Tutorial sheet outline solutions

TUTORIAL ANSWERS 1

Units in Modelling

a) The lightest mass is 20 g.

b) The shortest distance is 4.2 yards.

c) The largest area is largest 8.7 ft2.

d) The greatest volume is greatest 2 m3.

e) The highest temperature is 300K.

f) The smallest pressure is 7.8 bar.

g) The smallest power is 5000 Btu/hr.

Note: 1 slug = 37.17 lb, 1 Btu/s = 778 ft-lbf/s & 1 ft-lbf/s = 1.356 x 10-3 kW

1 Models can be developed by the engineer(s) and used to simulate the expected behaviour of the real system. If the system already exists, different scenarios can be tried using the model before tests being carried out on the real system. Alternatively if the system does not exist, the model can be used to help decide on the final design of a system. Often there are constraints on the design that need to be investigated e.g. constraints on cost, space, etc. Modification to systems once they exist can be expensive hence it is important to try and get design of systems ‘right-first-time’ and this is where modelling and simulation can be useful engineering tools. Example: see lecture notes week1 under section ‘Why is modelling important ?’.

2 See notes

3.

Components of system

Inputs

Outputs

States

Environment

Tank

Valve

Pipes

Inlet

Flows of A and B

Liquid level

Level change in tank

Upstream of inlet to tank and downstream of outlet valve

4. See notes

5. See notes

6. Bookwork (as coursework 1)

TUTORIAL ANSWERS 2

E1. A proportional relationship for a component is here considered to be an unchanging relationship (and is often referred to in modelling terms as a constitutive or physical relationship). These are the natural physical laws which the individual components of the system obey e.g. for an electrical system, the relationship between voltage and current and in the special case of an ideal resistor – Ohm’s Law v=R.i

E2. Kirchhoff’s Current Law : algebraic