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# Continuum Mechanics

## Module PH1007

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

### Module version of WS 2018/9

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
WS 2021/2WS 2020/1WS 2019/20WS 2018/9WS 2017/8WS 2015/6WS 2014/5

### Basic Information

PH1007 is a semester module in English language at Master’s level which is offered in winter semester.

This Module is included in the following catalogues within the study programs in physics.

• Theory courses for Biophysics
• Theory courses for Applied and Engineering Physics
• Complementary catalogue of special courses for condensed matter physics
• Complementary catalogue of special courses for nuclear, particle, and astrophysics
• Specialization Modules in Elite-Master Program Theoretical and Mathematical Physics (TMP)

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

300 h 90 h 10 CP

Responsible coordinator of the module PH1007 in the version of WS 2018/9 was Martin Zacharias.

### Content, Learning Outcome and Preconditions

#### Content

1. Kinematics of deformable media (velocity field of a fluid / continuity equation)

2. Hydrodynamics (stress tensor and viscosity / fundamental equations: Euler & Navier-Stokes / Bernoulli equation / Aerofoil theory / viscosity and Reynolds number / high Reynolds numbers and turbulence / small Reynolds numbers / waves / tsunamis)

3. Elasticity (stress tensor / energy balance / linear theory of elasticity: Hooke’s law / elastic waves / thin plates)

#### Learning Outcome

After successful completion of the module the students are able

1.  to know the meaning of the conservation quantities, balance equations and velocity fields, to understand the correlations and to calculate the descriptive quantities for simple systems
2.  to know the basics of the dynamics of liquids
3.  to describe the difference between laminar and turbulent flow, to know the conditions for the occurrence of both flow types and to calculate the relevant quantities.
4.  to know the basics of the deformation theory of elastic media and to understand and describe the formation and propagation of waves.
5.  to know the phenomena occurring in the reduction of extended media to one or two dimensions.

#### Preconditions

No preconditions in addition to the requirements for the Master’s program in Physics.

### Courses, Learning and Teaching Methods and Literature

#### Courses and Schedule

VO 4 Continuum Mechanics Zacharias, M. Mon, 14:00–16:00, PH HS2
Tue, 08:30–10:00, PH HS2
eLearning
UE 2 Exercise to Continuum Mechanics
Responsible/Coordination: Zacharias, M.
dates in groups eLearning

#### Learning and Teaching Methods

The modul consists of a lecture and exercise classes.

The lecture is designed for the presentation of the subject, usually by blackboard or beamer presentation. The focus resides on theoretical foundations of the field, presentation of methods and simple, illustrative examples. Command of basic methods is deepened and practised through homework problem sheets, which cover important aspects of the field. The homework problems should develop the analytic skills of the students and their ability to perform calculations. The homework problems are discussed by the students themselves under the supervision of a tutor in order to develop the skills to explain a physics problem logically.

#### Media

scriptum of lecture, exercise sheets, internet site associated with lecture, video of the lecture

#### Literature

* D.J. Acheson, Elementary fluid dynamics, Clarendon Press
* H. Stephani & G. Kluge, Theoretische Mechanik, Spektrum Akademischer Verlag
* Landau/Lifshitz, Theory of Elasticity (Theoretical Physics 7), Butterworth-Heinemann Ltd

### Module Exam

#### Description of exams and course work

There will be a written exam of 90 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using calculation problems and comprehension questions.

For example an assignment in the exam might be:

• Consider a 2D incompressible flow v = (v_x , v_y) with v_x = y^2/x. Determine the second (y) component of the velocity field.
• Consider the strain tensor ε_11 = c_1 r_1 (r_12 + r_22), ε_22 = (1/3) c_2 r_13, ε_12 = c_3 r_12 r_2, where c_1, c_2, c_3 are const. For which c_1, c_2, c_3 does this present a valid deformation state?
• Define the Reynolds number and give an interpretation.

#### Exam Repetition

The exam may be repeated at the end of the semester.

#### Current exam dates

Currently TUMonline lists the following exam dates. In addition to the general information above please refer to the current information given during the course.

Title
TimeLocationInfoRegistration
Exam to Continuum Mechanics
Tue, 2022-02-15, 14:15 till 16:15 Bitte beachten Sie die Hinweise unter https://www.tum.de/die-tum/aktuelles/coronavirus/corona-lehre-pruefungen/. // Please read the information at https://www.tum.de/en/about-tum/news/coronavirus/corona-teaching-exams/ carefully. till 2022-01-15 (cancelation of registration till 2022-02-08)
Thu, 2022-04-14, 14:15 till 16:15 Bitte beachten Sie die Hinweise unter https://www.tum.de/die-tum/aktuelles/coronavirus/corona-lehre-pruefungen/. // Please read the information at https://www.tum.de/en/about-tum/news/coronavirus/corona-teaching-exams/ carefully. till 2022-04-03 (cancelation of registration till 2022-04-07)
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