Civil Engineering Reference
In-Depth Information
7.3.1 governing equations for unsteady (or transient) flow
Hydraulic transient flow is also known as unsteady fluid flow. During a transient anal-
ysis, the fluid and system boundaries can be either elastic or inelastic:
• Elastic theory
describes unsteady flow of a compressible liquid in an elastic
system (e.g., where pipes can expand and contract). Research uses the MOC to
solve virtually any hydraulic transient problems.
• Rigid-column theory
describes unsteady flow of an incompressible liquid in a
rigid system. It is only applicable to slower transient phenomena. Both branches
of transient theory stem from the same governing equations. Transient analysis
results that are not comparable with actual system measurements are generally
caused by inappropriate system data (especially boundary conditions) and inap-
propriate assumptions [9-11].
tABle 7.1
Input data table including of -“x” & “x²” & “y”-for equation finding, transfer to
Regression software “SPSS”.
=+
(Line Equations)
y
a
ax
01
Equation
Model Summary
Parameter Estimates
R Square
F
df1
df2
Sig.
Constant
b1
b2
b3
Linear
.418
15.831
1
22
.001
6.062
.571
=++
(Second order Equation)
y
a
ax
a x
2
0
1
2
Equation
Model Summary
Parameter Estimates
R Square
F
df1
df2
Sig.
Constant
b1
b2
b3
Quadratic
.487
9.955
2
21
.001
6.216
-.365
.468
=++ +
(Third order Equation)
2
3
y
a
ax
a x
ax
0
1
2
3
Equation
Model Summary
Parameter Estimates
R Square
F
df1
df2
Sig.
Constant
b1
b2
b3
Cubic
.493
10.193
2
21
.001
6.239
.000
-.057
.174
(Compound)
kt
A
=
Ce
Equation
Model Summary
Parameter Estimates
b3
R Square
F
df1
df2
Sig.
Constant
b1
b2
Compound
.424
16.207
1
22
.001
6.076
1.089
(/
dA dT
)
=
KA
, (Growth)
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