Question

Figure P4.64 shows a fixed control volume. It has a volume VO = 1.0 ft3, a flow area A = 1.0 ft2, and a length 40 = 1.0 ft. Position x represents the center of the control volume where the fluid velocity VO = 1.0 ft/s and the density po = 1.800 slug/ft3. Also, at position x the fluid density does not change locally with time but decreases in the axial direction at the linear rate of 0.25 slug/ft4. Use the system or Lagrangian approach to evaluate dpldt. Compare this result with that of the material derivative and flux terms. Figure P4.64 System and control volume at time! |--p=1714 V. Po Al System at time I + st

Answer 1

Given; Volume Volume Vo=1 43 Vo=1 flow noco 'A = 10 f12 length il-lat Velocity 88 = 1 +11 dennity S = 1.8 Mug /ft3 Balance the forces on elements PIA - (P + d y at) da dimus (- of dr J A - 1 dhe lot) Palt vahe 1 d bolA = Ao to love ) t = 16 Love t - Ylv.25 Tt per unit time = 0.25 Aug / f1?