# Bernoulli's Theorem

**Topics:**Fluid dynamics, Bernoulli's principle, Pressure

**Pages:**5 (1420 words)

**Published:**March 7, 2013

ABSTRACT / SUMMARY

The main purpose of this experiment is to investigate the validity of the Bernoulli equation when applied to the steady flow of water in a tape red duct and to measure the flow rate and both static and total pressure heads in a rigid convergent/divergent tube of known geometry for a range of steady flow rates. The apparatus used is Bernoulli’s Theorem Demonstration Apparatus, F1-15. In this experiment, the pressure difference taken is from h1- h5. The time to collect 3 L water in the tank was determined. Lastly the flow rate, velocity, dynamic head, and total head were calculated using the readings we got from the experiment and from the data given for both convergent and divergent flow. Based on the results taken, it has been analysed that the velocity of convergent flow is increasing, whereas the velocity of divergent flow is the opposite, whereby the velocity decreased, since the water flow from a narrow areato a wider area. Therefore, Bernoulli’s principle is valid for a steady flow in rigid convergent and divergent tube of known geometry for a range of steady flow rates, and the flow rates, static heads and total heads pressure are as well calculated. The experiment was completed and successfully conducted.

INTRODUCTION

In fluid dynamics, Bernoulli’s principle is best explained in the application that involves in viscid flow, whereby the speed of the moving fluid is increased simultaneously whether with the depleting pressure or the potential energy relevant to the fluid itself. In various types of fluid flow, Bernoulli’s principle usually relates to Bernoulli’s equation. Technically, different types of fluid flow involve different forms of Bernoulli’s equation. Bernoulli’s principle complies with the principle of conservation of energy. In a steady flow, at all points of the streamline of a flowing fluid is the same as the sum of all forms of mechanical energy along the streamline. It can be simplified as constant practices of the sum of potential energy as well as kinetic energy. Fluid particles’ core properties are their pressure and weight. As a matter of fact, if a fluid is moving horizontally along a streamline, the increase in speed can be explained due to the fluid that moves from a region of high pressure to a lower pressure region and so with the inverse condition with the decrease in speed. In the case of a fluid that moves horizontally, the highest speed is the one at the lowest pressure, whereas the lowest speed is present at the most highest pressure.

AIMS / OBJECTIVES

1. To investigate the validity of Bernoulli equation when applied to asteady flow of water in a tapered duct.2. To measure flow rate and both static and total pressure heads in a rigid convergent / divergent tube of known geometry for a range of steady flow rates.

THEORY

The specific hydraulic model used in this experiment is Bernoulli’s Theorem Demonstration Apparatus, F1-15 The test section, which is provided with a number of hole-sided pressure tapings, connected to the manometers housed on the rig, is indeed an accurately machined clear acrylic duct of varying circular cross section. The tapings allow the measurement of static pressure head simultaneously. A flow control valve is incorporated downstream of the test section. Flow rate and pressure in the apparatus may be varied independently by adjustment of the flow control valve, and the bench supply control valve. Consider a system whereby Chamber A is under pressure and is connected to Chamber B, which is as well under pressure. The pressure in Chamber A is static pressure of 689.48 kPa. The pressure at some point, x along the connecting tube consists of a velocity pressure of 68.95 kPa exerted 10 psi exerted in a direction parallel to the line of flow, plus the unused static pressure of 90 psi, and operates equally in all directions. As the fluid enters chamber B, it is slowed down, and its velocity is...

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