Lab Report: Validating Bernoulli’s Theorem

Categories: Physics

Report, Pages 3 (656 words)

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Abstract

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.

1. Introduction

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.

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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.

1.1 Objective

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.

1.2 Literature Review

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.

2. Equipment

Stopwatch
Hydraulic bench
Bernoulli’s theorem demonstration apparatus

3. Methodology

The experiment involved the following steps:

Purge the system of air by allowing air to run through the apparatus.
Adjust the valve opening to various flow rates to collect data for laminar, development, and turbulent flow conditions.
Fill the beaker with water and record the time taken for the beaker to fill.
Measure the readings for both the manometer and the sensor manometer for different flow behaviors.
Record the distance from the end of the parallel location for each flow condition.

4. Equations

Several equations were used in the experiment:

Area (mm²)
Calculating Velocity head (mm/sec)
Calculating total head (mm)
Calculating Velocity (mm/sec)
Static head (mm)
Total Head

5. Results

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

6. Discussion

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.

7. Conclusion

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.