# Biomedical Engineering (MEng)

## Fluid and Solid Mechanics 2

### Module aims

This module will introduce the principles of fluid and solid mechanics. It aims to: Introduce you to the basic concepts of structural mechanics, showing the relevance of these concepts in design and risk analysis, and develop your analytical skills in stress analysis. Introduce you to key concepts and equations associated with the study of fluid mechanics and develop your ability to apply these concepts to fluids problems framed in a biomedical context.

### Learning outcomes

At the end of this module you will be able to: Recall, list, and define terms used in engineering properties of materials. Recall, list, and define terms in common solid mechanics and fluid mechanics equations Apply solid and fluid mechanics principles and equations appropriately to solve well-posed, constrained problems. Determine the deformations of beams, rods and shafts with arbitrary X-section under general loadings which are statically determinate or indeterminate Describe the mechanics of fluid flows using the Reynolds transport theorem and differential equations of fluid motion Interpret the results of a calculation in terms of their physical significance and be able to discuss relevant assumptions and limitations of numerical models Determine Young's modulus and stress concentration factors using experimental methods Analyse statically determinate and indeterminate force systems, deformable bodies and generalised two-dimensional stress and strain states in a solid

### Module syllabus

This module will cover the following topics: Solids: Revision of Newtonian mechanics – rigid body analysis, free body diagrams Very brief revision of engineering properties of materials, introduction of time-dependent properties. Pin jointed structures, Applied forces and deformations Internal forces and moments Stress and strain General procedures for solving problems that include deformations Selection and use of engineering materials Statically determinate and indeterminate systems Equilibrium equations for 2D stress systems – 2D strain compatibility equations Multi axial deformations and stress analysis – Poisson’s ratio, biaxial stress, hydrostatic stress, triaxial stress, thermal strain, stress transformations. Derivation and use of principal stresses. Knowledge and use of principal strains. Failure theories, safety, fatigue, stress concentration Uniformly loaded thin shells – pressurised thin walled cylinder; pressurised thin walled sphere, rotating rings; resisted thermal expansion Beam analysis – shear force and bending moments. Derivation and use of direct stresses in beams. Knowledge and use of shear stresses in beams. Derivation and use of second moment of area. Derivation and use of beam deflection. Unsymmetrical bending. Knowledge and use of combined bending and axial load. Torsion. Derivation and use of the torsion equation. Combined bending, torsion and axial loading. Use of principle of superposition. Buckling and eccentric loading in columns Fluids: The continuum approximation, Eulerian and Lagrangian description of fluid, definitions of fundamental kinematic and thermodynamic fluid properties, state relations for gases Force due to the pressure acting on a surface, hydrostatic pressure, gauge pressure, buoyancy force on a submerged or floating body (Archimedes' laws), stability of submerged or floating body, rigid-body motion of fluid Control volumes, statement of the Reynolds Transport Theorem, and its application to conservation of mass and linear momentum. Non-inertial reference frames. Awareness of conservation of angular momentum and energy. The Bernouilli equation The differential equations of fluid flow: the continuity equation, the momentum equation for a Newtonian fluid. Examples of exact solutions of equations.

### Teaching methods

Lectures: 18 hours Fluids, 18 hours Solids

Study groups: 9 hours Fluids, 9 hours Solids

Labs

### Assessments

Mastery examination 40%

Non-mastery examination 60% - taken if mastery passed at attempt 1 or 2

### Core

• #### Fluid mechanics

White, Frank M.,

Eighth edition., McGraw-Hill Education

• #### Fluid mechanics /

White, Frank M.

Eighth edition in SI units., McGraw-Hill Education,

### Supplementary

• #### Multimedia fluid mechanics online.

Homsy, G. M. (George M.), author.

Cambridge : Cambridge University Press

• #### Multimedia fluid mechanics

2nd ed., Cambridge : Cambridge University Press

### Background

• #### A first course in fluid dynamics

Paterson, A. R. (Andrew Robert), 1932- author.

Cambridge : Cambridge University Press

• #### A first course in fluid dynamics

Paterson, A. R.

Cambridge : Cambridge University Press

• #### Elementary fluid dynamics

Acheson, D. J., author.

Oxford : Clarendon Press

• #### Elementary fluid dynamics

Acheson, D. J.

Oxford : Clarendon