Open Channel Flow Measurement

Flow in open channels such as flumes and irrigation ditches can be measured with sluice gates and weirs / notches using Bernoulli equation.

A notch is an opening in the side of a measuring tank or reservoir extending above the free surface. A weir is a notch on a large scale, used, for example, to measure the flow of a river, and may be sharp edged or have a substantial breadth in the direction of flow.


For a notch of any shape as shown in Fig.(17), consider a horizontal strip of width \(b\) at a depth \(h\) below the free surface and height \(dh\). \[\begin{aligned} \text{Area of strip} &= b\;dh \\ \text{Velocity through strip} &= \sqrt{2gh} \\ \text{Volumetric flow rate through the strip}, dQ &= \text{area} \times \text{velocity} = b\;dh \sqrt{2gh} \end{aligned}\] Integrating from \(h = 0\) at the free surface to \(h = H\) at the bottom of the notch, \[\text{total theoretical volumetric flow rate} (Q) = \sqrt{2g}\int_0^H bh^{1/2} dh\] Before the integration of the above equation can be carried out, \(b\) must be expressed in terms of \(h\). \[\begin{align*} \text{Rectangular notch:} & \qquad & Q &=\frac{2}{3}BH^{3/2}\sqrt{2g} \qquad \text{(where $B$ = width of notch)} \\ \text{V notch:} & \qquad & Q &=\frac{8}{15}\tan(\theta/2)\,H^{5/2}\sqrt{2g} \qquad \text{(where $\theta$ = included angle)} \end{align*}\] In the forgoing calculations, it is assumed that the velocity through any horizontal element across the notch will depend only on its depth below the free surface. This is a satisfactory assumption for flow over a notch or weir in the side of a large reservoir, but, if the notch or weir is placed at the end of a narrow channel, the velocity of approach to the weir will be substantial and the head \(h\) producing flow will be increased by the kinetic energy of the approaching liquid to a value \[x = h + \frac{v_1^2}{2g}\] where \(v_1\) is the mean velocity of the liquid in the approach channel. As a result, the discharge through the strip will be \[dQ = b\;dh\sqrt{2gx}\]