CE 331 L Mauriot Lab Report 10

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CE 331 – INTRODUCTION TO FLUIDS MECHANICS AND HYDRAULICS LABORATORY Section Number: L-M02 Experiment Number: 10 Experiment: Impact of a Fluid Jet Submitted by: Louis Mauriot Submitted to: Zada Tawalbeh Date Experiment Performed: 04/13/23 Date Experiment Report Submitted: 04/20/23 Name of People Who Participated: Louis Mauriot Jarret Lee Dante Salazar John Paul Slape

Table of Contents Introduction ................................................................................................................................................. 1 Objectives .................................................................................................................................................... 2 Experimental Set-Up .................................................................................................................................... 2 Diagram: Impact of Jet Apparatus ....................................................................................................... 3 Picture: Impact of Jet Apparatus with Hydraulic Bench ....................................................................... 4 Pictures: Resultant Visual Representation of Jet Fluid Impact with Two Different Nozzles ................. 4 Results/Data Analysis .................................................................................................................................. 5 Graph: Theoretical Force Fy vs. Experimental Force ............................................................................ 6 Discussion and Conclusion ........................................................................................................................... 6 Appendix ..................................................................................................................................................... 8 References ................................................................................................................................................. 10 Tables: Table: Spreadsheet Data Table: Raw Data Equations/Calculations Theoretical Equations Sample Calculations 1

Introduction The amount of force fluids can produce can drastically increase when the velocity of the flow is increased. Two factors are taken into account in this case: magnitude and direction. When considering turbines powered by water flow or thrust in rockets, fluid force is studied and taken into account when designing the latter. The force exerted by fluids is measured through a contact surface that is linked to a spring scale or balance. We can then determine the force through the relationship between the rate of flow and the velocity of the jet. Objectives By observing the force exerted on a surface by a jet fluid, the consequent calculations of the theoretical force of the jet and comparison between the theoretical force calculated and the experimental force measured during the execution of the experiment were the objectives of this laboratory experiment. Experimental Set-Up For this experiment, we are equipped with the following apparatus: - Hydraulics bench and impact of a jet apparatus - 4 flow deflectors of 30, 90, 120 and 180 degrees - Various weights - A stopwatch 2

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Utilizing the different deflectors at our disposition, we test each one with three different amounts of mass to put on the spring at the top of the fluid jet apparatus. We use the level gauge to make sure the corresponding jet flow matches the amount of mass on the spring. Using the stopwatch, we measure the number of liters used for 60 seconds to keep that mass at the gauge level. This process is repeated for all 4 deflectors at our disposition. Every number of liters per 60 seconds for each amount of mass is recorded. Diagram: Impact of Jet Apparatus 3

Picture: Impact of Jet Apparatus with Hydraulic Bench Pictures: Resultant Visual Representation of Jet Fluid Impact with Two Different Nozzles 4

Results/Data Analysis Theoretical Equations Flowrate Equation: Q = V t Where: V is volume in m 3 t is time in seconds Velocity Equation: v = Q A Where: Q is the flowrate in m 3 /s A is the area in m 2 Mass Flow Equation: Q m = ρ×Q Where: ρ is the density in kg/m 3 of water Q is the flowrate in m 3 /s Theoretical Force Equation: F y = Q m ×v× ( cos ( θ ) + 1 ) Where: Q m is the mass flow in kg/s v is the velocity in m/s Θ is the angle of deflection in radians 5

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Experimental Force Equation: W = m×g Where: m is the mass applied in kg g is the gravitational acceleration 9.81 m/s 2 Graph: Theoretical Force Fy vs. Experimental Force Discussion and Conclusion The linear regression obtained on our plotted force data shows that the experimental procedure was successful, and the consequent linear regression equation can be considered a very satisfying equation since it is very close to 1.0 (only approximately 0.06 and 0.007 off which is a small value). The line is shaped as expected based on the example provided in the lecture PowerPoint. We were expecting a close to perfect linear regression for this plotted force data. 6

As the name says, the linear regression coefficients with obtained values being very close to 1 allow us to conclude that the relationship between the theoretical and experimental values is linear. Ideally, these coefficients should both be 1.00. However, they are within a small vicinity of being 1.00 and therefore the results of this lab are very satisfying and pleasing. A potential source of error which might have contributed to deviating our results from perfect 1.00 regression coefficients is the data collection over a period of 60 seconds for each amount of mass. The time was most likely slightly above 60 seconds or slightly below for most data measurements. A miscalibration between the weight support above the spring and the level gauge due to eye level not being quite at level with the gage might have contributed as well to increasing the percentage of error. When measuring for the higher amounts of mass, therefore requiring a more powerful jet flow, the latter was at certain moments pulsating very slightly causing a slight temporary miscalibration between the weight support and the level gauge while collecting data. The principle of fluid momentum and more specifically the force exerted on a surface by a fluid jet is important in two distinct applications. The first one is used in the hydroelectric power industry. More specifically within the turbine generator aspect of the hydroelectric power industry. The momentum caused by water flowing through the wicked gates and creating angular momentum for the turbines which fuel power to the generator is crucial to understand and be able to control to ensure the proper functioning of a hydrostatic generator (Water Science School, 2018). Another application is within the aerospace industry specifically for any type of rockets when studying the aerodynamics specifics. The relationship between thrust, the exhaust caused by the gas motion and the weight of the rocket is fundamental to understand. Fluid momentum is key when considering the mechanical forces generated by the interaction between a solid body with a fluid, a liquid, or a gas (NASA, 2014). 7

Our obtained regression coefficients for our plotted force data can allow us to safely conclude that the experiment objectives were achieved. All the calculations were performed correctly, and the obtained theoretical force calculations values compared to the experimental force values obtained can confirm this statement. Accuracy was well executed among all lab peers and helped contribute to a conducted experiment where we successfully were able to determine the force exerted by the change in momentum of a fluid flow through a jet when the jet of water flow strikes to a flat or curved surface and compare theoretical values of this force with the experimental results obtained. Appendix Sample Calculations Flowrate: Q = V t = 27.5 × 0.001 60 = 0.0005 m 3 / s Velocity: v = Q A = 0.0005 π × ( 8 × 10 − 3 2 ) 2 = 9.12 m / s Mass Flow: Q m = ρ×Q = 1000 kg m 3 × 0.0005 = 0.4583 kg / s Theoretical Force: F y = Q m ×v× ( cos ( θ ) + 1 ) = 0.4583 × 9.12 × ( cos ( 3.14 − 0.5236 ) + 1 ) = 0.564 N 8

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Experimental Force: W = m×g = 0.05 × 9.81 = 0.491 N Deflection Angle Alpha Def Angle Alpha Jet Angle Theta Mass m Volume V Volume V Converted Time t Flow Qt Mass Flow Qm Velocity V Theo Force Fy Experimental Force W degrees radian radian kg liters m3 m3/s kg/s m/s N N 30 0.5236 0.009139 0.05 27.5 0.0275 60 5E-04 0.4583333 9.122877 0.56352459 0.4905 30 0.5236 0.009139 0.07 35 0.035 60 6E-04 0.5833333 11.61093 0.9128167 0.6867 30 0.5236 0.009139 0.1 37.5 0.0375 60 6E-04 0.625 12.44029 1.04787631 0.981 30 0.5236 0.009139 0.12 36.5 0.0365 60 6E-04 0.6083333 12.10855 0.99273473 1.1772 90 1.5708 0.027416 0.1 14.5 0.0145 60 2E-04 0.2416667 4.810244 1.16432683 0.981 90 1.5708 0.027416 0.3 23 0.023 60 4E-04 0.3833333 7.630042 2.92950722 2.943 90 1.5708 0.027416 0.5 30 0.03 60 5E-04 0.5 9.952229 4.98403874 4.905 90 1.5708 0.027416 0.7 36.5 0.0365 60 6E-04 0.6083333 12.10855 7.3777618 6.867 120 2.09439 0.036554 0.1 10.5 0.0105 60 2E-04 0.175 3.48328 0.91520129 0.981 120 2.09439 0.036554 0.3 20 0.02 60 3E-04 0.3333333 6.63482 3.32045821 2.943 120 2.09439 0.036554 0.5 24.5 0.0245 60 4E-04 0.4083333 8.127654 4.98276259 4.905 120 2.09439 0.036554 0.7 29 0.029 60 5E-04 0.4833333 9.620488 6.98126338 6.867 180 3.14159 0.054831 0.1 9.5 0.0095 60 2E-04 0.1583333 3.151539 0.99798681 0.981 180 3.14159 0.054831 0.3 18 0.018 60 3E-04 0.3 5.971338 3.58280028 2.943 180 3.14159 0.054831 0.5 22 0.022 60 4E-04 0.3666667 7.298301 5.35208436 4.905 180 3.14159 0.054831 0.7 26 0.026 60 4E-04 0.4333333 8.625265 7.47522527 6.867 Table: Spreadsheet Data 9

Table: Raw Data References Department of Civil Engineering. (2023, Spring). CE 331 Lab Assignment 10. Las Cruces, New Mexico: New Mexico State University. Retrieved from class website: CE_331_Lab_10_Impact of Fluid Jet Department of Civil Engineering. (2023, Spring). CE 331 Lab Lecture 11. Las Cruces, New Mexico: New Mexico State University. Retrieved from class website: Lecture_11_Impact of a fluid Jet.pdf NASA. (2014). Rocket Aerodynamic Forces . Nasa.gov. https://www.grc.nasa.gov/WWW/K-12/rocket/rktaero.html Water Science School. (2018, June 6). Hydroelectric Power: How it Works | U.S. Geological Survey . Www.usgs.gov. https://www.usgs.gov/special-topics/water-science-school/science/hydroelectric-power-how-it- works 10