Page 69 - Design and Operation of Heat Exchangers and their Networks

56 Design and operation of heat exchangers and their networks

2.2.1 Frictional pressure drop
For a pipe flow, the frictional pressure drop can be expressed as
L 1 2
Δp f ¼ f D ρu (2.128)
d h 2
where f D is the Darcy friction factor.
The frictional pressure drop can also be expressed by the shear stress near
the wall with the Fanning friction factor defined by
1 2
τ w ¼ f ρu (2.129)
2
Because of the force balance Δp f A c ¼τ w PL, we have
PL1 2 2
Δp f ¼ f ρu ¼ 2f ρu L=d h (2.130)
A c 2
The Fanning friction factor should not be confused with the Darcy fric-
tion factor that is four times as large as the Fanning friction factor:

f D ¼ 4f (2.131)

2.2.1.1 Frictional pressure drop in circular tubes
A set of equations are given in Table 2.1 for the calculation of Darcy friction
factor for fully developed flow in a smooth circular tube in different ranges of
Reynolds number. For laminar flow, the friction factor is independent of the
surface roughness. However, in a fully developed turbulent flow, the friction
factor depends solely on the roughness (Colebrook, 1939):

1
p ffiffiffiffi ¼ 2lg 3:7d i =Rð Þ (2.132)
f D
In the transition zone, the friction factor not only depends on the surface
roughness but also depends on the Reynolds number. As a general formula,
the Colebrook-White equation (Colebrook, 1939)

1 2:51 R
p ffiffiffiffi ¼ 2lg p ffiffiffiffi + (2.133)
f D Re f D 3:7d i
is recommended for Re>4000. In the region of 2000<Re<4000, the
value of the Darcy friction factor is subject to large uncertainties. In the
absence of experimental data, a linear interpolation between the Hagen-
Poiseuille equation and Colebrook-White equation can be used to calculate