These three quantities are linked together by what is called the equation of state for the fluid. For other fluids knowledge of the equation of state is often incomplete. When an element of fluid is compressed, the work done on it tends to heat it up. In reversible adiabatic processes for such gases, however, the temperature rises on compression at a rate such that. For liquids the ratio between the isothermal and adiabatic compressibilities is much closer to unity. The molar specific heat is the amount of heat required to raise the temperature of one mole through one degree. This is greater if the substance is allowed to expand as it is heated, and therefore to do work, than if its volume is fixed.

The principal molar specific heats, C P and C V , refer to heating at constant pressure and constant volume, respectively, and. Solids can be stretched without breaking, and liquids, though not gases, can withstand stretching, too. Water owes its high ideal strength to the fact that rupture involves breaking links of attraction between molecules on either side of the plane on which rupture occurs; work must be done to break these links.

However, its strength is drastically reduced by anything that provides a nucleus at which the process known as cavitation formation of vapour- or gas-filled cavities can begin, and a liquid containing suspended dust particles or dissolved gases is liable to cavitate quite easily. Work also must be done if a free liquid drop of spherical shape is to be drawn out into a long thin cylinder or deformed in any other way that increases its surface area.

Here again work is needed to break intermolecular links. The surface of a liquid behaves, in fact, as if it were an elastic membrane under tension, except that the tension exerted by an elastic membrane increases when the membrane is stretched in a way that the tension exerted by a liquid surface does not. Surface tension is what causes liquids to rise up capillary tubes, what supports hanging liquid drops, what limits the formation of ripples on the surface of liquids, and so on.

Fluid mechanics physics. Written By: Thomas E. See Article History. Start Your Free Trial Today. Load Next Page. Table 9 shows for each dependent variable separately the results of testing hypothesis H 0,2a using a one-tailed t-test for independent samples.

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It can be seen that the hypothesis H 0,2a can be rejected only for the variables J. The value for J. Table 10 shows for each dependent variable separately the results of testing H 0,2b using a one-tailed t-test for independent samples. Again the two variables which show statistically significant results are J. The variables J. An objective measure of student knowledge and skill outcomes for the CFD interface as applied to the fluid mechanics curriculum was devised.

Some of the questions used in the test are shown in Table 11 , with the questions directed only at students of CFD group A. The most intuitive test of students' knowledge and skill outcomes is whether the post-test scores were significantly higher than those of the pre-test scores. Table 12 contains the results for the mean and variance, the number of students N taking the test is also shown and the test contained 20 questions.

It can be seen that the effect is substantial between pre- and post-tests and therefore represents significant improvement in outcomes of the students' knowledge and skills of CFD knowledge and skills. The students, after a relatively brief exposure to and with limited practice of CFD have shown considerable growth in their understanding of CFD concepts, principles and applied problems. The success of this introduction could not be assessed using a student comparison performance in CFD laboratories across the years as these data were not available or not in a form that would make for meaningful comparison.

This is not necessarily a weakness of the study as it has been suggested Lucas, that the measurements of differences in student assessment over time has limited value given the changing nature of student cohorts from one year to another.

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On the basis of these recommendations a questionnaire was developed to elicit perceptions of the introduction of CFD from students involved in the class. An anonymous online survey was conducted after students obtained their grades for the laboratory reports to aid formative evaluation of the introduction of CFD. Only students who had completed the course with CFD were surveyed. A questionnaire using 11 statements as listed in Table 13 was designed for this survey.

## Fluid dynamics

Students were requested to respond to each item in the questionnaire using a five-point scale: strongly agree, agree, neutral, disagree and strongly disagree plus a column for no opinion. An opportunity was also provided for students to comment on their experience at the end of the questionnaire to collect qualitative feedback on their experience so far with CFD. The responses to the survey are shown on Fig. In additional comments most of the students expressed the view that the amount of material introduced was correct, although some felt that the exercises took a long time to complete correctly.

Students were particularly appreciative that they could easily visualize flow using contour and vector plots and generally agreed that the combination of theory, experimental and CFD led to better understanding of fluid mechanics. Students also showed enthusiasm for learning more about CFD. It was noted that the students liked the hands-on and self-discovery approach, although at times some frustration was also noted.

## Understanding What Fluid Dynamics is

Once a demonstration was given there was only an interest to learn by themselves, back up when required by a Teaching Assistant's advice. The traditional view of CFD is that it has a steep learning curve, but with a structures CFD interface and with limited depth imposed it has been demonstrated that the gradient of the curve can be brought to an acceptable level. Of course, during the skills training at this level, no real mention was made of code development, as the purpose was to develop users of the code only. This can be remedied by a later course which improves the student as a user and starts showing ways of writing new code for special conditions.

The concept to represent this software package or any other package as a black box should be remedied as soon as possible in later courses. This paper has described the use and efficacy of integrating computational fluid dynamics into a traditional fluid mechanics course. The controlled experiment has shown that the inclusion of CFD laboratories gave students a better appreciation of fluid mechanics in general and the students gained better knowledge of simple concepts.

However, the inclusion of CFD laboratories had a detrimental effect on interest when compared to the purely experimental control group and the control group also did better when considering the more difficult aspects of the course. It was found from the study of student knowledge and skill outcomes for the CFD interface that the students could cope with CFD reasonably well, provided the subject is introduced with care. One of the main reasons for the inclusion of CFD was to contribute to the teaching of professional practice skills to intermediate level undergraduate students.

It was found that the interface design does provide students with hands-on experience, gained through an interactive and user-friendly environment, and encourages student self-learning. It was noted from the survey that the students liked the hands-on and self-discovery approach, although at times some frustration was also noted.

Help us write another book on this subject and reach those readers. Login to your personal dashboard for more detailed statistics on your publications. Edited by Chaoqun Liu. We are IntechOpen, the world's leading publisher of Open Access books. Built by scientists, for scientists. Our readership spans scientists, professors, researchers, librarians, and students, as well as business professionals. Downloaded: Introduction In this chapter, the development, implementation and evaluation of a suitable curriculum for students to use computational fluid dynamics CFD as part of a fluid mechanics course at intermediate undergraduate level are described.

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General concerns about introducing simulation into a curriculum Issues of concern arise when simulation is being introduced into a curriculum. Specific concerns about introducing CFD into a curriculum There are many issues, which if not carefully considered and implemented, can lead to teaching and learning difficulties. Outline of the chapter In Section 2 of this chapter, basic computational fluid dynamics elements introduced to students in two lectures at the start of their course to introduce CFD elementary theory, methodology and procedures are outlined.

Basic computational fluid dynamics elements This section outlines essential elementary CFD theory, which must be introduced students before they encounter hands-on experience in the laboratory. Discretization using the finite-volume method To keep the explanation simple, consider the following 1D equation.

Boundary conditions When solving the Reynolds-averaged Navier-Stokes equations and continuity equation, appropriate initial conditions and boundary conditions need to be applied. Basic numerical solvers In a practical problem, as mentioned above, a matrix would be extremely large, so needing a prohibitively large amount of memory to invert it directly. Turbulence modelling There are two different states of flow, laminar and turbulent.

Computational fluid dynamics teaching laboratories 3. Interface design specifications The CFD laboratory is designed so that practical procedures are user-friendly and easy to implement, and also to show students that CFD methodology needs to be systematic and rigorous. The Cartesian mesh can be automatically generated or built manually. Numerics Convergence monitoring, selection of numerical scheme. Post-processing Flow visualization, analysis, verification, validation using published experimental or empirical data. Table 1. Areas for systematic consideration. Integration of CFD laboratory into fluid mechanics curriculum 4.

Existing fluid mechanics undergraduate course The CFD laboratory was integrated into a fourth semester course, for students of mechanical engineering. The main learning outcomes are to understand the equations that govern fluid flow conservation of mass, momentum and energy and be able to apply them to a range of practical problems, including: predicting drag forces on bluff, streamline bodies and flat plates; analysing the flow in pipe systems; analysing performance of radial flow pumps and turbines; and, matching pumps and turbines for particular applications.

Complementary nature of CFD and experimental fluid mechanics During the first lecture, the students are introduced to the idea that theoretical fluid mechanics, experimental fluid mechanics and computational fluid dynamics are complementary in modern engineering practice. CFD methodology and procedures In the second lecture, the important part is a demonstration with full facilities for students to have 'hands-on' experience as the demonstration proceeds.

Teaching and learning evaluation The evaluation process was subdivided into three investigations, one in the form of a controlled experiment comparing the knowledge of the group with CFD in their course with those of a controlled group using only the conventional experimental laboratories, the second measuring student knowledge and skill outcomes for the CFD interface, and, the third in the form of an online questionnaire eliciting the views of students on using CFD.

Controlled experiment To investigate the effectiveness of introducing CFD laboratories into the fluid mechanics course, a controlled experiment applying a pre-test-post-test control group design was conducted Pfahl et al. Characteristics Average age Percentage female Preferred learning style s Reading with exercise Lecture Tutorial Laboratory Working in groups with peers Opinion of most effective learning style s Reading with exercise Lecture Tutorial Laboratory Working in groups Table 2.

Personal characteristics. Dependent variables J. Table 3. Experimental variables. What causes it? What is the effect of flow separation on the drag coefficient? Estimate the distance required for the boundary layer to completely fill the pipe for a Reynolds number of 2 x 10 5 , neglecting changes in core velocity U with x. Table 4. Example questions pre-test, post-test, subjective perceptions. Pre-test scores Post-test scores Difference scores J. Table 5. Scores of dependent variables.

Table 6. Scores of subjective perceptions. Variable d df t-Value Crit. Table 7. Results for 'post-test' versus 'pre-test' for group A. Table 8. Results for 'post-test' versus 'pre-test' for group B. Table 9. Results for 'performance improvement' Group A versus Group B.

Table Results for 'post-test improvement' Group A versus Group B. Student knowledge and skill outcomes for the CFD interface An objective measure of student knowledge and skill outcomes for the CFD interface as applied to the fluid mechanics curriculum was devised. This represents a considerable improvement and is statistically highly significant, i. Question No. Question 1 For flow over a cylinder, what is the cause of the different results found for CFD and in the experimental laboratory? The difference is caused by the experimental laboratory uncertainties.

The difference is caused by the errors from numericaland experimental laboratory uncertainties. The difference is caused by the errors from numerical methods. The difference is caused by the errors from numerical, modelling and experimental laboratory uncertainties. If the difference between the CFD and experimental data is less than the convergence limit.

If the difference between the CFD and experimental data is less than the experimental data uncertainties. If the difference between the CFD and experimental data is less than the combination of the experimental and CFD data uncertainties. Examples of test questions. Mean number of correct answers out of Online questionnaire An anonymous online survey was conducted after students obtained their grades for the laboratory reports to aid formative evaluation of the introduction of CFD.

Concluding remarks This paper has described the use and efficacy of integrating computational fluid dynamics into a traditional fluid mechanics course. How to cite and reference Link to this chapter Copy to clipboard. Cite this chapter Copy to clipboard Desmond Adair November 7th Available from:. Over 21, IntechOpen readers like this topic Help us write another book on this subject and reach those readers Suggest a book topic Books open for submissions.

More statistics for editors and authors Login to your personal dashboard for more detailed statistics on your publications. Access personal reporting. Solutions of the Navier—Stokes equations for a given physical problem must be sought with the help of calculus. In practical terms only the simplest cases can be solved exactly in this way. These cases generally involve non-turbulent, steady flow in which the Reynolds number is small.

For more complex cases, especially those involving turbulence , such as global weather systems, aerodynamics, hydrodynamics and many more, solutions of the Navier—Stokes equations can currently only be found with the help of computers.

This branch of science is called computational fluid dynamics. In practice, an inviscid flow is an idealization , one that facilitates mathematical treatment. In fact, purely inviscid flows are only known to be realized in the case of superfluidity. Otherwise, fluids are generally viscous , a property that is often most important within a boundary layer near a solid surface, [2] where the flow must match onto the no-slip condition at the solid. In some cases, the mathematics of a fluid mechanical system can be treated by assuming that the fluid outside of boundary layers is inviscid, and then matching its solution onto that for a thin laminar boundary layer.

For fluid flow over a porous boundary, the fluid velocity can be discontinuous between the free fluid and the fluid in the porous media this is related to the Beavers and Joseph condition. Further, it is useful at low subsonic speeds to assume that a gas is incompressible —that is, the density of the gas does not change even though the speed and static pressure change.

A Newtonian fluid named after Isaac Newton is defined to be a fluid whose shear stress is linearly proportional to the velocity gradient in the direction perpendicular to the plane of shear. This definition means regardless of the forces acting on a fluid, it continues to flow. For example, water is a Newtonian fluid, because it continues to display fluid properties no matter how much it is stirred or mixed. A slightly less rigorous definition is that the drag of a small object being moved slowly through the fluid is proportional to the force applied to the object.

Compare friction. Important fluids, like water as well as most gases, behave—to good approximation—as a Newtonian fluid under normal conditions on Earth. By contrast, stirring a non-Newtonian fluid can leave a "hole" behind. This will gradually fill up over time—this behaviour is seen in materials such as pudding, oobleck , or sand although sand isn't strictly a fluid.

Alternatively, stirring a non-Newtonian fluid can cause the viscosity to decrease, so the fluid appears "thinner" this is seen in non-drip paints. There are many types of non-Newtonian fluids, as they are defined to be something that fails to obey a particular property—for example, most fluids with long molecular chains can react in a non-Newtonian manner.

The constant of proportionality between the viscous stress tensor and the velocity gradient is known as the viscosity. A simple equation to describe incompressible Newtonian fluid behaviour is. For a Newtonian fluid, the viscosity, by definition, depends only on temperature and pressure , not on the forces acting upon it. If the fluid is incompressible the equation governing the viscous stress in Cartesian coordinates is. If the fluid is not incompressible the general form for the viscous stress in a Newtonian fluid is.

## Volume flow rate and equation of continuity

If a fluid does not obey this relation, it is termed a non-Newtonian fluid , of which there are several types. Non-Newtonian fluids can be either plastic, Bingham plastic, pseudoplastic, dilatant, thixotropic, rheopectic, viscoelastic. In some applications another rough broad division among fluids is made: ideal and non-ideal fluids.

An Ideal fluid is non-viscous and offers no resistance whatsoever to a shearing force. An ideal fluid really does not exist, but in some calculations, the assumption is justifiable. One example of this is the flow far from solid surfaces. In many cases the viscous effects are concentrated near the solid boundaries such as in boundary layers while in regions of the flow field far away from the boundaries the viscous effects can be neglected and the fluid there is treated as it were inviscid ideal flow.

The equation reduced in this form is called the Euler equation. From Wikipedia, the free encyclopedia. This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources.