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<br />II <br />I <br />I <br />II <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br /> <br />Lesson 2 <br /> <br />Basic Hydraulics - Participant Workbook <br /> <br />where: <br /> <br />Fx = <br />p = <br />Q = <br />J3 = <br />V = <br /> <br />Forces in the x direction <br />density of water <br />discharge <br />Momentum coefficient, normally assumed to <br />be one <br />velocity in the x direction <br /> <br />The momentum equation is derived from Newton's second law, which <br />states that the summation of all external forces on a system is equal to <br />the change in momentum. The equation is a vector relationship and the <br />form shown is for the x-direction, with a similar form in the y and z <br />directions. <br /> <br />The momentum concept is important in grate design, hydraulic jump <br />analysis, analysis of paved channels intersecting at angles and in design <br />of energy dissipators. <br /> <br />2.3 MANNING'S EQUATION <br /> <br />The culvert hydraulic operation often is a direct function of the unconstricted <br />channel flow characteristics. One of the most common methods of analyzing <br />open channel flow is the Manning's Equation. <br /> <br />MANNING'S EQUATION <br />(MERGED WITH CONTINUITY) <br /> <br />WETTED PERIMETER <br /> <br />AREA OF FLOW <br /> <br />n <br /> <br /> <br />Q = <br /> <br />1.486 213 '" <br />AR S <br /> <br />2.8 Manning's Equation <br /> <br />2.9 Wetted Perimeter <br /> <br />Manning's Equation describes uniform flow in a prismatic conveyance or <br />channel. The depth of flow associated with uniform flow is termed normal <br />depth. The original equation described uniform velocity. However, in <br />combination with the Continuity Equation, its more familiar format is given <br />as follows. <br /> <br />2-7 <br />