The uncertainty of the calculative value of the volumetric flow rate in open canals

The well-known Manning formula is usually used for the calculation of the volumetric flow rate (discharge) in a river or open canal. The discharge depends on the geometry of the channel, i.e. the water area, the wetted perimeter and the slope, as well as on the roughness coefficients. All these quantities are determined with some uncertainty. If these uncertainties are taken into consideration in the process of discharge calculation, then, as has been demonstrated for a hypothetical river channel, the ratio of the uncertainty to the calculated value of the discharge will change from several dozen percent in case of small flows to about ten percent in case of big, flood flows. The attached table contains the assumed data and the calculation of the uncertainty of the discharge.