Mass Flow Rate M 1 Flow rate out of a tank depends on tank temperature, pressure and size of throat.
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Mass Flow Rate MA T p p p T T R A RT M RT p AV m 0 0 0 0 (17) 1 1 0 0 ) 1 ( 2 1 2 A T p M M R m M 1 0 0 Ap T m Flow rate out of a tank depends on tank temperature, pressure and size of throat.
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Transcript of Mass Flow Rate M 1 Flow rate out of a tank depends on tank temperature, pressure and size of throat.
Mass Flow Rate
MAT
p
pp
TT
RARTM
RT
pAVm
0
0
0
0
(17) 1
10
0
)1(21
2
AT
p
M
M
Rm
M1
0
0
Ap
Tm
Flow rate out of a tank depends ontank temperature, pressure and size of throat.
Mass Flow Rate
For a Diatomic Gas (e.g.,Air):
Mass flow/unit area slbf
RlbmMRf
Ap
Tm
.
.532.0),,(
0
0
0
0),,(T
pMRf
A
m
M1
A
m
Mach #-Area Relation
(18) 2
11
1
21
),,(
)1,,(
)1,,(1
),,(1
)1(2
1
2*
0
00
0*
MMA
A
MRf
MRf
MRfp
TmMRf
p
TmA
A
Values of A/A* tabulated over a range of Mach #s)
M=1
A* A
Two values for M at AOne subsonic, One supersonic.Solution depends on p.
Mach #-Area Relation
• If the M = 1 at throat the flow is chocked.
• For each value of A/A* there are two solutions, one subsonic, the other supersonic.
• If M=1 at the smallest cross-sectional area the mass flow rate is largest.
• If M < 1 at minimum area (A > A*), pretend.
• If A reduced below A*, decreases.
Ý m
Converging Nozzle Flow• Steady, adiabatic, reversible, no work flow• If backpressure pB = patm: no flow• As pB is lowered: flow• Assume here pB = pe • Eventually pB so low,
(pe/p0=.528), Me = 1• Nozzle chocked; lowering pB no longer changes
conditions in nozzle (message of lower pB cannot pass through sonic throat).
Here pB no longer equal pe (see later)
pB
Pe
Mep0=patm
Converging Nozzle Flow
• If nozzle chocked, flow rate fixed for given upstream stagnation pressure and temperature.
• Use as flow-meter (chocked orifice meter).
• Assumed flow from atmosphere to partially evacuated vessel; similar from pressurized vessel to atmosphere or lower pressure vessel
