{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

p06100

# p06100 - 714 CHAPTER 6 CONTROL-VOLUME METHOD 6.100 Chapter...

This preview shows pages 1–2. Sign up to view the full content.

714 CHAPTER 6. CONTROL-VOLUME METHOD 6.100 Chapter 6, Problem 100 U, p V u V f Roughness 2 R 2 R 2 R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Figure 6.100: Asymmetric flow through a pipe. 6.100(a): First consider the upper branch. By definition, the average velocity is V u = 1 π R 2 8 2 π 0 8 R 0 V u ( r ) rdrd θ = 2 π π R 2 (1 . 173 V ) 8 R 0 w 1 r R W 1 / 9 rdr = 2 . 346 V 8 R 0 w 1 r R W 1 / 9 w r R W d w r R W = 2 . 346 V 8 1 0 η 1 / 9 (1 η ) d η = 2 . 346 V 8 1 0 p η 1 / 9 η 10 / 9 Q d η = 2 . 346 V } 9 10 η 10 / 9 9 19 η 19 / 9 ] η =1 η =0 = 2 . 346 V } 9 10 9 19 ] = 2 . 346 w 81 190 W V = V where we use the change of integration variables η 1 r/R in the second line. Similarly, for the lower branch, V f = 1 π R 2 8 2 π 0 8 R 0 V f ( r ) rdrd θ = 2 π π R 2 (1 . 224 V ) 8 R 0 w 1 r R W 1 / 7 rdr = 2 . 448 V 8 R 0 w 1 r R W 1 / 7 w r R W d w r R W = 2 . 448 V 8 1 0 η 1 / 7 (1 η ) d η = 2 . 448 V 8 1 0 p η 1 / 7 η 8 / 7 Q d η = 2 . 448 V } 7 8 η 8 / 7 7 15 η 15 / 7 ] η =1 η =0 = 2 . 448 V } 7 8 7 15 ] = 2 . 448 w 49 120 W V = V Therefore, the average velocity at both the upper and lower branches is V . Now, using the stationary control volume indicated in Figure 6.100, which lies entirely outside the

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

p06100 - 714 CHAPTER 6 CONTROL-VOLUME METHOD 6.100 Chapter...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online