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2 Department of Civil Engineering Lab 4: Jet Impact Fluid Mechanics Laboratory Section 1 Prepared by: Dorsey, Fahim – Discussion McManus, Harrison – Introduction & Full Report Review Moreno, Jesus – Conclusion Partain, Ethan – Results Rosenberg, Austin – Executive Summary, Materials and Methods, & Template Design ENGR 3345 – Fluid Mechanics Laboratory David S. Ancalle, P.E September 13 th , 2023

2 Table of Contents: Cover Page ………………………………………………………………………………………………………………. 0 Table of Contents …………………………………………………………………………………………………….. 1 Executive Summary …………………………………………………………………………………………….……. 2 Introduction ……………………………………………………………………………………………………….…….. 2-3 Materials & Methods ……………………………………………………………………………………………….. 3-4 Results ………………………………………………………………………………………………………….………….. 4-5 Discussion ………………………………………………………………………………………………………………... 5-6 Conclusion ……………….…………………………………………………………………………………………..….. 6 References …………………………………………………………………………………………………………..….. 7 Appendix …….…………..…………………………………………………………………………………………..….. 8

2 Executive Summary This Fluid Statics Lab was completed to develop a method for measuring hydrostatic pressure by applying principles of statics. Using a special water tank setup featuring a tank and an attached beam. The water level was incrementally adjusted, with the addition of weights on the beam to maintain equilibrium. Both theoretical and experimental assessments were completed to determine the hydrostatic force and its location on the submerged wall. The experiment showed a consistent one-third rule for the center of pressure, which is valid for water depths up to 100 mm but may be different for greater depths. This experiment showed the application of statics equations (∑ 𝐅 = 0, ∑ 𝐌 = 0) in deriving hydrostatic pressure while proving the need to recognize the constraints of theoretical models in real-world scenarios. Introduction The goal of this week’s lab was to learn and evaluate the principles of hydrostatic forces acting on a given surface. Hydrostatic forces are defined as the sum of all forces acting on a submerged surface at a given location. By understanding the forces acting on a submerged surface, engineers are able to better predict and anticipate how structures will react when submerged. With this information, engineers are able to better tailor and develop their designs to fit more specific purposes. The principle of hydrostatic forces is commonly used in many fields of engineering. One specific case that would require the use and understanding of hydrostatic forces would be during the development of hydro dams. During their development, it is important for engineers to understand how strong and the location of the hydrostatic force the water

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2 exerts on the dam. With this information engineers are able to anticipate the moment that will be acting on the dam, allowing them to design and anticipate how large the dam needs to be as well as its shape. Materials and Methods In this lab, the central aim is to construct an approach for measuring hydrostatic pressure through the application of statics principles. The experimental device has a large water tank with a beam attached to keep the device in equilibrium. Ensuring the proper level of the device is important, and this is achieved using the bubble level, which can be adjusted with the 1 newton weights that can be attached to the beam. The initial steps involved measuring the width of the container and then gradually filling the tank with water until the water level reached the 40 - 50mm mark The image above shows group 3 observing the device to ensure that equilibrium was reached. Shown is the device that includes the water tank and bubble level.

2 on the tank, causing an initial imbalance in the beam. It was at this point that the temperature would have been taken in order to calculate density. However, we assumed room temperature, and a standard density of 1000 kg/m³ is assumed. The next step was to place the weight onto the hook attached to the left arm of the beam and move it until the bubble level indicates equilibrium. The weight of the hook (1 N) and the distance it is moved to reach equilibrium is recorded. If equilibrium is impossible, additional weights can be added, and the total weight will be recorded. This process is repeated three more times, with the water level being increased in intervals of approximately 10 to 15 mm, ensuring that the water depth does not exceed 100 mm. It is with this process that the results were obtained and used in this report. Results Table 1

2 Width of container: 7.5cm (75mm) Table 2 Discussion There is some percentage error in between the experimental and theoretical values for the hydrostatic forces and the length at which they act. The errors are relatively small with the length having an error of 3.04%, while the force had an error of 6.74%. This error can be explained due to the water depth (h) not having a fully accurate measurement. Another reason for the error could be an inaccurate measurement of the length from the weight to the pivot point, which could lead to the system not being completely balanced. Both values cannot be attained at the same time because they are two unknowns. When solving for two unknown variables you need at least two equations to solve for both. Also, by using the theoretical value of length when solving for the experimental force and the theoretical value of force when solving for experimental length, you will produce an answer with less margin of error. It is better to solve for experimental location using the theoretical force. According to our calculations there seems to be less margin for error when using this method. The

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2 experimental location had an average percent error of about 3.04%. The experimental force had an average percent error of 6.74%. This is because the pressure acts on a rectangular or square surface. This means that the pressure distribution is triangular. When it is triangular, the pressure acts at the center of the triangle which is located 1/3 from the base of the triangle. When the water depth is greater than 100mm the water applies a pressure on a different shape, which means that the pressure distribution shape will change. When the pressure distribution changes, a new center of pressure must be calculated. Conclusion The purpose of the lab was to find hydrostatic pressure using equations of statics. Using the equipment of a water tank with a quadrant and a beam attached to the top. The equations of statics used where the sum of all the forces acting on an object at rest is equal to zero (∑ 𝐅 =0), and the sum of all moments acting on an object at rest is equal to zero (∑ 𝐌 = 0). When water was added to the tank it the beam became off balanced. Additional weights were added to the beam and balanced to obtain equilibrium. By combining the two equations the external forces are cancelled making the formula p=pgh known as hydrostatic pressure.

2 References: There were no outside sources used in this report.

2 Appendix No charts or graphics were referenced in this report.

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