Fluid Mechanics(1)

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Fluid Mechanics Lab. ENME 312 The objective of Fluid Mechanics Lab would be able to:

• Name different types of flow meters, frequently used in industry. • To understand the basic principle of operation of head type flow meter. • To distinguish the constructional differences between orifice meter and venturi meter and

Rotameter. • To calculate the actual mass flow rate by dividing the mass or volume flow rate by time. • To calculate the theoretical flow rate of water from the pressure difference of both venturi

and orifice devices. • To compare between actual and theoretical flow rate through the discharge coefficient

concept. • To investigate the characteristics of radial pump such as head, flow rate, mechanical,

electrical power and efficiency. • To observe the circumstances under which a floating body is stable and unstable. • To understand the hydrostatic pressure distribution and to verify the location of center of

pressure. Methods of measurement of flow rate of liquids and gases Accurate measurement of flow rate of liquids and gases is an essential requirement for maintaining the quality of industrial processes.

1. Head (or obstruction) type (differential pressure or variable area) 2. Inferential or turbine type. the product to be measured is pumped through the meter

where it drives a turbine suspended within the flow. The rotation of the turbine is proportional to the volume passed through it for a given set of temperature, pressure and flow rate values.

3. Electromagnetic. Often called "mag meter"s or "electromag"s, use a magnetic field applied to the metering tube, which results in a potential difference proportional to the flow velocity perpendicular to the flux lines. The potential difference is sensed by electrodes aligned perpendicular to the flow and the applied magnetic field. The physical principle at work is Faraday's law of electromagnetic induction.

4. Positive displacement (integrating), PD. PD flow meters measure the volumetric flow rate of a liquid or gas by separating the flow stream into known volumes and counting them over time. Vanes, gears, pistons, or diaphragms are used to separate the fluid. PD flow meters provide good to excellent accuracy and are one of only a few technologies that can be used to measure viscous liquids.

5. fluid dynamic (vortex shedding). Anemometer. Ultrasonic Mass flow meter (Coriolis). and others.

Hydraulic bench Hydraulic bench is a very useful apparatus in hydraulics and fluid mechanics. It consists of a molded plastic sump tank which supports Glass-fiber Reinforced Polyester, (known as GRP) bench top incorporating a flow channel and volumetric measuring tank and is mounted on wheels. A centrifugal pump discharges water from the sump tank and delivers to a top measuring tank, then water drains and return to sump tank through flow channel and control valve. Flow control valve and by-pass valve are fitted in water line to conduct the experiment on different flow rates. Flow rate of water is measured with the help of measuring tank and stop watch. A dump valve in the base of the measuring tank is operated by a remote actuator. Lifting the actuator opens the dump valve allowing the water to return to the sump for recycling.


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Fig 1: Hydraulic bench

Head type flow meter The head or obstruction type flow meters are of two types: differential pressure type and variable area type. Orifice meter, Venturi meter, Pitot tube fall under the first category, while rotameter is of the second category. In all the cases, the head or obstruction is created in the flow passage and the pressure drop across the obstruction is related with the flow rate. Bernoulli’s Equation: For an incompressible fluid ρ is constant, Bernoulli’s Equation is:

HZg

P2gu2

=+ρ

+ 1

HZg

P2guZ

gP

2gu

22

22

11

21 =+

ρ+=+

ρ+ 2

Each of the three terms on the left-hand side is measured in m H2O:

• The term 2gu2

is referred to as the Dynamic Head (also known as Kinetic or Velocity

Head), represents the kinetic energy of fluid per 1 kg.

• The term g

Pρ

is referred to as the Pressure Head and represents the energy per 1 kg of

fluid required to raise the pressure by an amount equal to P. The term ρg is the gravity force or the weight per unit volume, the specific weight.

• The term Z represents the elevation of the fluid above some datum level and represents the potential energy of the fluid per 1 kg measured from this datum.

• The term H is a constant usually called the Total Head.

It is sometimes convenient to refer to the sum of the terms ( Zg

Ph +ρ

= ) as the piezometric

head or the Static Head, h, in which case the Bernoulli’s equation may be written in the form of Total Head is equal to the Static Head plus Dynamic Head.

2guhH

2+= 3


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Fig. 2: Total Head, Static head and Dynamic Head for flow of a fluid through a pipe. Measuring steady flow rate by the volume or mass–time method The flow rate measurement requires a container to capture the entire flow, a scale to measure the volume or mass of flow of the captured fluid, and a stopwatch to measure the time it takes to capture a quantity (volume or mass) of fluid. The method is quiet simple. If in a given time Δt in s, the conduit issues a quantity of fluid having a volume V in m3 into the container, and if the flow is steady, then the volume flow rate Q is:

t

VQ∆

= 4

Therefore, volume flow rate Q is measured as meter cube per seconds.

s

mQ3

= 5

The mass flow rate m& , is calculated as the product of density multiplied by volume flow rate,

ρ×= Qm& ……… 3

3

mkg

smm ×=& 6

Therefore, mass flow rate m& is measured as kilograms per seconds.

s

kgm =& 7

Pitot Tube The Pitot (pronounced pee-toe) static tube system is an ingenious device used by airplanes and boats for measuring forward speed. The device is really a differential pressure gauge and was invented by Henri Pitot in 1732. A schematic of a Pitot tube and an example of an air pressure gauge is a tire pressure gauges are shown below, Fig. 3. The Pitot tube measures a fluid velocity by converting the kinetic energy of the flow into potential energy, which it takes place at the stagnation point, located at the Pitot tube entrance. Its basic principle can be understood from Fig. 4, where the velocity of fluid at the entrance point will be zero. Then considering the fluid to be incompressible, from eqn. 3 and multiplying the equation by ρg


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Fig. 3: Typical Pitot Static tube & tire pressure gauges

+×ρ=×ρ h2gugHg

2

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Knowing that Total Pressure Pt = ρgH and Static Pressure Ps = ρgh, we have:

{ }st PP2u −×ρ

= 9

Fig. 4: Cross-section of a Typical Pitot Static Tube

Rotameter: The rotameter is an industrial flow meter used to measure the flow rate of liquids or gases. It consists of a vertical tapered tube and float, Fig. 5.

Fig. 5: Rotameter


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Principle of Operation The rotameter's operation is based on the variable area principle: fluid flow raises a float in a tapered tube, increasing the area for passage of the fluid. The greater the flow, the higher the float is raised. The height of the float is directly proportional to the flowrate. The float moves up or down in the tube in proportion to the fluid flowrate and the annular area between the float and the tube wall. The float reaches a stable position in the tube when the upward force exerted by the flowing fluid equals the downward gravitational force exerted by the weight of the float. A change in flowrate upsets this balance of forces. The float then moves up or down, changing the annular area until it again reaches a position where the forces are in equilibrium. Multi Tube Manometer and U Tube Manometer

Fig. 6: Multi Tube Manometer

Fig. 7: Venturi Meter and Multi Tube Manometer


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Fig. 8: Venturi Meter and U Tube Manometer


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Laboratory Report Format The purpose of this lab is not only to apply your understanding of Fluid Mechanics to a simple experiment but also to give you practice in communicating your findings. As such, the quality of the writing will be evaluated in terms of grammar, spelling, clarity, organization, and legibility of figures and tables. The report should be understandable to someone who is not necessarily familiar with the specifics of the lab. The quality of the writing will count for at least half of your grade. Reports must be typed double-spaced with suitable margins. Please use only one side of the page, normal white paper. The following format is required for the organization of the Formal Report:

• Title Page • Abstract • Objective • Theory • Exp. Procedure • Sample Calculation. • Results and Analysis • Discussion and Conclusions • Appendices (pre-lab, Original data sheet,)

Fig. 9: Format for Technical reports and Formal Reports Title Page The Title Page should include the title of the lab, number of the experiment, experimenter’s name and experimenter's partners' names, as well as the date on which the lab was performed. Please make this a separate page. Abstract: An abstract should be one paragraph of 100-200 words. It summarizes four essential aspects of the experiment or report: the purpose, key findings, main significance, and major conclusions. Abstract is important because they give a first impression of the document that follows, letting


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readers decide whether to continue reading and showing them what to look for if they do. It is a description of an entire document, so you can write an abstract only for a document that is complete. An abstract is a succinct overview of the main elements of an experiment. It also must be clear enough so someone who is unfamiliar with your experiment could understand why you did what you did, and what the experiment indicated in the end. It explains why the experiment was performed and what conclusions were drawn from the results obtained. Typically, an informative abstract answers these questions: • Why did you do this study or project? • What did you do, and how? • What did you find? • What do your findings mean?

Objectives Describe the specific actions you are being asked to perform in the lab, such as measure something, analyze something, test something, etc. Objectives are the activities you are being asked to do in order to complete the lab experiment. Be sure to list them as such: to measure, to analyze, to determine something. Theory The theory section should contain a complete analytical development of all important equations pertinent to the experiment, and how these equations are used in the reduction of data. The theory section should be written textbook-style. Calculations: The calculations take you from the data to the final result. If many similar calculations are involved, just include one sample calculation in detail. It's a good idea to write out all the formulas you use in your calculations. Personally, I like to work through the problem using just the formula, and then plug in the numbers at the end to get my final answer. One more point is to be sure to include the units when you are doing a calculation, and don't drop the units halfway through the calculation. Include the errors in raw data and the final result. Results and Analysis In the Results and Analysis section, you should summarize and explain the results of the experiment, including Tables and Graphs. This section should be strictly factual, pointing out agreement and discrepancies between your results and those predicted by theory. All numerical results should be non-dimensional or reported in SI units. This is where most of the items you calculate and plot in the "Required Calculations and Analysis" section should go. Discussion and Conclusions For the Discussion and Conclusions, examine whether the lab satisfies the stated purpose, explaining what you have learned. Also postulate why any differences might have arisen between the theoretical (or standard experimental) values and your own results. Appendix The Appendices should contain • Original data sheet. • Relevant information that is not in the body of the lab report, such as the pre-lab, the and

details of calculations made both in lab and as part of your data analysis. • Bibliography listing all references used.


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Technical Report:

• Title Page • Abstract • Objective • Sample Calculation. • Results and Analysis • Discussion and Conclusions • Appendices (pre-lab, Original data sheet,)

Example of writing a Table and plotting a Graph Result Table 1: The measured and theoretical values of mass flow rate against head

Time

Mass Flow

Head Mass Flow Rate

Inlet Outlet Head Dif t m H H DH mth mact

s kg cm H2O

cm H2O m H2O kg/s kg/s

0 0 0 100 6 68 58 0.1 0.08 0.06

85.71 9 0.2 0.13 0.105 9 0.3 0.16 0.133 12 0.4 0.185 0.155 12 0.5 0.21 0.148 12 0.6 0.23 0.195 12 0.7 0.245 0.209 12 0.8 0.255 0.216

54.29 12 0.9 0.26 0.221 53.33 12 1 0.262 0.225

Fig. 10. Theoretical and actual mass flow rate through a venturi meter as a function of head loss.

s/kg,m&


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Report Format and Grading Formal Report Technical Report Report Format 5 5 Abstract 10 10 Objective 5 5 Theory 10 Exp. Procedure 5 Calculations 15 20 Results 15 20 Discussion of Results 10 15 Appendices & References 5 5 Total 80 80 Quiz 20 20 Total 100 100

Fluid Mechanics(1)

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