lab 1 report

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Louisiana State University *

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2250

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Mechanical Engineering

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Apr 3, 2024

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CE 2250 Fluid Mechanics Laboratory Lab 1 Data Analysis with Excel Performed By: Group 2 Section 2 Submitted by: Chelsie Franck Jodie Robinson Nicholas Vu Rachel Bancroft Christopher Issa Date Performed: September 01, 2023 Date Submitted: September 15, 2023 Department of Civil and Environmental Engineering Louisiana State University Fall 2023

Table 1: Percent Errors for Slope and Intercept Equation 1 Figure 1: Voltage and Deviations

Figure 2: Velocity profile - Relation between Velocity and Elevation Figure 3: Partial Velocity Profile - Relation between Velocity and Elevation, if Elevation < 10cm Table 2: Percent Error for Roughness and Shear Velocity

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Figure 4: Relation of the Velocity Profile . Table 3: Percent Error for u* and z0 estimates The results from Problem 1 illustrate various graphs and calculations. The data presents the calibration process of a micro-propeller. In Figure 1, the data falls on a linearly distributed path established on the voltage applied compared to the manufacturer’s supplied velocity. The linear function increases throughout the graph when given different voltages. In Figure 2, a comparison of data from the voltages applied to the tested velocities can be observed. This graph presents the difference between the voltages and the new velocities. Values tend to stay linear around lowed voltages but around 0.5 V and higher, the values start becoming more dispersed

off of the regression line. In Figure 3, the deviation in velocity between the experimental velocity and the change in calibration needed is shown compared to the applied voltage. This graph shows more dispersed points than the previous 2 figures making it the least linear. The graph shows the relationship getting less and less linear as the voltage increases. Having these variations identified at specific voltages, it’ll be easier to find issues with calibration. Table 1 presents the potential issues as percent error values for both the slope (0.99% error) and intercept (57.22% error). The data calculated from problem 2 shows the relationship between data from the exponential and linear regressions that were used. The error found in the regression equations of shear velocity and bed roughness is higher in the linear regression where the natural logarithm of the elevation is taken than the exponential regression. This can be seen since two forms of analysis were used. In Figure 5, the partial velocity profile shown includes the data points under 10 cm and can be assumed to be more accurate than the full velocity profile in Figure 4 since there is a smaller profile to present. The reason for the full velocity profile being less accurate is because the exponential trend shows several values compared to one value. The most accurate presentation for bed roughness and shear velocity is calculated from an exponential regression equation with elevation under 10 cm. This will show a clearer and more precise exponential trend. Approximations can be useful to calculate data when a large set of information is given. In an open channel flow, the profile for the velocity is estimated with the law of the wall and is expressed linearly or exponentially. Comparing both sets of results together will give the most accurate data.