Lab Report 3

1 TEXAS TECH UNIVERSITY DEPARTMENT OF CIVIL, ENVIRONMENTAL, AND CONSTRUCTION ENGINEERING Lab Report #3: Flow Measurement CE 3105 – Fluid Laboratory Section: 303 Team Number: 2 Instructor: Theodore Cleveland Authors: Bradley Brooks Conner Jeter Ruben Ramos Gabriel Vega Date of Experiment: 2/19/2024 Date of Submission: 2//2024

2 Table of Contents Theory ........................................................................................................................ 3 Apparatus ................................................................................................................... 3 Procedure ................................................................................................................... 4 Results ........................................................................................................................ 5 Table 1: Recorded and Calculated Results from Buoyancy Measurements ............. 5 Table 2: Calculated Results from Buoyancy Measurements .................................... 5 Table 3: Recorded and Calculated Results from Center of Pressure Measurements (Partial Submerge) .................................................................................................. 6 Table 4: Recorded and Calculated Results from Center of Pressure Measurements (Full Submerge) ....................................................................................................... 6 Discussion .................................................................................................................. 6 Data Appendix ............................................................................................................ 8 Error Calculations ....................................................................................................... 9 Sample Calculations ................................................................................................. 10

4 Temperature (C) -Volume of water (mL) -Mass of asphalt, wood, and concrete (g) -Volume of asphalt, wood, and concrete (m^3) -Buoyant force acting on asphalt, wood, and concrete (N) -Density of water, asphalt, wood, and concrete (g/m^3) -Balance (degrees) -Weights (g) -Height of water (mm) -Ruler to measure distance to outer edge of water (mm) -Moment (Nm) -Approximate Vertical Force (N) -Water weight per unit volume Procedure Part 1: Displacement volumes and weight 1. Take the water temperature measurement. 2. Begin by filling a graduated cylinder with water and noting the initial volume level. 3. Weigh the first object. 4. Submerge the first object in the water and record the updated volume level. Remove the object and record the volume of water displaced. 5. Repeat this process three times for each object, resulting in nine measurements. Part 2: Center of pressure

5 1. Measure the temperature of the water. 2. Ensure both tanks are empty before each experiment and adjust the assembly to bring the submerged plane to the vertical position. 3. Use a transfer pipette to add water into the trim tank until the balance reaches the 0 position. Add weight hangers and masses as needed to achieve proper trimming. 4. Add additional weights as required, using the second weight hanger if necessary. 5. Pour water into the quadrant tank until the assembly is level again. Record the additional weights and the water level (h). 6. Measure the distance from the planar surface to the outer edge of the water surface (the "length" of the free surface, b) using a ruler. 7. Repeat the procedure for a full range of weights, including at least three measurements for partially submerged and fully submerged cases. Results Table 1: Recorded and Calculated Results from Buoyancy Measurements This table shows calculated results from Part 1 of the Lab Experiment, Displacement Volumes and Weights. These measurements were conducted at a water temperature at 55°F. Material V initial (ml) V final (ml) ∆V (ml) V o geomet ry ( cm 3 ) V o displaceme nt (ml) Mass (g) submerg ed Rock-1 700 727 27 N/A 27 60.885 Yes Rock-2 700 715 15 N/A 10 48.132 Yes Composite -1 690 750 60 N/A 60 52.107 Half Composite -2 690 750 60 N/A 60 54.136 Half Wood-1 700 710 10 21.28 N/A 10.535 No Wood-2 700 720 20 23.69 N/A 14.787 No Table 2: Calculated Results from Buoyancy Measurements With these values, we can find and calculate the buoyancy force, density, and volumes of the objects.

7 underlying fluid statics and the resultant forces experienced by immersed objects. Through multiple measurements, our objective extends to quantifying the buoyancy force acting on various objects of differing densities and shapes. Additionally, we endeavor to ascertain the hydrostatic thrust exerted on a flat surface fully submerged in water. By systematically analyzing the forces at play in these scenarios, we aim to deepen our understanding of fluid mechanics and its practical applications. For the first experiment, we conducted a series of steps to explore fluid statics and buoyant forces. There were six total objects used, two rocks, two composite, and two pieces of wood. First, using a graduated cylinder, we carefully fill it with water and record the initial volume level. Next, we weigh the first object and immerse it into the water within the cylinder, noting the new volume level. After removing the object, we record the volume of water displaced, indicative of the buoyant force acting on the object. This process is repeated three times for each of the three objects, resulting in a total of nine measurements. By systematically analyzing the changes in volume and weight, we aim to quantify the buoyant forces exerted on different objects and gain insights into fluid mechanics principles. Using different materials, we can conclude that certain materials are buoyant than others. In our results, we can conclude that both rock specimens sank to the bottom of the water, the composite pieces had somewhat floated, and the wood pieces completely floated. For our second experiment, the open-air pressure lab, as described in the provided steps, aims to investigate the interplay between water depth, added weights, and pressure distribution on a submerged plane. By systematically varying these parameters and recording corresponding data, the experiment seeks to elucidate how changes in depth and weight influence the balance and trim of the submerged surface, thereby affecting pressure distribution. This exploration of hydrostatic principles offers students a hands-on opportunity to grasp the relationship between fluid mechanics concepts and real-world applications. Discussion/Interpretation 1) Archimedes' Principle states that when a body is partially or wholly submerged in a fluid, it experiences an upward buoyant force equal to the weight of the fluid it displaces. In simpler terms, it means that any object immersed in a fluid (liquid or gas) will experience an upward force equal to the weight of the fluid it displaces. This principle is crucial in understanding buoyancy and flotation, and it's commonly applied in various fields, including engineering, physics, and naval architecture. Archimedes' Principle is named after the ancient Greek mathematician and scientist Archimedes, who discovered and formulated it in the third century BCE. 2) If the rock sinks to the bottom of the beaker of water, it means that the buoyant force acting on the rock is less than the weight of the rock. According to Archimedes' Principle, the buoyant force experienced by an object submerged in a fluid is equal to the weight of the fluid displaced by the object. Since the rock sinks, it displaces a volume of water equal to its own

8 volume, and the buoyant force exerted by the water on the rock is insufficient to counteract the downward gravitational force acting on the rock (its weight), causing it to sink. Therefore, in this scenario, the buoyant force on the rock is less than the weight of the rock. If the buoyant force were greater than or equal to the weight of the rock, the rock would either float on the surface of the water or be in equilibrium at some level within the water, respectively. 3) To prevent overturning, we have to ensure that the moment exerted by the water on the embankment’s base is balanced by the moment exerted by the embankment itself. The moment exerted by the water is calculated by finding the weight of water acting at it’s center of mass. Volume of Embankment = height x width x thickness Volume of water = 20m(2)(50m) = 10,000m³ Weight of water = 1000 kg/m³ (10,000 m³) = 10,000,000 kg Moment of water = 10,000,000 kg (25m) (9.81m/s²) = 2,452,500,000 N*m Moment of embankment = 2400kg/m³ (20m) (50m) (thickness of embankment) (25m)(9.81m/s²) =24,000(V) N*m To prevent overturning, the moment of the embankment must be greater than or equal to the moment of the water. 24,000(t) N*m > 2,452,500,000 N*m Volume of the embankment must be greater than or equal to 102,187.5 meters.

10 Error Calculations Due to only practicing one trial on each experiment, we were unable to calculate variance.

11 Sample Calculations