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Unformatted text preview: ew pipes, and the relative
roughness of pipes may increase with use as a result of corrosion, scale
buildup, and precipitation. As a result, the friction factor may increase by a
factor of 5 to 10. Actual operating conditions must be considered in the design
of piping systems. Also, the Moody chart and its equivalent Colebrook equation involve several uncertainties (the roughness size, experimental error,
curve fitting of data, etc.), and thus the results obtained should not be treated
as “exact.” It is usually considered to be accurate to 15 percent over the entire range in the figure.
The Colebrook equation is implicit in f, and thus the determination of the
friction factor requires tedious iteration unless an equation solver is used.
An approximate explicit relation for f is given by S. E. Haaland in 1983
(Ref. 9) as
1
f 1.8 log 6.9
Re /D
3.7 1.11 (874) The results obtained from this relation are within 2 percent of those obtained
from Colebrook equation, and we recommend using this relation rather than
the Moody chart to avoid reading errors.
In turbulent flow, wall roughness increases the heat transfer coefficient h by
a factor of 2 or more [Dipprey and Sabersky (1963), Ref. 5]. The convection
heat transfer coefficient for rough tubes can be calculated approximately from
the Nusselt number relations such as Eq. 8–70 by using the friction factor
determined from the Moody chart or the Colebrook equation. However, this
approach is not very accurate since there is no further increase in h with f for
f 4fsmooth [Norris (1970), Ref. 20] and correlations developed specifically for
rough tubes should be used when more accuracy is desired. TABLE 8–3
Equivalent roughness values for
new commercial pipes*
Roughness,
Material
Glass, plastic
Concrete
Wood stave
Rubber,
smoothed
Copper or
brass tubing
Cast iron
Galvanized
iron
Wrought iron
Stainless steel
Commercial
steel ft mm 0 (smooth)
0.003–0.03 0.9–9
0.0016
0.5
0.000033 0.01 0.000005
0.00085 0.0015
0.26 0.0005
0.00015
0.000007 0.15
0.046
0.002 0.00015 0.045 *The uncertainty in these values can be as much
as 60 percent. Developing Turbulent Flow in the Entrance Region
The entry lengths for turbulent flow are typically short, often just 10 tube
diameters long, and thus the Nusselt number determined for fully developed
turbulent flow can be used approximately for the entire tube. This simple approach gives reasonable results for pressure drop and heat transfer for long
tubes and conservative results for short ones. Correlations for the friction and
heat transfer coefficients for the entrance regions are available in the literature
for better accuracy. r
0 Turbulent Flow in Noncircular Tubes
The velocity and temperature profiles in turbulent flow are nearly straight
lines in the core region, and any significant velocity and temperature gradients
occur in the viscous sublayer (Fig. 8–25). Despite the small thickness of
laminar sublayer (usually much less than 1 percent of the pipe diameter), the
characteristics of the flow in this layer are very important since they set the
stage for flow in the rest of the pipe. Therefore, pressure drop and heat transfer characteristics of turbulent flow in tubes are dominated by the very thin (r)
Turbulent layer
Overlap layer
Laminar sublayer FIGURE 8–25
In turbulent flow, the velocity
profile is nearly a straight line in the
core region, and any significant
velocity gradients occur in the
viscous sublayer. cen58933_ch08.qxd 9/4/2002 11:29 AM Page 444 444
HEAT TRANSFER viscous sublayer next to the wall surface, and the shape of the core region is
not of much significance. Consequently, the turbulent flow relations given
above for circular tubes can also be used for noncircular tubes with reasonable
accuracy by replacing the diameter D in the evaluation of the Reynolds number by the hydraulic diameter Dh 4Ac /p. Flow through Tube Annulus
Tube Di Do Annulus Some simple heat transfer equipments consist of two concentric tubes, and are
properly called doubletube heat exchangers (Fig. 8–26). In such devices, one
fluid flows through the tube while the other flows through the annular space.
The governing differential equations for both flows are identical. Therefore,
steady laminar flow through an annulus can be studied analytically by using
suitable boundary conditions.
Consider a concentric annulus of inner diameter Di and outer diameter Do.
The hydraulic diameter of annulus is FIGURE 8–26
A doubletube heat exchanger that
consists of two concentric tubes. TABLE 8–4
Nusselt number for fully developed
laminar flow in an annulus with
one surface isothermal and the
other adiabatic (Kays and Perkins,
Ref. 14)
Di /Do Nui
—
17.46
11.56
7.37
5.74
4.86 3.66
4.06
4.11
4.23
4.43
4.86 4 (D2
o
(Do 4Ac
p Nui hi Dh
k (b) Roughened surface Roughness FIGURE 8–27
Tube surfaces are often roughened,
corrugated, or finned in order to
enhance convection heat transfer. Do Di (875) and Nuo ho Dh
k (876) For fully developed turbulent flow, the inner and outer convection coefficients are approximately equal to each other, and the tube ann...
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 Spring '10
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