded the time it took for this to happen and for the system to level. We recorded the heights of the manometers twice for each flow rate we used.
PRESENTATION AND DISCUSSION OF RESULTS
The data collected from this experiment can be found in the Appendix section of this report. Pressure increases and velocity decreases during a flow expansion. This is evident when we look at the Bernoulli’s equation. Bernoulli’s law shows that when a fluid flowing in a pipe, where there are different cross sections, the pressure is low through the convergence and the velocity is high through the convergence.
Figure 4 Flow rate as a function of rotameter height
Figure 2 depicts the rotamer height as a function of the flow rate. The trendline indicates that the flow rate increases in a linear fashion as the height of the rotamer increases. The formula for the slope of the line is:
Rotameter height =9.759 x Q -0.068
Figure 5 Pressure Drop in Venturi VS Actual Flow rate
Figure 3 compares the pressure drop in the Venturi meter (or change of height) and the actual flow rate. It is evident that we may have taken false readings from the manometers because we should expect a quadratic increase in the pressure drop. This is because Bernoulli’s equation states that the pressure drop is equivalent to the square of the velocity. The results of our graph appears more linear rather than parabolic.
Figure 6 Flow Rate VS Discharge Coefficient
Figure 4 shows the comparison of the flow rate to the discharge coefficient for both the venturi and orifice meters. The discharge coefficient increase as the flow rate increases for both the venturi and orifice meters. As expected, the discharge coefficient for the venturi was around 1.0 and 0.6 for the orifice.
Figure 7 Reynold’s Number Vs Discharge Coefficient
Figure 5 shows the comparison between the Reynold’s number and the discharge coefficient. Plotting the discharge coefficient and the Reynold number is more efficient than plotting against the flow rate because the Reynold’s number is easier to calculate.
CONCLUSIONS
During a flow expansion, the pressure increases because the volume is decreasing. There is a loss of velocity in a flow expansion that increases the pressure. We noticed that as we increased the rotameter height, the actual flow rate also increased. There is a linear relationship between the two that can be seen in figure 4. We would have expected to see an exponential increase to the flow as the difference in pressures increased. This is because Bernoulli’s equation states that the pressure drop is equivalent to the square of the velocity. Our results were as expected for the discharge coefficient of both meters. The Cd for the venturi is expected to be greater than that of the orifice. This is because the venturi meter contains a gradual change in pipe diameter whereas the orifice plate contains a sudden and drastic change in diameter where the fluid is flowing. It is not possible for the discharge coefficient to be greater than 1. However, some of our results were more than 1. This is probably due to human error in recording the data. For future labs, I would suggest more than one person take the readings and then we can double check to ensure proper recording.
SAMPLE DATA ANALYSIS
Sample Calculations for Venturi meter
Qactual=ΔmρH20Δt=13.6 kg1000kgm3*2.8 s=0.0004719m3s
A2=πd24=π(.02)24=0.000314m2
p1–p2=ρH20gh1–h2=1000kgm39.81m2s(
0.3-0.065 m) = 2305Pa
Qideal=V2A2=A22(p1–p2)ρ(1–d4D4)=.000314m222305 Pa1000kgm31–0.0164m0.0264 m=0.0004665m3s
Cd=QactualQideal=mactualmideal=0.00047190.0004665=1.0115
Re=
pVdu
=
(1000kgm3)(2.319ms2)(0.016 m)(1.0020 mPa)(1 Pa1000 mPa)
=37,029
APPENDIX
Flow Rate
H1 Average
H2 Average
H3 Average
H5 average
H6 average
180
300.0
65.0
267.0
287.0
20.0
160
308.0
123.0
280.5
297.5
87.5
140
313.5
174.5
292.0
304.5
148.0
120
308.0
122.0
280.0
296.0
87.0
100
311.0
238.5
298.5
306.0
225.0
Figure 8 Average height data
Manometer
P1-P2
P2-P3
P5-P6
180
2305.4
-1981.62
2619.3
160
1814.9
-1545.075
2060.1
140
1363.6
-1152.675
1535.3
120
1824.7
-1549.98
2050.3
100
711.2
-588.6
794.6
Figure 9 Pressure Differences
Manometer
Qideal Venturi
Qideal orifice
Qactual
Cd venturi
Cd Orifice
180
0.0004665
0.0007277
0.0004719
1.0116
0.6485
160
0.0004139
0.0006454
0.0004158
1.0047
0.6444
140
0.0003588
0.0005571
0.0003588
1.0003
0.6441
120
0.0004150
0.0006438
0.0003041
0.7327
0.4723
100
0.0002591
0.0004008
0.0002542
0.9810
0.6342
Figure 10 Ideal Flow Rate, Actual Flow Rate, and Discharge coefficient
Manometer
V(Orifice)
Re(Orifice)
V(venturi)
Re(venturi)
180
2.314447211
46196.55113
2.320050976
37046.72217
160
2.052585688
40969.77421
2.058493312
32870.15268
140
1.771939216
35368.04823
1.784312822
28492.0211
120
2.047692747
40872.11073
2.064049309
32958.87121
100
1.274776822
25444.64714
1.288642942
20577.1328
Figure 11 Calculated Velocity and Reynolds Number
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