Steady free-surface flows. Conservation of Mass. Simply it means that the mass of the system is constant.
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Liquid is assumed incompressible
The change in the linear momentum of the flow can be expressed as:
= sum of horizontal components of average velocities of flow at section 1 and 2, respectively
and = horizontal components of pressures acting at section 1 and 2, respectively
= horizontal component of W sin ϴ
= horizontal component of unknown force acting between sections 1 and 2
= weight of fluid between sections 1 and 2
= specific weight of fluid
momentum correction coefficients
= channel slope angle
distances to centroids of respective flow areas and from free surface
Example 3.10 from (Crowe, 2009)
Fig. A.1 (Crowe, 2009)
For a specific q
Fig. 3-2 (Chow, 1959)
This is a cubic equation in which b is channel width.