Summary

The objectives of the experiment is to study the validity of the Bernoulli equation and to determine the coefficient of discharge, Cd, by calibrating the venturi tube as a flow meter. To investigate the validity of the Bernoulli equation, the static pressure is taken at each tapping and the total head is determined for the maximum difference setting. The velocity head is calculated using the Bernoulli equation. To calculate Cd, the volumetric flow rate is measured for the maximum and minimum settings and for eight intermediate values. From the experimental analysis, it can be deduced that the total head does not remain constant due to frictional losses and experimental errors and thus the Bernoulli equation is not obeyed. The value of Cd calculated from figure is 0.92, close to the actual value, within experimental errors.

Introduction

The flow along a venturi tube is another simple application of Bernoulli’s equation. The principle of the venturi meter was demonstrated in 1971 by the Italian Giovanni Battista Venturi (1746- 1822) but it was not until 1887 that the principle was applied by the American Clemens Herschel (1842- 1930), to a practical instrument for measuring the rate of flow of a fluid. The device consists essentially of a convergence in pipe- line, followed by a short parallel- sided throat and a divergence, called as a diffuser. Venturi meters are one among the many flow meters used in industries to measure flow rate. They are widely used in large diameter pipes such as those found in waste treatment plants.

The aims of the experiment is to check the validity of the Bernoulli equation when applied to the steady flow of water in a tapered duct and to calibrate the venture as a flow meter to determine the coefficient of discharge, Cd.

The total head for the maximum difference setting was calculated and was found to be 0.2675m. From the experimental results, it was deduced that the theoretical and actual values differ due to the limitation of the Bernoulli equation and experimental errors. The value Cd determined is 0.92 close to the actual value within experimental errors.

Experimental Methods

Equipment

1.A hydraulic bench is used which contains a water tank, the sump, which supplies the experimental equipment mounted on it.

2.A venturi tube is set horizontal in which six holes are drilled.

3.Each hole in the venturi tube is connected to a manometer. The tubes of the manometers are placed in front of a scale to record the level of water in the tubes.

4.A one litre measuring cylinder is used to measure the volume of water collected.

5.A stopwatch is needed to measure the time over which a specific volume of water is collected.

Procedures

1.It is ensured that the venturi tube is set horizontal.

2.The outlet valve is opened to fill the whole system with water and it is ensured that no air bubble is trapped within the tube.

3.The water flow is adjusted to obtain the maximum head difference in manometers h6 and h5 corresponding to the inlet and throat. Readings of the water level in all manometer tubes are taken including the total pressure.

4.The flow rate is determined at this maximum setting.

5.The flow rate is reduced to obtain the minimum difference in pressure head between the inlet and the throat. The flow rate is measured at this setting.

6.The pressure difference is determined for eight intermediate values between the maximum and minimum readings. The flow rate is also determined for these eight intermediate values.

Materials

The raw material used in this experiment is water only. Water is used as the working fluid for ease of use and also because of its low viscosity.

Discussion

1.Figure 1, which displays the graph of total head against distance from inlet, it can be deduced that the total head decreases non linearly along the venturi tube. Figure 2 also shows a...