A simple flow-measurement device for streams and channels is a notch, of angle , cut into the side of a dam, as shown in Fig.

A simple flow-measurement device for streams and channels is a notch, of angle α, cut into the side of a dam, as shown in Fig. P5.69. The volume flow Q depends only on α, the acceleration of gravity g, and the height δ of the upstream water surface above the notch vertex. Tests of a model notch, of angle α = 55°, yield the following flow rate data:
δ, cm: 10 20 30 40 Q, m3/h: 8 47 126 263 (a) Find a dimensionless correlation for the data. (b) Use the model data to predict the flow rate of a prototype notch, also of angle α 55°, when the upstream height δ is 3.2 m.