Page 62 - Modelling in Transport Phenomena A Conceptual Approach

3.1. FRTCTION FACTOR 43

Equation (3.1-5) can be generalized in the form

(3.1-7)

in which the terms Ach, characteristic area, and Kch, characteristic kinetic energy,
are defined by

Wetted surface area for flow in conduits (3.1-8)
for flow around submerged objects
1
Kch = 5 pvzh (3.1-9)

where Vch is the characteristic velocity.
Power, *, is defined as the rate at which work is done. Therefore,

Work (Force)(Distance)
Power = - - - = (Force)(Velocity) (3.1-10)
Time Time

(3.1-11)

Example 3.1 Advertisements for cars in the magazines give the complete list of
their features, one of which is the fraction factor (or, drag coeficient) based on the
,frontal area. Sports cars, such as Toyota Celica, usually have a frzction factor of
around 0.24. If the car has a width of 2m and a height of 1.5m,
a) Determine the power consumed by the car when it is going at 100 km/ h.
b) Repeat part (a) if the wind blows at a velocity of 30km/h opposite to the
direction of the car.
c) Repeat part (a) if the wind blows at a velocity of 30km/h in the direction of
the car.

Solution
Physical properties

For air at 20°C (293K) : p = 1.2kg/m3
Assumption

1. Air is at 2OOC.
Analysis

a) The characteristic velocity is
(::::)
vch = (100) - 27.78 m/s
=