MME_2273_ Test 1

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School

Western University *

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Course

2273

Subject

English

Date

Oct 30, 2023

Type

pdf

Pages

Uploaded by ChiefLapwing3739

By uploading my answers I hereby confirm that this (exam/quiz/assignment) represents my own work . I confirm that it has been completed in adherence to the Senate Policy on Academic Honesty, without unapproved collaboration or the use of unpermitted aids or resources. I recognize the importance of academic integrity and understand there is no tolerance towards academic dishonesty within the Lassonde School of Engineering. I am aware that any suspected breaches will be reported to the Academic Honesty unit within the Student Welcome and Support Centre, and may result in additional penalties in accordance with the Academic Honesty Policy. Question 1 ( 8 mark – 13 min ) - Two immiscible liquids of equal thickness, h, are being sheared between a fixed and a moving plate, as in Figure shown. Gravity is neglected, and there is no variation with x . Using the concepts from differential approach in fluid dynamics, find an expression for the velocity at the interface.

Page 1 of 2 Clearly mark your answers for different sections of the question (e.g. (a), (b), (c), etc.) if you write your answer in a sheet other than this one Question 2 ( 9 mark – 17 min ) - Answer the following questions: (a) Answer the following True or False questions. To discourage guessing the following marking scheme will be used: For every correct answer you will receive 0.5 mark. For every wrong answer you will get - 0.25 (mark deduction); if no answer, then a mark of zero will be assigned. (a-1) It is possible that a flow that is going over a curved surface (i.e., turning) on the macro scale, be irrotational on the micro scale (or fluid element level). T □ F □ (a-2) The stream function concept can be used for any type of flow (steady, transient, etc.) as long as it is considered a 2D flow. T □ F □ (a-3) In fluid mechanics, the basic conservation laws are those of volume, energy, and momentum. T □ F □ (a-4) A force is equivalent to a rate of transfer of momentum. T □ F □ (b) What is a streamline? When it is equivalent to a path line? (c) For a problem of the type given below, which of the three main approaches to solve fluid dynamics problems is the most suitable approach to be used? (no need to solve the problem). Explain why to receive credit.

Page 2 of 2 (d) One of the application of additives to make a fluid non- Newtonian is in drag reduction for pipelines. The plot shows velocity profiles for different types of fluid at a location within a pipeline where the flow is fully developed. Knowing that the velocity profile, in black is for a Newtonian fluid, the other velocity profiles shown are for which type of non-Newtonian fluid? To get credit you must provide the reason for the type of non- Newtonian fluid you select. Label each of the green and blue velocity profiles. y is the local coordinate that is normalized with respect to the diameter of the pipe (H); V is the local velocity that is normalized with respect to the average velocity in the pipe (V avg ), if it was a uniform flow. (e) Bernoulli’s 1738 book “Hydrodynamica” contains many excellent sketches of flow patterns related to his frictionless relation. One, however, redrawn below, seems physically misleading. Can you explain what might be wrong with the figure?

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