Stage discharge curve and its application

A stage–discharge curve (rating curve) is a graph or equation relating the stage (water surface level, G) at a gauging site to the discharge (Q) of the river at that site. Once it is established from a number of current-meter measurements over a range of flows, discharge can be read directly from a simple daily water level reading.

Development

1. Measure Q (by current meter) and the stage G at the same time, many times over low, medium and high flows.
2. Plot G against Q; fit a smooth curve.
3. Usual equation:

$$Q = C_r(G - a)^{\beta}$$

where $a$ = gauge reading for zero flow, and $C_r$, $\beta$ are found by plotting $\log Q$ against $\log(G - a)$ (least squares). 4. Extend to high flood levels by log-log extrapolation, or by Stevens or conveyance methods.

 Stage G (m)
   |                  .  *
   |             *  .
   |         * .
   |      *.
   |   *.
 a |*_____________________ Q (m3/s)

Applications in a hydropower project

• Converts long records of daily gauge readings into a discharge series, from which hydrographs, flow duration curves and firm flow are drawn for fixing the design discharge and installed capacity.
• Gives the tailwater level for each discharge, needed for net head, turbine setting and draft tube design.
• Gives water levels at the headworks/intake for different flows: intake sill level, weir crest, freeboard.
• Gives flood levels for design of the dam/weir, spillway, river training works and powerhouse floor level.
• Used in real-time operation: estimating inflow, managing pondage and spills.

Limitations: a shifting river bed (common in Nepal's sediment-laden rivers) changes the curve, so it must be checked regularly.