Uniform discharge in a rectangular flume

I non-uniform discharge, II uniform discharge;

h depth of discharge, Js uniform bottom slope, Jw slope of water surface profi le, L0 length of the flume with bottom slope Js and constant width, v flow velocity, red frame control volume

In uniform open-channel flow the discharge depth h remains equal, i.e. parallel to the bottom. This also means that the flow velocity v remains constant. The discharge depth h can also be described as a pressure head (a component of the specifi c energy). These energy heads are often applied in the form of what are known as grade lines. In the energy grade line J the most significant component in many cases is the discharge depth h. In uniform open-channel flow the energy grade line J is equal to the bottom slope Js and thus equal to the discharge depth h. In uniform open-channel flow the normal discharge prevails, i.e. the bottom slope Js balances out the friction losses in the discharge Q. The energy grade line, water surface profile and bottom slope are all parallel.

blue energy grade line J: hv/L=(E1-E2)/L

green slope of water surface profi le Jw: [(h1+z1)-(h2+z2)]/L

red bottom slope Js: (z1-z2)/L

According to Bernoulli, the total energy Etot is composed of three components:

  • velocity head (v²/2g)

  • pressure head (h=p/ρg)

  • elevation (z)

Flow formulae

Flow formulae describe the relationship between the discharge Q and the discharge depth h at a given shape of cross-section and roughness characteristic. The shape of cross-section is taken into account in the hydraulic radius; the discharge depth h comes into play via the energy grade line J.

Commonly used formulae for general flumes are

  • Darcy-Weisbach

  • Manning-Strickler (also Gauckler-Manning-Strickler).

Flow formulae are based on empirical values.