Lab Report: Flow Measurement

Lab Report: Flow Measurement

Introduction

The experiment of flow measurement apparatus aimed at demonstrating how to measure the discharge of an incompressible fluid using various methods, namely a Venturi meter, an Orifice plate meter, and Rotameter. This experiment has further explained how Bernoulli’s and Steady-Flow Energy principles are useful in understanding fluid flow. These principles or equations were used to define and determine the head losses of each method or meter. The comparison of the results obtained was based on two TecQuipment hydraulic benches, namely HlD and Hl, that provides the basis of flow rate evaluation and liquid services (Yang, 2018).

Fig. 1: Showing an apparatus for flow measurement (Source: TecQuipment Ltd, 2010).

Thus, a flow measurement experiment was carried out to check the fluid velocity over the cross-sections, as shown in Fig. 2, to deduce the flow rate across each cross-section. This experiment aimed at exploring an incompressible fluid flow discharge using a rotameter, an orifice meter, and a Venturi meter. This experiment also determined the characteristics of the three metering devices and how accurate they measure the flow rate. Understanding head loss, mass flow rate, and volumetric discharge concepts are essential for drawing comparisons on the accuracy of the three metering devices. Lastly, the rates of head loss in the right-angled diffuser and wide-angled diffuser against the Venturi, Orifice, and Rotameter meters were also determined.

Theory

Various theoretical dispositions have guided this experiment, with the first being the existence of pressure in the flow rate. Often, the flow rate is measured by checking the forces that are apparent in it, with the main force being the pressure, which is the force exerted per unit area either usually or perpendicularly (Bar-Meir, 2013). The pressure of system pressure is generally expressed as N/m². An incompressible fluid with a steady and adiabatic flow, along with stream experiment, was conducted, as illustrated below.

Fig. 2: Demonstrating steady flow energy equation (TecQuipment Ltd, 2010).

Fig. 2 demonstrates Bernoulli’s Equation for a steady flow of an incompressible fluid, which is written as;

……………………………..1

One of the assumptions made in this experiment is that the head loss, , arises due to[ stream vortices. Besides, there is an existing wall shear stress, which is caused by the viscous fluid flow; hence pressure is needed to overcome the viscous flow. The viscous flow should be overcome to reduce the increasing flow work. Often, in any section, there is a higher kinetic energy per unit mass    that Bernoulli’s Equation does not address. Despite this challenge, the head loss is one of the experimental parameters that can be assessed by any means. The reason being, stream boundaries with incompressible fluids often decrease due to a corresponding divergence but increases due to uniform flow, thus making head loss insignificant between two contracting duct endpoints, as illustrated in Fig. 3. In this experiment, the , together with  terms, are assumed to be negligible and thus does not have any significance on the fluid flow between the contracting duct ends,  . Therefore, discharge through the discharge is calculated using the equation;

………………………………………………….2

Where,

Fig. 3: Showing Orifice meter constriction

According to the University of Hull (2015), most fluids tend to flow from areas that are typically characterized by high pressure to areas that have low pressure. The inexistence of other forces during the process of flow often undermines the fluids flow rate. The inclusion of static pressure allows for the management of the fluid whenever it is not moving.  The static pressure works in tandem with the hydrostatic head to influence the impact of gravity on the fluid. Thus, the hydrostatic head is calculated using the equation below:

The second theory applied in the analysis of the flow rate is the fluid in motion disposition, which states that the flow can either come in the form of turbulent or laminar. Turbulent flow focuses on the irregular fluid flow while the laminar flow occurs when the fluid is moving smoothly. The turbulent flow is characterized by the changing nature of the speeds relative to fluid direction and magnitude. According to scientists, specifically, mechanical engineers often find it hard to transfer chemicals from one plant to the other due to the lack of knowledge on the turbulent and laminar flow rates. That is, they often fail to consider factors like the fluids flow rate to determine how they can transport these fluids through the use of the passing system. Two factors are used to determine the results of fluid, namely the fluid mass and volumetric flow rate.

University of Hull (2015) adumbrates that the flow of a liquid through a piping system is influenced by the velocity, which is described as vi (m.2). The mean velocity is then implemented in determining the cross-sectional area of the piping system. It is also used in assessing the impact of the area of the tube on the volumetric discharge. The second last theory is the head loss theory, which states that the loss of liquid in laminar flow is equal to velocity, as well as the fact that the velocity is inversely proportional to the friction factor. Head loss theory is used in evaluating the energy dissipated by the piping network as a result of friction. It takes into account the total number of energy losses that come from the length of the pipe and other factors like valves, fittings, and systemic structures (University of Hull, 2015).  The theory is divided into two sections, with the first analyzing the head loss that is caused by resistance from viscous forces that are extensive throughout the circuit length.

The second section evaluates the manner through which localized effects of installed equipment in the piping system can lead to heat loss and sudden changes in the expansion and contraction of the flow area. The overarching head loss combines both categories in the calculation process. Besides, the calculation often implements the interference caused by neighboring devices, especially in circuits that might pass as being complex (University of Hull, 2015).  The theory ensures that the difference between the total head loss and the estimated losses are included in the final tally.

The final theory is Bernoulli’s equation, which states that an influx in a fluid’s speed is often simultaneous to a decrease in the potential energy and the static pressure. The principle is usually applied to the fluid flow analysis, especially for incompressible flows. It follows the conversation of energy principle, which argues that the sum of every energy form in a fluid is the same at every pint in the streamline. The equation helps in determining whether the flow is laminar or turbulent with the internal, potential, and kinetic energy is calculated. It also states that an increase in the fluid’s speed will affect the potential energy and static pressure. In the case that the fluid is being channeled out of a reservoir, then the energy forms will be summed with the expected outcome being that they are equal everywhere (University of Hull, 2015). The principle follows the second law of motion formulated y Isaac Newton in evaluating the flow of fluids from different sections with divergent pressure levels. Lastly, it offers an insight into the net force exerted on the volume and how it decelerates or accelerates along a streamline.

Method

The experiment used three metering devices, namely the rotameter, the orifice plate meter, and the venturi meter shown in Fig. 4.

Fig. 4: Flow measurement set-up (Source: Lecture Lab. Manual, 2020).

in determining the manner through which an incompressible fluid is discharged. The flow measurement apparatus was inclusive of the three metering devices plus a wide-angle diffuser and a water loop, all of which were arranged in a series. The experimenter moved forth to connect the supply line of the fluid to the bench containing the volumetric hydraulic measuring device. This was momentous in ensuring that the flow rate was evaluated step by step without any interruptions in the supply line.

The researcher then analyzed the state of the experimental setup before starting the experiment. The first step in the analysis focused on evaluating whether the air purge valve in the apparatus had been switched off. The second step involved the closing of the valve, which controlled the H10, after which it was opened by a third. The hydraulic bench pump was put on with the regulator being opened. The researcher let the water to flow up until the moment the tool used for assessment was filled adequately. A hand pump was connected to the air purge valve with the water being pumped up until the moment that the manometer tubes had read 330 millimeters.

Any entrapped air in the experimental setup was then dislodged, with the water levels being set at a constant level. Recommendations from research highlight that the purge valve was bound to leak when and only if the water level would rise above the constant. The second step in the methodology was focused on the experimental procedure, wherein the researcher had to check on the viability and overarching efficiency of the systems put in place.

Experimental Procedure

After setting up the apparatus, the valve remained opened until the rotameter read about 10 mm. The flow was then maintained steadily, and this was measured using a hydraulic bench. The manometer readings were then recorded during this period and after that recorded onto the lab book, as shown in Table 1. The procedure was repeated10 times when the manometer registered the maximum pressure values.

Results

Results and Calculations

Sample Calculations (Test Number 1 data values)

1. Discharge calculation

The principle of operation of Rotameter, Orifice meter, and Venturi meter all depend on the Bernoulli’s Equation. As such, the experimental results were used to calculate every parameter as follows;

1. Calculating discharge for Venturi Meter

The Venturi meter discharge was calculated as;

Where;

Based on the test 1 data, the meter bores at (A) was 26mm and at (B) was 16 mm, thus,

g was assumed to be 9.81m.s^-2

were the manometric heights for pipe A and pipe B, respectively.

was the density of water and was taken as 1000kg/m3, then;

Therefore, the mass flow rate was found as;

From test 1 data, = 0.310 m and =0.306 m

1. Discharge for Orifice Meter

The orifice discharge was calculated between tapings E and F. For this Orifice meter, the coefficient of discharge, C, ass per BS1042 (1981) was 0.601. The water diameter at F was 20mm, while the bore diameter at E was 51.9 mm. Therefore, orifice meter discharge was computed as;

Where;

From test 1 data, = 0.308 m and =0.306 m

1. Head Loss Calculation

1. Calculating head loss of Venturi meter

Based on the experimental values in test result 1, the kinetic head of the inlet is given as;

But,

In the experiment, at

The kinetic head was therefore computed as;

Head loss was thus obtained as;

1. Calculating head loss of Orifice

The Orifice head loss was calculated from taps E and F by substituting the kinetic head with hydrostatic head. Therefore, as per BS1042-section 1.1 (1981), the orifice head loss can be obtained by approximation, which is usually taken as 0.83 times the head difference obtained.

Therefore;

But the diameter of the orifice is 51.9 mm, which is nearly double the diameter of inlet Venturi, which is 26mm. As such, the orifice inlet kinetic head can be estimated as  to that of Venturi as below;

Thus, head loss at orifice was given as;

1. Calculating head loss of Rotameter

The head loss at Rotameter was calculated as;

As such, the orifice inlet kinetic head can be estimated as  to that of Rotameter’s as below;

Thus, head loss at rotameter was given as;

1. Wide-Angled Diffuser head loss

The wide-angled diffuser head loss was calculated from tap points C and D.

Since  the value of

Head loss was thus obtained as;

1. Right Angle Bend

The Right-Angled bend head loss was calculated from tap points G and H were the bores were 51.9 mm and 40 mm, respectively.

At the inlet G, the kinetic head is

At the outlet H, the kinetic head is

Therefore,

Head loss was;

Discussion

These results were calculated based on test number 1 values. All the values calculated were dependent on the same principle; that is, the fluid flow through the cross-sectional area of systems. From the experiment, it can be demonstrated that both the Venturi meter and Rotameter’s discharge coefficients depended wholly on how the stream flow through a small cross-sectional area (Yang, 2018). This explains why the difference in the discharge range between Rotameter and Venturi meter is insignificant. The extreme value of head loss of Rotameter could also be attributed to its incompactness, which thus reduced its capacity and ability to provide accurate or anticipated discharge range.

Based on the head losses, it is clear that the internal flow systems of both Rotameter and Venturi meter were more significant, at 2485 and 2.9869 inlet kinetic heads, respectively than that of Orifice meter that remained at 0.04185. These considerable losses are attributed to the difficulty in containing the expanding streams of both Rotameter and Venturi meter. For these reasons, it is always essential to consider the directions of flow changes as well as the cross-sectional areas expansions for both Rotameter and Venturi meter as the most presumably responsive meters as far of the systems as far as their head losses are concerned (Monni et al., 2014). This consideration would help improve the functionality of these systems, thereby reducing head losses.

Moreover, the head loss produced by Rotameter is hugely more significant than those produced by other meters, which is primarily attributed to its extreme discharge range. Additionally, there are typical head losses generated by the right-angled bend and the wide-angled diffuser of the Rotameter, which can be reduced by selecting the desired angle. For example, one can lower the diffuser head loss angle of 45^o to 15^o to minimize the head loss. Similarly, it is possible to achieve a sustainable bend loss by reducing the right-angled bend to a desirable angle, such that the stream flows or the arc shapes do not result in considerable losses.

Conclusion

The objectives of this experiment were achieved; for example, the discharge range for both Rotameter and Venturi meter was insignificant. However, it can be concluded that the Rotameter results showed high sensitivity of 103.19 inlets kinetic head loss when it closer to bend (elbow than at a right angle, which could be attributed to high inlet velocity distribution. Similarly, the sensitivity of the orifice was noticed at the inlet flow, which is associated with the differently induced upstream at the wide-angle diffuser. On the same note, Venturi meter still showed negligible variation due to its vena contracta anticipated assumption.

Reference List

Bar-Meir, G 2013, Basics of fluid mechanics. Chicago, IL: Bar-Meir.

Ganchev, V 2017, ‘About the calibration of rotameter’, Recent, Vol. 18, no. 3(53), pp. 184-188.

Monni, G., De Salve, M., and Panella, B., 2014. Two-phase flow measurements at a high void fraction by a Venturi meter. Progress in Nuclear Energy, 77, pp.167-175.

Yang, L., 2018. Analysis Of Pressure Distribution Along Pipeline Blockage Based On The Cfd Simulation. University of Hull, 2015, Laboratory exercise. Hull: University of Hull Press.