186
P. Liu
Fig. 3.13 Section-velocity distribution and average velocity of the cross-section
time is called the discharge (volume discharge) and its value is
Q =
¨
A
ud A = V A
where A is the total flow cross-section and V is the average velocity of the
section.
V =
Q
A
=
˜
A ud A
A
If each physical quantity is expressed by the average value of the cross
section of the water flow, the total flow at this time can also be regarded
as one-dimensional flow. The theory, thus obtained is called the total flow
theory, and this method is also called the total flow analysis method.
Its biggest feature is that it ignores the change in the physical quantity
perpendicular to the cross section and uses the average value of the cross
section.
By integrating the energy equation of the stream of microelements on the
cross section of the total flow, the energy equation expressed by the average
physical quantity of the cross section can be obtained as follows:
z 1 +
p 1
γ
+
α 1 V 2
1
2g
= z 2 +
p 2
γ
+
α 2 V 2
2
2g
+ h w1−2
This is the total flow energy equation. The equation shows that the average
total head of 1-1 cross section is equal to the average total head of 2-2
cross section plus the mechanical energy loss of the total flow between 12 cross sections, where α 1 is the kinetic energy correction coefficient of
section 1-1, and α 2 is the kinetic energy correction coefficient of section 2-2.