Page 117 - Modelling in Transport Phenomena A Conceptual Approach

4.5. FLOW IN CIRCULAR PIPES 97

11. Turbulent flow
W Calculate lAPl or &; given Q and D
For the given values of Q and D, the Reynolds number can be determined using Eq.
(4.510). However, when the values of Re and E/D are known, determination of f
fkom Eq. (4.59) requires an iterative procedure since f appears on both sides of
the equation. To avoid the iterative solutions, efforts have been directed to express
the friction factor, f, as an explicit function of the Reynolds number, Re, and the
relative pipe wall roughness, &ID.
Gregory and Fogarasi (1985) compared the predictions of the twelve explicit
relations with J3q. (4.5-9) and recommended the use of the correlation proposed
by Chen (1979):

(4.5 16)

where
1.1098 1.1490 0.8981
A=(%) +(Re) (4.51 7)

Thus, in order to calculate the pressure drop using Eq. (4.516), the following
procedure should be followed through which an iterative solution is avoided:
a) Calculate the Reynolds number from Eq. (4.510),
b) Substitute Re into Eq. (4.516) and determine f,
c) Use Eq. (4.56) to find the pressure drop. Finally, the pump size can be
determined by using Eq. (4.5-2).

Example 4.12 What is the required pressure drop per unit length in order to
pump water at a volumetric flow rate of 0.03 m3/ s at 20 "C through a commercial
steel pipe (E = 4.6 x m) 20cm in diameter?
Solution

Physical properties
p = 999 kg/ m3
For water at 20 "C (293 K) : cL = lool 10-6 kg/ m.

Analysis

The Reynolds number is determined from Eq. (4.5-10) as