Venturi Meter Analysis: Fluid Flow & Discharge Coefficient

Abstract:

This experiment aims to analyze and understand the properties of fluid flow in a convergent-divergent section, such as a venturi meter, which is used to measure flow rates. The continuity equation and Bernoulli's principle are investigated, with practical implications. Water, an incompressible fluid, is used as the working medium. The experiment maintains constant inlet and throat areas. Flow rates are measured, and pressure values at the throat and inlet are recorded. The relationship between different parameters is graphically presented.

Introduction:

Fluid flow analysis is essential in understanding the behavior of fluids within various engineering systems.

In this experiment, we aim to analyze and comprehend the properties of fluid flow in a convergent-divergent section, specifically using a venturi meter. Venturi meters are widely employed to measure flow rates of fluids, making them a crucial component in industries ranging from water supply to aerospace engineering.

The primary objectives of this experiment are to investigate the continuity equation and Bernoulli's principle in a practical context.

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We utilize water as our working fluid due to its incompressible nature, allowing us to study the fundamental principles of fluid dynamics.

The experiment maintains constant inlet and throat areas to isolate variables and focus on the relationship between different parameters. We record pressure values at the throat and inlet, measure flow rates, and represent the findings graphically.

Observations and Calculations:

The areas of the inlet and throat remained constant during the experiment.

Flow rate (Q) is calculated as:

Q = Quantity / Time

Given values:

D1 = 31.8 x 10^-3 m

D2 = 15.0 x 10^-3 m

A1 = 793 x 10^-6 m²

A2 = 176 x 10^-6 m²

Raw data for flow rate and pressure heads:

Flow Rate and Pressure Difference:

Using the value of flow rate, velocities at different points along the venturi meter are calculated:

Q = A1 * V

So V1 = 0.0053 / (793 x 10^-6 m²)

V1 = 6.683 m/s

V2 = 0.0053 / (176 x 10^-6 m²)

V2 = 30.11 m/s

From the observations and calculations, the continuity effect is verified, as the area of the venturi meter decreases, the velocity of the fluid increases, and vice versa.

Since Q actual = 0.0053 m³/s, the discharge coefficient (Cd) is calculated as:

Cd = Q actual / Q theoretical

For the 4th observation:

Q theoretical = 0.00466 m³/s

Cd = 0.8358

For the 7th observation:

Q theoretical = 0.0035 m³/s

Cd = 0.42

Results:

The pressure head decreases along the throat area, while the velocity increases. This confirms the Bernoulli equation's principle, where pressure decreases as velocity increases, and vice versa. Theoretical flow rates are calculated using basic mathematical equations with given parameters and compared with actual flow rates. The ratio between the two is called the discharge coefficient (Cd). The Cd decreases as the pressure head at the inlet decreases, which is consistent with the experiment's expectations.

Conclusion:

From the data and calculations, it is concluded that a drop in pressure occurs when velocity increases, and velocity is lower where pressure is high, confirming the Bernoulli equation's behavior. The discharge coefficient decreases with decreasing pressure head at the inlet, as theoretically expected. Theoretical calculations suggest a Cd of around 0.25 based on the throat and inlet areas.

References:

1. R. A. Serway, “Bernoulli’s Principle – 'Physics for Scientists and Engineers',” Saunders College Publishing, pp. 422, 434, 1996.
2. M. Belevich, “On the continuity equation,” Journal of Physics A: Mathematical and Theoretical, Published 28 August 2009 • 2009 IOP Publishing Ltd.
3. Christian Seis, “A quantitative theory for the continuity equation,” Institut für Angewandte Mathematik, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany, pp. Volume 34, Issue 7, December 2017, Pages 1837-1850.
4. A. H. Meshal, “Comparison of discharge coefficients over water,” Atmosphere, 08 Nov 2010.

Coefficient of Discharge vs Pressure Head:

Pressure Head and Flow Rate: