User:Jkf

Open channel flow is gravity driven flow of fluid in a conduit in which a free surface occurs. In contrast, pipe flow occurs when a fluid is in contact with all points along the perimeter of a containing conduit. Open channel flows are ofter more difficult to analyze as the location of the free surface is an additional unknown.

Classification

• Open channel flow are termed steady if the depth of the fluid is constant as a function of time and unsteady if depth varies with time.
• A flow is continuous if the volumetric flow through a cross section of the conduit is a constant along the length of the flow and discontinuous otherwise. Discontinuous flow occur when fluid is added or removed along the length of the flow.
• Flow are classified as uniform if the fluid depth is constant along the length of the flow and non-uniform or varied if fluid depth changes along the length.
  • Varied flows are further classified as rapidly varied if sharp changes in fluid depth occur over relatively short distances (e.g. a hydraulic jump) and gradually varied otherwise.

Uniform Flow

Uniform flow is described by

$Q=CA{\sqrt {R_{h}S}}$

where:

Q	is the volumetric flow rate (m3/s)
C	is an empirical coefficient called the Chezy Coefficient (s-1)
A	is the channel cross sectional area [m2]
Rh	is the Hydraulic radius (m)
S	is the channel slope (m/m)

$Q={\frac {1}{n}}{\frac {A^{\frac {5}{3}}}{P^{\frac {2}{3}}}}{\sqrt {S}}$

where...

Non Uniform Flow

Non uniform steady flow in a channel of varying width and depth is described by

${\frac {dh}{dt}}={\frac {S-{\frac {Q^{2}}{C^{2}A^{2}R_{h}}}\left(1-{\frac {C^{2}R_{h}}{gA}}\left({\frac {\partial A}{\partial x}}\right)\right)}{1-Fr^{2}}}$

where...