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<br />This is not a severe limitation when applying the kinematic wave method <br />for design purposes. Generally speaking, sewer systems are designed to convey flow <br />as an open channel. However, in situations where the sewer system will pressurize, <br />flow will back up into the street gutters and flow to the nearest low point where it <br />may enter the sewer system again. In the case where a culvert or a storm sewer <br />pressurizes and creates a large backwater, the backwater area should be modeled <br />separately with a technique that can handle pressure flow. <br /> <br />The use of the kinematic wave method for main channels should be <br />limited to urban areas or moderately sloping channels in headwater areas. The <br />limitation results because a hydrograph's peak discharge does not attenuate when it <br />is routed with the kinematic wave technique. This is an adequate approximation in <br />urban areas, or any small, quick responding basin. However, flood waves <br />overestimate peak discharges in this type of stream. Therefore, in natural streams, <br />where it is likely that hydrograph attenuation will occur, the kinematic wave method <br />should not be used for main channel routing. <br /> <br />6. CHANNEL ROUTING. <br /> <br />6.1. The Equations of Motion. <br /> <br />The equations that describe one-dimensional unsteady flow in open <br />channels, the St. Venant equations, consist of a continuity equation (5), and a <br />momentum equation (6). The solution of these equations defines the propagation of <br />a flood wave with respect to distance along the channel and time. <br /> <br />MV + VB~ + B~ = q <br />ox ox ot <br /> <br />(5) <br /> <br />Sf = So - ~ - V oV - 1 oV <br />ox g ox g ot <br /> <br />(6) <br /> <br />Where: <br /> <br />A = cross. sectional flow area <br />V = average velocity of water <br />x = distance along the channel <br />B = water surface width <br />y = depth of water <br />t = time <br />q = lateral inflow per unit length of channel <br />S f = friction slope <br />So = channel bed slope <br />g = gravitational acceleration <br /> <br />7-64 <br />