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The aim of this study is to test the practicality and legitimacy of Bernoulli's theorem, which describes the behavior of fluids in motion. We conducted experiments involving water flow in a round tapering pipe to determine the validity of the theorem. Through a review of existing literature and conducting our own experiments, we confirm the applicability of Bernoulli's theorem to fluid flow, with some minor variations attributable to measurement errors and environmental factors.
The Bernoulli theorem, proposed by Daniel Bernoulli in 1738, is a fundamental principle in fluid dynamics that describes the relationship between pressure, velocity, and elevation in a fluid in motion.
This theorem is essential in various fields of science and engineering, and its practical application is of great importance. In this study, we aim to investigate the validity of Bernoulli's theorem by conducting experiments on water flow in a round tapering pipe.
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The primary objective of this experiment is to affirm the validity of Bernoulli's theorem when applied to water flow in a round tapering pipe. We aim to determine whether the pressure, velocity, and elevation of the fluid remain consistent in laminar flow conditions.
Several studies have investigated the application of Bernoulli's theorem in various scenarios. Narciso (2015) found differences between theoretical and real head values, suggesting the hypothesis is true, but variations may arise from system defects or calculation errors. Another study by N et al. (2014) confirmed the validity of Bernoulli's theorem through computational fluid dynamics (CFD) research.
Martín Eduardo Saleta (2004) emphasized the importance of Bernoulli's equation with losses in various scientific and engineering applications.
The study we present aims to provide a simple and cost-effective approach to analyzing fluid drainage using the Bernoulli equation.
The experiment involved the following steps:
Several equations were used in the experiment:
| OBSERVATION NO | VOLUME (L) | TIME (SECONDS) | FLOW RATE (L/sec) | FLOW RATE (mm3/sec) | AVERAGE DISCHARGE (mm3/sec) |
|---|---|---|---|---|---|
| 1 | 3 | 35.15 | 0.085 | 85348.5 | 86095.55 |
| 2 | 3 | 34.83 | 0.086 | 86132.6 | 86095.55 |
| 3 | 3 | 34.56 | 0.087 | 86805.5 | 86095.55 |
| OBS.NO | TABLE NO | DIAMETER (mm) | AREA OF C/S (mm2) | Man. level (mm) | PROBE LEVEL (mm) | PROBE DST (mm) |
|---|---|---|---|---|---|---|
| 1 | a | 25 | 490.9 | 165 | 166 | 141.54 |
| 2 | b | 13.9 | 151.7 | 148 | 166 | 81.26 |
| 3 | c | 11.8 | 109.4 | 132 | 165 | 72.86 |
| 4 | d | 10.7 | 89.9 | 114 | 165 | 68.36 |
| 5 | e | 10 | 78.5 | 90 | 164 | 60.46 |
| 6 | f | 25 | 490.9 | 101 | 143 | 0.0 |
| TUBE NO | STATIC HEAD (mm) | VELOCITY (mm/sec) | EL. HEAD (mm) | EL. HEAD (measured) (mm) | VELOCITY (CALCULATED) mm/sec | TOTAL HEAD (MEASURED mm) | TOTAL HEAD (CALCULATED) |
|---|---|---|---|---|---|---|---|
| a | 165 | 175.7 | 1.57 | 1 | 140.1 | 166 | 9.4 x 10-3 |
| b | 148 | 567.5 | 16.4 | 18 | 594.3 | 166 | 0.026 |
| c | 132 | 786.9 | 31.56 | 33 | 804.6 | 165 | 0.040 |
| d | 114 | 957.68 | 46.74 | 51 | 1000 | 165 | 0.057 |
| e | 90 | 109.67 | 61.22 | 74 | 1204.9 | 164 | 0.079 |
| f | 101 | 175.38 | 1.57 | 42 | 207.76 | 143 | 0.047 |
The results of this experiment support the validity of Bernoulli's theorem in describing the behavior of fluid in a circular duct, particularly when friction is negligible. The pressure head and velocity head calculations show consistency, indicating that the hypothesis is accurate. However, small measurement errors and environmental factors may have influenced the results, leading to minor variations.
In conclusion, this experiment affirms the accuracy of Bernoulli's theorem when applied to fluid flow. Although slight discrepancies between actual and theoretical values may exist, they are primarily attributable to human errors and environmental influences. Overall, the experiment demonstrates that Bernoulli's hypothesis is valid under the given conditions.
Lab Report: Validating Bernoulli’s Theorem. (2024, Jan 04). Retrieved from https://studymoose.com/document/lab-report-validating-bernoulli-s-theorem
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