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<br />hydrograph. The main advantage of the kinematic wave method is that the response of <br />both the open and impervious areas can be accounted for in a single subbasin. <br /> <br />2. THE KINEMATIC WAVE EQUATIONS OF MOTION. <br /> <br />The kinematic wave equations are based on the conservation of mass and <br />the conservation of momentum. The conservation principles for one-dimensional open <br />channel flow (St. Venant equations) can be written in the following form: <br /> <br />Conservation of Mass <br />Inflow - Outflow = the rate in change of channel storage <br /> <br />A av + VB gy + B gy = q <br />ax ax at <br /> <br />(1 ) <br /> <br />Conservation of Momentum <br />Sum of Forces = gravity + pressure + friction = mass x fluid acceleration <br /> <br />S , = So - gy - V av - 1 av <br />ax gax gat <br /> <br />(2) <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 ,= friction slope <br />So = channel bed slope <br />g = gravity <br /> <br />, The kinematic wave equations are derived from the St. Venant equations <br />by preserving conservation of mass and approximately satisfying conservation of <br />momentum. In approximating the conservation of momentum, the acceleration of the fluid <br />and the pressure forces are presumed to be negligible in comparison to the bed slope <br />and the friction slope. This reduces the momentum equation down to a balance between <br />friction and gravity: <br /> <br />7-57 <br />