# Laboratory Experiment on Venturi Meter and Orifice Meter

4330 words (17 pages) Essay in Physics

23/09/19 Physics Reference this

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1. 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.

(2)

Where g equals the force of gravity, z equals the height, P equals the pressure, and

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.

$\stackrel{̇}{m}=\frac{∆m}{∆t}$

(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:

${Q}_{\mathit{actual}}=\frac{∆m}{\rho ∆t}$

(4)

Since we will be recording the height difference from the manometers, we can relate the height difference to the pressure drop as follows:

(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

$\rho$

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:

$\frac{{V}_{1}^{2}}{2}+\frac{{P}_{1}}{\rho }=\frac{{V}_{2}^{2}}{2}+\frac{{P}_{2}}{\rho }$

(6)

The ideal flow rate considers the ratio of the different sections of the pipe and we can substitute this value into equation 6:

${Q}_{\mathit{ideal}}={V}_{2}{A}_{2}={A}_{2}\sqrt{\frac{2\left({P}_{1}–{P}_{2}\right)}{\rho \left(1–\frac{{d}^{4}}{{D}^{4}}\right)}}$

(7)

The discharge coefficient is the ratio of the actual flow rate to the ideal flow rate:

${C}_{d}=\frac{{Q}_{\mathit{actual}}}{{Q}_{\mathit{ideal}}}$

(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:

$\mathit{Re}=\frac{\mathit{\rho VD}}{\mu }$

(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. (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.

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.

V. CONCLUSIONS

1. SAMPLE DATA ANALYSIS

Sample Calculations for Venturi meter

${A}_{2}=\frac{\pi {d}^{2}}{4}=\frac{\pi {\left(.02\right)}^{2}}{4}=0.000314{m}^{2}$

${p}_{1}–{p}_{2}={\rho }_{{H}_{2}0}g\left({h}_{1}–{h}_{2}\right)=\left(1000\frac{\mathit{kg}}{{m}^{3}}\right)\left(9.81\frac{{m}^{2}}{s}\right)\left($

0.3-0.065 m) = 2305Pa

${C}_{d}=\frac{{Q}_{\mathit{actual}}}{{Q}_{\mathit{ideal}}}=\frac{{m}_{\mathit{actual}}}{{m}_{\mathit{ideal}}}=\frac{0.0004719}{0.0004665}=1.0115$

Re=

$\frac{\mathit{pVd}}{u}$

=

=37,029

 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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