Experiment 4-Ideal Fluid Flow

ADAMSON UNIVERSITY

ADAMSON UNIVERSITY COLLEGE OF ENGINEERING CHEMICAL ENGINEERING DEPARTMENT

Chemical Engineering Laboratory 1 Experiment No. 4 IDEAL FLUID FLOW

Submitted by: Group 3 Apacible, Cyrus Basco, Brenda Leah Belason, Verna L. Dizon, Ma. Carolina Reyes, Aldrin Marc

Submitted to: Engr. Rowena Carpio

July 30, 2012

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ADAMSON UNIVERSITY ABSTRACT

In this experiment, entitled “Ideal Fluid Flow” demonstrated the fluid flow associated with sinks and sources in a two-dimensional plane specifically the formation of Rankine “half body”, Rankine Oval, and Doublet with the used of Laminar Table Flow. Fluid mechanics as a highly visual subject deals with the behavior of fluids at rest or in motion and its interaction with solids or other fluids. Fluids which have no viscosity; surface tension and they are incompressible called ideal fluid. If the ideal fluids no resistance is encountered as the fluid moves. Rankine full body and Rankine half body, Doublet are the combination of simple flow patterns which defined the stream functions and velocity potential functions, rotational and irrotational flows in two dimensions, and the designation of source, sink, vortex, circulation. The Laminar Flow Table is important equipment for fluid mechanics and hydraulics laboratories which used for flow visualization. Important technique in fluid mechanics and is used to recognize the flow patterns around bodies of interest. It is floor mounted equipment designed to show the ideal flow streamline flow patterns. The flow principle behind this experiment is the Hele Shaw flow principle. The working section, upstream and downstream ends, is connected to the inlet and discharge tanks. In general, water is used as effective fluid and is allowed to flow over the equipment. Colored dyes or tetrachloride solvents are injected into the flow to visualize streamline patterns.

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ADAMSON UNIVERSITY LETTER OF TRANSMITTAL

July 30, 2012

Engr. Rowena Carpio Chemical Engineering Department Adamson University Ermita, Manila

Engr. Carpio: In compliance with the fulfillment of the requirements on the subject “ChE Lab 1”, the group would like to present this experiment report entitled “Ideal Fluid Flow” in accordance with your instructions. The main purpose of this experiment report is to determine the air pressure differential as a function of air flow rate down the dry column and also as a function of air flow rate for different water flow rates. We hope that this experiment report will meet you approval.

Respectfully Yours, Group 3 Apacible, Cyrus Basco, Brenda Leah Belason, Verna L. Dizon, Ma. Carolina Reyes, Aldrin Marc

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ADAMSON UNIVERSITY I.

OBJECTIVES To demonstrate fluid flow associated with sinks and sources in a two-dimensional

plane specifically the formation of Rankine “half body”, Rankine Oval, and Doublet. II.

MATERIALS / EQUIPMENTS:

1.

Laminar Flow Table

2.

Water Soluble Dye

3.

Water

III. EQUIPMENT SET UP:

Schematic diagram showing pipework for one sink and source

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Laminar Flow Table

IV. THEORY: Ideal fluids are those that have zero viscosity. They are inviscid fluids which experience no resistance to movement, either past solid objects or past adjacent portions of the fluid that are moving at different velocities.

In analyzing of fluid flow it is useful to visualize the flow pattern. This can be done by drawing stream lines joining points of equal velocity - velocity contours. A useful technique in fluid flow analysis is to consider only a part of the total fluid in isolation from the rest. This can be done by imagining a tubular surface or stream tube formed by streamlines along which the fluid flows.

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ADAMSON UNIVERSITY The applicability of a two-dimensional approximation is improved by two additional effects: the stratification of the medium and the rotation of the earth, which tends to reduce variations in the vorticity field with height and means that in any cross-sectional plane, the flow is effectively two-dimensional. In such circumstances a two-dimensional approximation to the fluid motion can provide very accurate insights into the behavior of the physical system.

The two- and three-dimensional fluids behave in qualitatively different fashions. In three-dimensional flows energy typically flows from large-scale features to small ones until it is dissipated by the viscosity of the fluid while in two dimensional fluids the phenomenon tends to reverse itself, and the energy concentrates itself in a few large vortexlike structures. The stream function, ψ, is a function of x and y it is defined in terms of flow velocities as

On line of constant ψ, dψ=0, and the equation can be arranged to solve for the slope as

Potential Factor, Ø, is defined in terms of equation,

On a line of constant, Ø, dØ=0 equation can be arrange to solve for slope as,

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ADAMSON UNIVERSITY Combining slope equation of stream function and Velocity potential yields,

At any point (x,y) in a flow field the stream line is normal to the potential line as shown in the figure

Orthonogality of stream lines and potential lines V.

PROCEDURE:

1.

Level the working area using the screw adjusting feet provided. The level may be

accurately checked using a spirit level on the lower glass laid normal, parallel, and diagonal to the direction of flow. 2.

Clean the inside surfaces of the glass plates using a de-greasing solvent such as

carbon tetrachloride. 3.

Close the entire sink and source taps and the drain cocks on the inlet and outlet tanks.

4.

Ensure that the water supply and drain facilities are connected.

5.

Start water flowing through the apparatus and adjust the inlet valve, bypass valve and

downstream overshot weir to give a depth of flow approximately level with the bottom face of the top glass.

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ADAMSON UNIVERSITY 6.

Lower the top glass to make the final adjustment to the flow and level control weir.

This operation must be performed carefully to ensure that air bubbles are eliminated from the space between the glass plates. The leading edge of the top glass plate should coincide with the leading edge of the bottom plate. With water flowing across the apparatus and the flow and depth adjusted as describe above, the front edge of the glass is lowered slowly into position pivoting about rear edge. The water surface should contact the lower surface of the glass progressively to ensure complete air expulsion. Failure to exclude air may be due to the ff causes: (a) Depth of water is insufficient. (b) Dirt or grease on glass, (c) source or sink not fully closed, and (d) Rapid or uneven lowering of the glass. 7.

Remove air in the sink or source line by opening the valves and flushing the lines

through. Air bubbles introduced between the glass plates through the source line may be removed as described in procedure 6. 8.

Clean the fine tubes of the injector by flushing water through it. Passing fine wire

along the tubes may clear any blockages. 9.

Fill dye reservoir with a water dye and open regulating valve.

10. Ensure that the dye rake discharges are submerged and that dye flows freely from each rake. 11. Blockages caused by air bubbles may be relieved by a light tap or by pressurizing the free surface of the dye in the reservoir. 12. Determine the flow rates associated with each of the source or sink orifices in the floor of the working section. Measurement of the sink flow rate is determined by removing the sink drain pipe from the sink manifold and collecting the discharged water in a measuring cylinder. During this operation the corresponding source control valve should be fully closed and the orifice pinch clip fully open. Measurement of the source flow rate is determined via a sink drain pipe in the same way. During this operation the corresponding sink control valve should be fully open and the orifice pinch fully close. After measurement, the sink control should be fully closed and the pinch clip fully opened. 13. Adjust the weir plate, inlet control valve, and bypass valve to give the minimum steady flow rate available, without admitting air between the glass plates. The

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ADAMSON UNIVERSITY corresponding low water velocity through the test section will provide near-ideal flow conditions. 14. Open and adjust the dye-regulating valve to give fine, clearly defined dye streams, which indicate relevant streamlines. 15. To form a pattern known as Rankine “half body”, introduce flow from a central source orifice by opening the respective control valve. Separation of the central dye streams is semi-infinite provided the source flow rate is constant. The source flow rate may be adjusted to demonstrate the change in size of the body produced. 16.

To form a pattern known as “Rankine Oval”, repeat procedure 16 with the addition

of a sink downstream of the source. As the flow rate of the sink increased, the half body is modified in shape. When the source and sink flow rates are equal, the streamlines close to produce a Rankine Oval. 17. To form a Doublet, introduce flow from a central orifice on the table, which are in fact two orifices in close proximity such that a coincident sink and source can be demonstrated. The result is a circular streamline surrounding the Doublet, which acts like a solid cylindrical boundary to external flow. Within this boundary, circulation patterns exist which may be demonstrated by introducing a few crystals of potassium permanganate. This effect is an extension of rankine oval with sinks and source coincidence. 18. Repeat procedures 15 to 17 for different combinations of sinks, sources and flow rates. 19. After the experiment, the whole system must be flushed through with clean water to remove traces of dye.

VI. RESULTS AND DISCUSSIONS: In rankine half body performed by opening the central control source, considered the flow pattern generated by a source located at the origin in a uniform laminar flow while the rankine oval obtained if the rankine half body is closed by means of sink of equal strength downstream of the source. The figure below showed the difference of flow patterns between of rankine oval and rankine half body.

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ADAMSON UNIVERSITY Rankine Half Body

Rankine Oval

A doublet is located at the centre of the pattern. This is obtained from the combination of two vortices in equal strength but opposite direction and equidistant from the origin in a uniform flow. The direction may be clockwise, and counter clockwise. The figure had shown below.

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ADAMSON UNIVERSITY VII. CONCLUSIONS: In this experiment, a trial and error process in opening, draining and adjustment of flow in the sinks applied until the desired pattern is obtained. The Rankine "half body" was performed by opening the central control source. The Rankine oval was performed by opening the sink downstream of the source same condition as in the "half body". Doublet pattern was performed by introducing flow from 2 sources and 2 sinks orifice that are coinciding. The carbon tetrachloride is injected through the equally spaced needles to visualize the flow of water between the glass plates and the position of each streamline is clearly indicated. Failure to eliminate bubbles in the working area causes disturbance on the flow pattern during the experiment. The diffuser in the inlet tank and adjustable weir plate in the discharge tank help to promote a uniform flow of water. Based on the given different combinations of the sink and sources during the experiment, the different flow patterns for the fluid flow was demonstrated and attained. By adjusting the specified sources and sinks, variety of size, shape and different combinations of flow patterns can be visibly observed.

VIII. REFERENCES:

McCabe, W. L., Smith, J. C. & Harriot, P. (2006). Unit Operations of Chemical Engineering. 7th ed. Published by McGraw-Hills Education (Asia). Geankoplis, Christie, (1993). Transport Processes and Unit Operations.3rd Ed. Published by Prentice Hall PTR

Eugene, W. Vortices and Two-Dimensional Fluid Motion

Fall, (2001), Stream Functions and Potential Velocity

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ADAMSON UNIVERSITY APPENDICES

Appendix A: Experimental Data

Rankine Half Body

Rankine Oval

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Doublet

Appendix C: Attendance Sheet

Name:

Student no.

1. Apacible, Cyrus

2007

2. Basco, Brenda Leah

2008

3. Belason, Verna L

200713529.

4. Dizon, Ma. Carolina

200813962

5. Reyes, Aldrin Marc

200714252

Signature:

.

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