For laminar flow, friction factor (f) is given by

And frictional losses are given by Hagen Poiseuille equation:

Example 4.8: Water flows through a pipe having inside diameter 0.5 in at 7.25 ft/s. The pipe is 100 ft long. Determine the pressure drop if the pipe is made of (a) drawn brass tubing, (b) drawn lead tubing, (c) drawn glass tubing, (d) commercial steel, (e) wrought iron, (f) asphalted cast iron, (g) galvanized iron, (h) cast iron, (i) concrete, or (j) riveted steel. Use the following information:

Density of water = 62.37 lb/ft³, viscosity of water = 1.12 cP

Solution:

C Inside diameter of the pipe, d = 0.0417 ft.

C Viscosity of water, μ = 7.526 ´ 10^-4 lb/(ft·s).

C Reynolds number Re (Equation 4.14):

Note that the materials of construction of the pipes are different for each case.

C Roughness of the pipes (Table 4.1):

C Friction factor, f (Figure 4.3):

C Frictional losses, h_fs (Equation 4.11):

C

C

C Pressure drop, ΔP:

C Results are presented below:

Material	ε/ft	RR = ε/d	f	hf	ΔP/psi
Drawn brass, lead, glass tubing	4.92 ´ 10^-6	1.81 ´ 10^-4	0.0062	48.7	21.1
Commercial steel, wrought iron	1.5 ´ 10^-4	4 ´ 10^-3	0.0079	62	26.8
Asphalted cast iron	4 ´ 10^-4	0.01	0.0099	78	33.7
Galvanized iron	5 ´ 10^-4	0.012	0.0106	83	36.0
Cast iron	8.5 ´ 10^-4	0.02	0.0126	99	42.8
Concrete	1.0 ´ 10^-3	0.024	0.0134	105	45.5
Riveted steel	3 ´ 10^-3	0.072	0.0215	169	73.1