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

$$ Q = C A \sqrt {R_h S} $$

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)
 * }
 * Rh || is the Hydraulic radius (m)
 * S || is the channel slope (m/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

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

where...