This document appears to be lecture notes on the control volume approach. It discusses key concepts like the continuity equation, Reynolds transport theorem, and differential form of the continuity equation. Examples are provided for problems involving mixtures passing through pipes and throats of venturi meters. The notes conclude with the control volume approach and solutions to example problems.

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SOLVED PROBLEMS
CONTROL VOLUME
APPROACH
CHAPTER (5)

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CONTROL VOLUME APPROACH
3. Continuity equation outin
cv
mm
dt
dM
&& −=
Volume Flow Rate Mass Flow Rate
1. Velocity is constant:
2. Velocity is variable:
AVQ =& AVQm ρρ == &&
∫=
A
VdAQ& QVdAVdAm
AA
&& ρρρ === ∫∫
5. The extensive property is defined as )(B
6. The intensive property ⎟
⎠
⎞
⎜
⎝
⎛
=
mass
B
b
21 )()( AVAV ρρ =21 mm && =4. Continuity equation in a pipe

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CONTROL VOLUME APPROACH
0=
∂
∂
+
∂
∂
+
∂
∂
z
w
y
v
x
u
10. Differential form of continuity equation
2
1
0
2
1
V
pp V
ρ
σ
−
=9. Cavitation index
7. Reynolds transport theorem( in general) ∫∫ •+=
cscv
sys
dAVbdQb
dt
d
dt
dB
ρρ
8. Reynolds transport theorem( for mass) ∫∫ •+=
CSCV
sys
dAVdV
dt
d
dt
dM
ρρ

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CONTROL VOLUME APPROACH

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CONTROL VOLUME APPROACH

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Problem 5.55
(p. 176)
Mixture

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Problem 5.75
(p. 181)
Table (5)
Throat

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CONTROL VOLUME APPROACH
THE END