River Discharge Calculator

Discharge is the continuity statement for an open channel: volume passing a section per unit time equals wetted area times the mean velocity normal to that section. The difficulty is entirely in the word mean, because velocity varies from near zero at the bed and banks to a maximum slightly below the surface in mid-channel. Standard gauging splits the section into 20 to 30 verticals, none carrying more than about 5 to 10 percent of total flow, and measures depth and velocity at each. Where depth is under roughly 0.75 m a single reading at 0.6 of the depth below the surface approximates the vertical mean; in deeper water the average of readings at 0.2 and 0.8 of depth is used, because the vertical profile is close to logarithmic. The mid-section method then sums the products of point velocity, depth, and width. For scale, a small upland stream carries 0.01 to 1 m3/s, a moderate river 10 to 100 m3/s, and the Amazon around 209,000 m3/s; one m3/s equals 35.31 cubic feet per second. Because continuous metering is impractical, gauging stations record stage and convert it through a rating curve of the form Q = a(h - h0)^b, calibrated by periodic direct gaugings. Uncertainty is typically 5 to 6 percent for a good current-meter measurement in stable conditions but exceeds 20 percent where the rating is extrapolated above the highest measured flow. On rapidly rising or falling stages a loop rating appears, and scour, fill, ice, or weed growth shift the rating, so it must be rechecked.

The velocity-area principle needed a dependable current meter before it could become practical. Reinhard Woltman, a German hydraulic engineer, described a vane-wheel meter in 1790 for measuring water velocity, and rotating-element instruments were refined through the nineteenth century. In the United States, William Gunn Price developed a cup-type meter in the 1880s; the Price AA meter that descended from it became the US Geological Survey standard and stayed in routine service for more than a century, its clicks counted through headphones to give revolutions per second. Systematic stream gauging in the United States began in 1888 and 1889, when John Wesley Powell, then director of the USGS, launched an irrigation survey of the arid West. Frederick Newell established a training camp and the first gauging station on the Rio Grande at Embudo, New Mexico, where hydrographers learned to survey cross-sections, meter velocities, and build and maintain rating curves. That program grew into the national streamgage network. The procedures were later internationalised, notably in ISO 748, which codifies the number of verticals and the depth-point sampling rules used worldwide. Acoustic Doppler current profilers, brought into river work in the early 1990s, replaced point-by-point metering on large rivers by profiling the whole section from a moving boat, and index-velocity ratings now allow continuous discharge estimates in tidal or backwater-affected reaches where stage alone is not a unique function of flow.