T= 500 K Volume = 100,000 L p= 1.00 MPa Air (k = 1.4) T= 20.0 °C Volume = huge %3D A, V. Ma, Tank b Tank a Throat area = 0.07 m2
The converging–diverging nozzle sketched in Fig. C9.1 is
designed to have a Mach number of 2.00 at the exit plane
(assuming the fl ow remains nearly isentropic). The fl ow travels
from tank a to tank b, where tank a is much larger than
tank b. (a) Find the area at the exit Ae and the back pressure
pb that will allow the system to operate at design conditions.
(b) As time goes on, the back pressure will grow, since the
second tank slowly fi lls up with more air. Since tank a is
huge, the fl ow in the nozzle will remain the same, however,
until a normal shock wave appears at the exit plane. At what
back pressure will this occur? (c) If tank b is held at constant
temperature, T = 20°C, estimate how long it will take for the
fl ow to go from design conditions to the condition of part
(b)—that is, with a shock wave at the exit plane.
Given,
- T1 = 500K
- P1 = 1 MPa
- k = 1.4
- V1 = ∞
- T2 = 20C = 20+273 = 293K
- V2 = 100,000L
- Mae = 2.0
- Area of throat = 0.07m2
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