Fluid Mechanics and ThermodynamicsWeekly Assessed Tutorial Sheets

Tutor Sheets: WATS 9.

The WATS form a collection of weekly homework type problems in the form of out-of-class tutorial sheets.

Each WATS typically comprises of a couple of main questions of which each has around four/five linked supplementary questions. They were developed as part of an LTSN Engineering Mini-Project, funded at the University of Hertfordshire which aimed to develop a set of 'student unique' tutorial sheets to actively encourage and improve student participation within a first year first ‘fluid mechanics and thermodynamics’ module. Please see the accompanying Mini-Project Report “Improving student success and retention through greater participation and tackling student-unique tutorial sheets” for more information.

The WATS cover core Fluid Mechanics and Thermodynamics topics at first year undergraduate level. 11 tutorial sheets and their worked solutions are provided here for you to utilise in your teaching. The variables within each question can be altered so that each student answers the same question but will need to produce a unique solution.

FURTHER INFORMATION

Please see http://tinyurl.com/2wf2lfh to access the WATS Random Factor Generating Wizard.

There are also explanatory videos on how to use the Wizard and how to implement WATS available at http://www.youtube.com/user/MBRBLU#p/u/7/0wgC4wy1cV0 and http://www.youtube.com/user/MBRBLU#p/u/6/MGpueiPHpqk.

For more information on WATS, its use and impact on students please contact Mark Russell, School of Aerospace, Automotive and Design Engineering at University of Hertfordshire.

© University of Hertfordshire 2009 This work is licensed under a Creative Commons Attribution 2.0 License.

Fluid Mechanics and ThermodynamicsWeekly Assessed Tutorial Sheet 9 (WATS 9)

TUTOR SHEET – Data used in the Worked Solution

Q1). The torque required to rotate a 5.90 m diameter flat disc in a gas is to be found by measuring the torque required to rotate a geometrically similar disc of 468 mm diameter in a liquid at 567 rad/s.

i) Calculate the dynamic viscosity (N s /m2) of a suitable liquid. [9 dp](2 marks)ii) If the torque required for the smaller disc is 215 Nm calculate the torque (Nm) required

to rotate the full size disc at 5.70 rad/s. [2 dp] (2 marks)

For the gas you may assume that the density is 3.70 kg/m3 and its dynamic viscosity is2.77 x 10-5 N s/m2. For the liquid you may assume that the density is 840.00 kg/m3.

Q2) Alternating, oscillating vortices are usually shed from a cylinder when it is exposed to flow conditions having a ratio of inertial forces to viscous forces in the region of 90 – 1000.

Assuming a 9.40 mm diameter cylinder is exposed to a fluid with a dynamic viscosity of17.81 x 10-6 N s/m2 and a density of 1.29 kg/m3 calculate -

i) the lowest speed (m/s) likely to cause vortex shedding to occur and [4 dp](1 marks)ii) the highest speed likely (m/s) to cause vortex shedding occur. [4 dp](1 marks)

_______________________________________________________________________________________________WATS 9.

Mark Russell (2005)Student number 51 School of Aerospace, Automotive and Design Engineering

University of Hertfordshire

WATS 9 Worked solution

This sheet is solved using the TUTOR data set.

It is assumed for this that you already have the correct dimensionless groups. In some instances, however, these groups may be given, whereas in others you may have to construct them yourself. This exercise tries to get you recall and use them.

Q1 i) This part of the question is aimed at getting you to use the dimensionless groups and use this information to relate each case to each other. Using your notes the

dimensionless group for this case is

Therefore = where the subscripts g and l relate to the gas and liquid

configurations respectively.

Since all the data is know for the gas case

= = 26503354

Which, by definition, must also be the same value that arises from solving the dimensionless group for the liquid case. i.e.

26503354 =

Substituting the known values gives 26503354 =

Therefore, = 0.0039358 N s/m2 = 3.936 * 10-3 N s/m2

Q1 ii) The second part of the question uses the following relationship

and as before =

_______________________________________________________________________________________________WATS 9.

Mark Russell (2005)Student number 51 School of Aerospace, Automotive and Design Engineering

University of Hertfordshire

For the gas group we can write

For the liquid group we can write

Relating these two groups together gives =

From which we can find the torque required to rotate the big disc in gas i.e. ( )

In this case this is = 30.477 Nm

_______________________________________________________________________________________________WATS 9.

Mark Russell (2005)Student number 51 School of Aerospace, Automotive and Design Engineering

University of Hertfordshire

Q2. This question requires you to recall the fact the ratio of inertial forces to viscous forces is the much used ‘dimensionless group’ knows as the Reynolds Number.

The question also reinforces the idea of dimensional analysis and shows how dimensionless groups can be used in engineering studies. i.e. in this case it is not the fluid velocity or the fluids viscosity that are singularly important. For this vortex shedding pattern to occur then it is the combination of these variables, with others, that determine the likely-hood of this phenomenon.

For the lower velocity RE = 90. Recalling the definition of the Reynolds Number i.e.

and for this flow configuration the characteristic length, L, is the cylinder

diameter. Applying the student unique data into the above gives

Hence the lower velocity, Cmin, is 0.132 m/s

For the higher velocity, i.e. RE = 1000 and application of the student unique data gives –

Hence the higher velocity, Cmax, is 0.1.469 m/s

If you see any errors or can offer any suggestions for improvements then please e-mail me at m.b.russell@herts.ac.uk

_______________________________________________________________________________________________WATS 9.

Mark Russell (2005)Student number 51 School of Aerospace, Automotive and Design Engineering

University of Hertfordshire

CreditsThis resource was created by the University of Hertfordshire and released as an open educational resource through the Open Engineering Resources project of the HE Academy Engineering Subject Centre. The Open Engineering Resources project was funded by HEFCE and part of the JISC/HE Academy UKOER programme.

© University of Hertfordshire 2009

This work is licensed under a Creative Commons Attribution 2.0 License.

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The HEA logo is owned by the Higher Education Academy Limited may be freely distributed and copied for educational purposes only, provided that appropriate acknowledgement is given to the Higher Education Academy as the copyright holder and original publisher.

_______________________________________________________________________________________________WATS 9.

Mark Russell (2005)Student number 51 School of Aerospace, Automotive and Design Engineering

University of Hertfordshire