Page 514 - Modelling in Transport Phenomena A Conceptual Approach

494 APPENDIX A. MATHEMATICAL PR.EZIMEVAR.lES

However, while one of the room is very comfortable, the other is very uncomfort-
able. With the mean value theorem in mind, how would you explain the difference
in comfort levels of the two rooms? What design alterations would you suggest to
make the room that is uncomfortable comfortable?

A.2 Wind speed is measured by anemometers placed at an altitude of 10 m from
the ground. Buckler (1969) carried out series of experiments to determine the effect
of height above ground level on wind speed and proposed the following equation
for the winter months
v = v10 (G)
0.21

where a is the vertical distance measured from the ground in meter and v10 is the
measured wind speed.
Ektimate the average wind speed encountered by a person of height 1.7m at
the ground level if the wind speed measured by an anemometer 10m above the
ground is 30 km/ h.
(Answer: 17.1 km/ h)

A.3 SLOPES ON LOG-LOG AND SEMI-LOG
GRAPH PAPERS

A mathematical transformation that converts the logarithm of a number to a length
in the x-direction is given by
e, = L, log 5 (A.3-1)
where e, is the distance in the x-direction and L, is the cycle length for the
x-coordinate. Therefore, if the cycle length is taken as 10 cm, the distances in the
x-direction for various values of x are given in Table A.l.

Table A.l Distances in the x-direction for a logarithmic x-axis.
e,
2
1 0
2 3.01
3 4.77
4 6.02
5 6.99
6 7.78
7 8.45
8 9.03
9 9.54
10 10.00