Chapt06

664 in the form of eq 665 red 8 12 log d 37 1775 gd3hf

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Unformatted text preview: uide 6.5 Three Types of Pipe-Flow Problems 353 Now enter Eq. (6.66) to find the Reynolds number: [8(5.3 E7)]1/2 log Red 0.0002 3.7 1.775 5.3 E7 72,600 The velocity and flow rate follow from the Reynolds number: V Q (2 E-5 m2/s)(72,600) 0.3 m Red d V d2 4 4.84 m (0.3 m)2 s4 4.84 m/s 0.342 m3/s Ans. No iteration is required, but this idea falters if additional losses are present. Iterative Solution By definition, the friction factor is known except for V: f hf d 2g L V2 (8 m) 2(9.81 m/s2) V2 0.3 m 100 m or f V2 0.471 (SI units) To get started, we only need to guess f, compute V 0.471/f, then get Red, compute a better f from the Moody chart, and repeat. The process converges fairly rapidly. A good first guess is the “fully rough” value for /d 0.0002, or f 0.014 from Fig. 6.13. The iteration would be as follows: Guess f 0.014, then V 0.471/0.014 5.80 m/s and Red Vd/ 87,000 and /d 0.0002, compute fnew 0.0195 [Eq. (6.64)]. 87,000. At Red New f 0.0195, V 0.481/0.0195 4.91 m/s and Red Vd/ 73,700 and /d 0.0002, compute fnew 0.0201 [Eq. (6.64)]. 73...
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