Page 217 - Chemical process engineering design and economics

200 Chapter 5

Each term has the dimensions of energy per unit of mass - in this case,
ft-lb/lb. The factor, a, in the kinetic energy term, Av2/2ag, corrects for the
F M c
velocity profile across a duct. For laminar flow in a circular duct, the velocity
profile is parabolic, and a = 1/2. If the velocity profile is flat, a = 1. For very
rough pipes and turbulent flow, a may reach a value of 0.77 [10]. In many en-
gineering applications, it suffices to let a = 1 for turbulent flow.
The second term in the mechanical-energy balance, Equation 5.1, is the
change in potential energy and requires no comment. The third term is "pressure
work" and its evaluation depends on whether the fluid is compressible or in-
compressible. Because the increase in pressure across the fan is small, we treat
the flow as essentially incompressible. Thus, the fluid density may be removed
from the integral sign and the mechanical energy balance becomes

2
A(v /a) Ap AP
———— + — Az + —— + W + E = 0 (5.2)
2 gc gc P

The last two terms are the work done by the system, W, and the friction loss,
E. The system is defined by the fan inlet and discharge. Because the density of a
gas at atmospheric pressure is small, Az can be neglected. Since W is defined as
the work done by the system, the work done on the gas by the fan is -W H. Thus,
Equation 5.2 becomes

W H + E = 0 (5.3)

The frictional loss term, E, can be included in an hydraulic efficiency which
accounts for the gas frictional losses in the fan according to

WH-E
r|e = ———— (5.4)
W H

2
1 F A(v ) AP 1
W H =—— I ————— —— (5.5)
T!H L 2g c p J

where T|H is a hydraulic efficiency that accounts for pressure losses caused by
fluid friction in the fan.
In addition to the work lost by fluid friction, some work is lost because of

Copyright © 2003 by Taylor & Francis Group LLC