Consider the water channel shown in Figure 2.2. The channel becomes narrower and shallower in a downstream direction.
Three groups of terms are used to describe these flows. Firstly, the flow in the wider upper section is clearly slower than the flow in the narrower
lower section, and the flow accelerates through the changing cross-sections. By definition:
• Uniform flow has a constant velocity with distance (A-B and C-D)
• Non-uniform flow has a variable velocity with distance (B-C).
• Steady flow is constant through time (for example, a river system).
• Unsteady flow varies through time (for example, a tidal system).
Thirdly, a surface wave travels at a speed that depends upon the square root of the water depth. The ability of a surface wave to travel upstream, against the current, thus depends upon the water depth. This provides another set of descriptive terms:
• Subcritical flow exists when the surface wave is able to progress upstream against the current.
• Critical flow exists when the surface wave travels upstream with the same celerity as the current.
• Supercritical flow exists when the surface wave is unable to travel upstream against the current and is swept downstream.
In general, tidal flows accelerate, decelerate, and reverse over varying depths and are therefore unsteady and non-uniform and can vary from subcritical, through critical, to supercritical within each tidal cycle. Since the volume of fluid passing through A-B, Q (m3 s-1), must be identical to the volume of fluid passing through C-D, it follows that
Q = w1d1U1 = w2 d2 U2
where U1 and U2 are the velocities, w1 and w2 are the widths, and d1 and d2 are the depths at section (A-B) and (C-D) respectively. Hence