CE343_Lab7

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343

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Dec 6, 2023

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1 Orifice Flow Peter Martin CE343 – Section 6 Pin-Ching Li 10/19/2022

2 Executive Summary This experiment is an implementation of three different aspects, involving the pitot tube, piezometer, and the shard/bevel edge orifice meters. In finding the basic data from the experimental setup, we then use the conservation of mass and momentum for the analysis of the data. The objective of the experiment is to see how two different orifice meters effect the streamline and flow rate. An orifice meter is an opening in a thin wall of a tank located normal to the vena contracta that constricts the flow and in hand increases the velocity of the water. In conclusion, at the end of the report we will know the relationship between discharge and H 0 on different types of plots which will allow us to calculate the C d value. In addition, the difference between the plot of root H 0 and root H tank will be shown in how that difference in height effects the discharge value.

3 Table of Contents 1. Introduction………………………………………………… (page 4-5) 2. Background………………………………………………… (page 5-7) 3. Results……………………………………………………… (page 8-11) 4. Conclusion ………………………………………………… (page 11) 5. References…………………………………………………. (page 12) 6. Appendix…………………………………………………… (page 12)

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4 Introduction Much like venturi meters, orifice meters use the flow constriction to base its measurements and then further analyze it using Bernoulli theorem and other equations. Depending on the flow conditions such as flow area, flow velocity and flow constrictions, a different type of orifice should be used such as the sharp and bevel edged orifices, which this lab will cover tests and calculations for. The way this lab is using this tool is by establishing a relationship between the flow rate, Q, and the head height H. For the calculations to be more accurate the flow of the weir must be surrounded by atmospheric pressure, this is called a well-aerated condition which is hard to achieve most times. These conditions that need to be met call for the use of approximations and simplifications, therefore the introduction of the discharge coefficient (C d ) is essential, and its analysis is one of the objectives of this lab. Figure 1: (Hydraulics and Hydrology Group) a) Flow through an orifice in the bottom of a large tank b) Exploded view of the flow below the orifice In the physical lab portion of this report, the values of L, time in seconds, and the height of the tank (H tank ) were recorded for further data analysis. As well as the pitot tube level (H Pt ) and the orifice diameter values were recorded for both the sharp and bevel edged orifice.

5 As the water enters the supply tube and passes through the first valve, the water is a straight streamline, meaning that the pressure distribution is hydrostatic. The water then enters the tank where the piezometer is set up to measure the total head. When the water moves its way down the tank it will meet the orifice and immediately increase in velocity as it passes through the pitot tube, which measures the head at the vena contracta that is parallel to the stream, so it includes the velocity head as well. I believe we are studying this problem to notice and record how the different orifice meters effect the flow rate or discharge of the water out of the opening. This has real world application in people’s everyday life whether its is taking a shower, watering flowers, or even larger scale in a water dam. Figure 2 – (Hydraulics and Hydrology Group) Orifice tank apparatus Theoretical Background There are plenty of similarities when comparing the different flow meters like venturi meters and orifice meters in how they mostly vary withing their geometries. The Bernoulli theorem proves to be one essential tool to understand flow behavior since it analyzes the relationship between the velocity at the nappe and the velocity in the approach flow on the same streamline. Performing an integration of that calculation allows for the many geometries to be considered and showing the different each one of them will make and help an Engineer, for example, to choose that shape for the flow they desire. To perform the necessary calculations for

6 this lab the following equations were used and were assigned an equation number to facilitate further referencing. Equation 1: (Hydraulics and Hydrology Group) – This begins with the conservation of mass where the A values are the cross-sectional areas of the tank at the free surface and jet. The V represents the velocity of the flow at the section. Equation 2: (Hydraulics and Hydrology Group) – This is the conservation of momentum which is expressed in the Bernoulli theorem for steady flow. Points labeled A and B were chosen and will now be analyzed. Equation 3: Derivation (Hydraulics and Hydrology Group) – In analyzing the system we can find that p A =0, V A =0, and p B =0 to simplify our Bernoulli’s equation to the above. This allows for the flow rate or mass conservation formula to be plugged into the formula and solved in the next steps. Equation 4: Analysis (Hydraulics and Hydrology Group) To ensure that the discharge coefficient is used, it is plugged into the discharge formula in Equation 3 to find the final formula to solve for discharge in the below equation. Equation 5: Final Formula (Hydraulics and Hydrology Group) Final discharge formula.

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7 To evaluate the relationship between Q and H, in this lab some assumptions were made to facilitate the calculations while maintaining them accurate within a restriction of time and skills of the students performing the experiment and calculations. The assumptions are that there is no friction in the system, the pressure is zero at all points. So, C d will be used to make up for these and still provide an accurate representation of the Q vs H relationship. Experimental Description This experiment consists of the piezometer, pitot tube, tank, and the two different orifice meters. While these pieces of equipment are slightly aged, they are not going to be as accurate in measurement and efficient flow to and from the tubes. In addition, I would say that the most uncertainty is in the times measurement. This measurement is taken from someone eyeing out the volume, so their exact time is not going to be exactly accurate. This experiment was done very well because it gave us a look at different orifice meters and how they show the flow of water at different volumes. Images 1 & 2: On the left is the Piezometer and Pitot Tube and on the right is the orifice and streamline coming out of the opening.

8 Results Bevel Plot 1: The slope of the trendline is 0.0067 which roughly corresponds to the theoretical value. This is different due to the uncertainty and errors that may have occurred throughout the experiment. Bevel Plot 2: The slope of the trendline is 0.0102 as it relates to the origin with no y-intercept. C d = m / A o sqrt (2g) = 0.925

9 Bevel Plot 3: The slope of the trendline is 0.0109 as it relates to a y-intercept of zero. C d = m / A o sqrt (2g) = 0.989 The difference in C d values from the previous plot is 0.063. Sharp Plot 4: The slope of the trendline is 0.0042 which roughly corresponds to the theoretical value. This is different due to the uncertainty and errors that may have occurred throughout the experiment.

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10 Sharp Plot 5: The slope of the trendline is 0.0082 as it relates to the origin with no y-intercept. C d = m / A o sqrt (2g) = 0.744 Sharp Plot 6: The slope of the trendline is 0.0088 as it relates to the origin with no y-intercept. C d = m / A o sqrt (2g) = 0.798 The difference between the previous C d value and this one is 0.054.

11 In looking at the total head of the jet compared to the total head at the water surface in tank, the total head at the water surface is greater than the jet because of the elevation. The z value of the head is much higher at the surface. The calculated C v and C d values can be seen in the Appendix for both the sharp and bevel edge orifices. The area of the jet at the vena contracta is one half of the diameter of the orifice and can also be seen in the appendix tables. The error in the discharge computation would be committed if the exit jet distance were neglected. In the height of H 0 , it includes the exit jet distance which would make an error in the discharge calculation. While I believe this experiment had minimal uncertainty, there was one aspect that could have caused slight error. In timing out, the volume of water was done by the participant so a slight difference in reaction time could cause a difference in the future calculations, but like I said that would be very minimal. I think this because the experimental and theoretical values were close enough to not be too troublesome. Summary  There is a direct correlation between the discharge value and the height of both the tank and the H o  Participants got sufficient use of the water tank and its capabilities to understand how it represents different aspects of Hydraulics  There a small difference in C d values between the H tank and H o showing how the use of H o would have cause an error in discharge calculation  Gained an understanding of how to implement both the conservation of mass and momentum (Bernoulli’s Formula) to solve for the discharge (Q)

12 References Hydraulics and Hydrology Group; Hydraulics Laboratory Manual (2021), School of Civil Engineering, Purdue University Appendices Chart 1: Bevel Edge Data and Calculation Chart 2: Sharp Edge Data and Calculation

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