4[0.57 log(ε/D)]²'

where is the absolute roughness of the pipe. Compare the values

predicted by this equation and those indicated on the Moody chart.

8.47 The Swamee and Jain formula for the friction factor is

f

Compare this equation for e/D=0.00001, 0.0001, 0.001, and 0.01

and Reynolds numbers of 104, 105, 106, and 107 with the Moody

chart and decide whether it is an acceptable replacement for the

Colebrook formula.

8.48 The Haaland formula for the friction factor is

0.3086

f=

where

{log[6.9/Re+ (8/3.7D) ¹.¹¹]}²*

Compare this equation for f for e/D = 0.00001, 0.0001, 0.001,

and 0.01 and Reynolds numbers of 104, 105, 106, and 107 with the

Moody chart and decide whether it is an acceptable replacement

for the Colebrook formula.

8.49 The Churchill formula for the friction factor is

12

18 [ ( 2 ) ² + (A + B)³¹5)

8

1

Re

1.5

f = 8

A =

B =

0.25

[log(e/3.7D+5.74/Re0⁹)]²*

{

1

-2.457 In

0.9

16

7

7 In [(2²2) + 3.7D]}'";

Re

37,530 16

Re

11/12

Compare this equation for f for both the laminar and turbulent

regimes for ε/D = 0.00001, 0.0001, 0.001, and 0.01 and Reynolds

numbers of 10, 10², 10³, 104, 105, 106, and 107 with the Moody

chart and decide whether it is an acceptable replacement for the

Colebrook formula.

Section 8.4.2 Minor Losses

8.50 Air at standard temperature and pressure flows through a

1-in.-diameter galvanized iron pipe with an average velocity of

8 ft/s. What length of pipe produces a head loss equivalent to

(a) a flanged 90° elbow, (b) a wide-open angle valve, or (c) a

sharp-edged entrance?

8.51 Given 90° threaded elbows used in conjunction with copper

pipe (drawn tubing) of 0.75-in. diameter, convert the loss for a

single elbow to equivalent length of copper pipe for wholly tur-

bulent flow.

8.52 To conserve water and energy, a "flow reducer" is installed

in the shower head as shown in Fig. P8.52. If the pressure at point

(1) remains constant and all losses except for that in the flow

reducer are neglected, determine the value of the loss coefficient

(based on the velocity in the pipe) of the flow reducer if its pres-

ence is to reduce the flowrate by a factor of 2. Neglect gravity.