Page 120 - Modelling in Transport Phenomena A Conceptual Approach

100 CHAPTER 4. EVALUATION OF TRANSFER COEFFICIENTS

The procedure to calculate the pipe diameter becomes:
a) Calculate N from Eq. (4.522))
b) Substitute N into Eq: (4.5-24) and determine the pipe diameter.

Example 4.14 Water at 20°C is to be pumped through a commercial steel pipe
(E = 4.6 x m) at a volumetric flow rate of 0.03 m3/ s. Determine the diameter
of the pipe if the allowable pressure drop per unit length of pipe is 40 Pa/ m.

Solution
Physical properties

p = 999 kg/ m3
For water at 20 "c (293 K) :
ct = lool 10-6 kg/ m.
Analysis
Equation (4.5-22) gives

n2]AP( 'I5
= (32pLQ2)
n2 (40)
= [ (32) (999) ( 0.03)2 = 1.69

Hence, Eq. (4.524) gives the pipe diameter as
({ -115
-
D = - [log(EN) + 5.806 (L)] 0.1'71}')
0.575
N PQN

- 0.171 ,'> -1'5 = 0.2 m

4.5.2 Heat Transfer Correlations
For heat transfer in circular pipes, various correlations have been suggested
depending on the flow conditions, i.e., laminar or turbulent.

4.5.2.1 Laminar flow correlation

For laminar flow heat transfer in a circular tube with constant wall temperature,
Sieder and Tate (1936) proposed the following correlation:
1 Nu = 1.86 [RePr (D/L)]'I3 (p/pW)O.l4 1 (4.525)