p0544

# p0544 - 5.44 CHAPTER 5 5.44 Chapter 5 Problem 44 Problem...

This preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: 5.44. CHAPTER 5, PROBLEM 44 639 5.44 Chapter 5, Problem 44 Problem: Body A travels through kerosene at a constant speed of UA = 20 ft/sec. Velocities at points B and C are induced by the moving body and have magnitudes of UB = 7 ft/sec and UC = 3 ft/sec. If the density of kerosene is 1.58 slug/ft3 and effects of gravity can be ignored, what is pB − pC in psi? UB U ... .................. .. . ......... .. . A ............................... ... .................................... . ..................................... ................................... ...... ......................................... ......................................... .. .......................................... . ................................................................................. .. ........................................... . ... ... .. . . . .................................................................. . . ................................. ..................... ........................................... .............. .. .... .......................................... . ....................................... ........................................ ... .................... . ........................................ .................................. .... .................................. ................................ .. ........................ ... .............. ...... ... .... UC . .. .. .. .. .. .. .. .. . . ............ ........... .. .. .. .. .. .. .. .. .. ...... ...... . • B • A • C Solution: We must make a Galilean transformation in order to make the flow steady, wherefore we can use Bernoulli’s equation. The velocities transform as indicated in the figure below. ........ . ........... ............... .... .... ... ................. .................................. . ................................... ... ............ .... ....................................... .......................................... A . ............................................... .. . ............................................ . . ............................................ .............................................................. . . ... . ... . . .. .. . . .............................................. ............... . . ............................................... ............................................. .. . ............................................ . . . . .. . . ............................................ ... .......................................... ..................................... ..................................... ... ........................................................ .... .......................... .. .......... ... .... ... . U = 20 UB = 7 . . •.................. • ... .... ..... .. ........ ..... ..... .......................... ............................ . .................................... .. ... ...................................... ......................................... .. ........................................... ............................................ .............................................. . . ... .. . .............................................. . .............................................. . .............................................. . . .............................................. .............................................. . ............................................ ........................................... .. . ......................................... ...................................... .................................... . .................................... ............................... .................... .......... . ...... . UC = 3 . . •......... U∞ = 0 • (Unsteady) UA = 0 UB = 13 .................• . ................... . . • ........ UC = 17 • .. ........................ ....................... U∞ = 20 • . . ............................ ............................ (Steady) Then, from Bernoulli’s equation, 1 1 2 2 pB + ρ (UB ) = pC + ρ (UC ) 2 2 =⇒ 1 2 2 pB − pC = ρ (UC ) − (UB ) 2 Hence, since the density of kerosene is 1.58 slug/ft3 , the pressure difference is pB − pC = 1 slug 1.58 3 2 ft 289 ft2 ft2 − 169 sec2 sec2 = 94.8 slug = 0.66 psi ft · sec2 ...
View Full Document

## This note was uploaded on 02/09/2012 for the course AME 309 taught by Professor Phares during the Spring '06 term at USC.

Ask a homework question - tutors are online