# Modelling principles and analogies

This is the first chapter in the theme on modelling and simulation of linear models. These resources look at primarily of 1st and 2nd order systems. Use the left hand toolbar to access the other chapters and themes.

It is implicit in several of these chapters that students have core competence in some mathematical topics such as polynomials, roots, complex numbers, exponentials and Laplace. More information on these can be found in the Mathematics theme on the left hand toobar. |

This chapter contains the following topics. Under each topic there are hardcopy (pdf) notes, a video talk through of key derivations with example problems and also a tutorial sheet for users to test themselves.

- Modelling resistors in series.
- Modelling fluid pipes in series.
- Modelling heat conductors in series.
- Modelling resistors in parallel.
- Modelling heat conductors and pipes in parallel.
- Modelling springs in parallel.
- Modelling springs in series.
- Analogies between arrangements of springs, resistors and pipes.
- Concepts of linearity, superposition and coping with non-linear models.
- Quick questions and extra tutorial sheets on modelling.

## Modelling 1 - Resistors in series

Modelling electrical circuits with series arrangements of resistors and an introduction to Kirchhoff's voltage law.

- A summary of key facts, derivations and a tutorial sheet is given in the pdf file.
- A talk through video is on youtube.
- For more questions go to the end of the page.

Resistors in series have which property given a fixed applied voltage? |

## Modelling 2 - fluid pipes in series

Modelling the flow rate of fluids through series arrangements of pipes and analogies with electrical resistor circuits. |

- A summary of key facts and derivations is given in the pdf file.
- A talk through video is on youtube.

Fluid pipes of the same cross-sectional area and material arranged in series have which property for a fixed flow rate? |

## Modelling 3 - heat conductors in series

Modelling the flow rate of energy (or heat) through series arrangements of heat conductors with different temperatures at each end and analogies with electrical resistor circuits.

- A summary of key facts and derivations is given in the pdf file.
- A talk through video is on youtube.

For a fixed temperature difference, which statement is true? |

## Modelling 4 - resistors in parallel

Modelling electrical circuits with parallel arrangements of resistors and an introduction to Kirchhoff's current law.

- A summary of key facts, derivations and a mini tutorial sheet is given in the pdf file.
- A talk through video is on youtube.

For resistors in parallel, which statement is false?. |

## Modelling 5 - fluid pipes and heat conductors in parallel

Modelling the flow rate of fluids through parallel arrangements of pipes and the flow of heat through parallel arrangements of conductors and analogies with electrical resistor circuits. |

- A summary of key facts and derivations is given in the files of section 2 and section 3.
- A talk through video is on youtube.

Arranging pipes in parallel has the following effect, compared to a single pipe. |

## Modelling 6 - Springs in parallel

Modelling parallel arrangements of springs and analogies with electrical resistor circuits. | |

- A summary of key facts, derivations and mini-tutorial sheet is given in the pdf file.
- A talk through video is on youtube.

For springs arranged in parallel, which statement is true? |

## Modelling 7 - Springs in series

Modelling series arrangements of springs and analogies with electrical resistor circuits.

- A summary of key facts, derivations and mini-tutorial sheet is given in the pdf file.
- A talk through video is on youtube.

For springs arranged in series, which statement is true? |

## Modelling 8 - Summary of analogies

Summary of analogies between resistor circuits, fluid flow systems, heat conductors and systems of springs.- A summary of key facts and derivations is given in the pdf file .
- A concise tutorial sheet is here.
- A talk through video is on youtube.

Which is analogous to set of insulating materials in series (such as cavity walls in a house or multiple layers of clothing)?. |

## Modelling 9 - Concepts of linearity, superposition and dealing with non-linear systems

The first video gives an introduction to the concept of superposition and a link to transfer functions. The second video shows how linearisation of non-linear systems implies that superposition can still be used, within a small domain around the linearisation point and includes some simple examples.- A summary of key facts and derivations is given in the two files. File1 and file2.
- Talk through video 1 is on youtube.
- Talk through video 2 is on youtube.

## Extra questions on modelling

The coulomb is a unit of what quantity ? |

Which of the following equations does NOT correctly describe Ohm's Law? |

In a parallel arrangement of resistors R1 and R2, which of the following are false? |

In a series connection of light bulbs to the mains . When one bulb burns out, what is the effect on the other bulbs ? |

The Newton is a unit of what quantity ? |

In a series arrangement of springs k1 and k2 (extensions x1 and x2), which of the following are false? |

The Joule is a unit of what quantity ? |