Basic Hydraulics: Rating curve

Definition & terminology Rating curve, also known as stage–discharge curve, is a graph showing the relation between the water height (stage), and the volumetric flow-rate (discharge). Channels and hydraulic structures can have rating curves

Definition & terminology An accurate stage–discharge relationship is necessary for design to evaluate the interrelationships of flow characteristics (depth and discharge) The stage-discharge relationship also enables you to evaluate a range of conditions as opposed to a preselected design flow rate.

How Rating Curves are Constructed - I Record stage (depth) during an interesting runoff event Measure velocity across the channel (or structure) Compute discharge as produce of the flow area and velocity ADV Probe Cross Section – Measure V at different stations. Q=  VA Wading during flow Boat mounted for deeper/faster water

How Rating Curves are Constructed - II Stage and measured discharge recorded for several different flow events A curve is fitted to these event pairs, and that curve is the “Rating Curve”

Rating Curves for Hydraulic Structures Certain hydraulic structures force flow through critical depth, where the specific energy is a minimum. Knowledge that critical depth will occur along with geometry and an appropriate discharge coefficient produces an indirect measurement of discharge Weir equations Orifice equations Sluice gate equations

Weir flow Q weir Weir = obstruction in open channel over which water flows Flow over a weir directly related to water depth (head) upstream of weir (A rating curve!)

Sharp crested weir Discharge Coefficient (from tables, but derived from rated weirs) Width into the figure

For US units, weir discharge coefficient of C D = 3.3 commonly used Example: If upstream head is 1.2 ft above weir crest, and weir length (normal to the flow) is 8 ft, what is the flow over weir? Q = C D Lh 3/2 = 3.3(8)(1.2) 3/2 = 34.7 cfs Sharp crested weir flow calculation

Broad crested weir Equation for discharge is the same Head often measured to total energy line Discharge coefficient C D = 2.34 to 3.32

Broad crested weir discharge coefficients

Connecting rating curves to flood frequency curves