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<br />a 3 fool diameter pipe flowing full the area of flow would be 1t r' or 1t l.S' K 7,06 fl', The area of flow <br />for circular channels flowing less than full becomes more complicawd, but ,;an be readily solved, <br /> <br /> T T <br />,-- -I Q~~L.,.. . <br />[;Id P ~~b -E <br /> " "l.-_ <br /> , -- <br /> Rectangular TrapezoitkJJ <br /> T~ T <br /> . <br /> <br /> <br /> <br /> <br /> <br />Circular <br /> <br />Parabolic <br /> <br />Triangular <br /> <br />T = top width, P = Wetted Perimeter, y = depth of flow, b ,= bottom width, e = vertical offset. d = diameter <br /> <br />Figure I <br /> <br />The hydraulic radius, R, is the property defined as the Area of Flow divided by the Wetted Perimeter, The <br />Wetted Perimeter, P, is the part of the channel that the fluid physically touches. In the rectangular channel <br />above, the wetted perimeter is the bottom width plus the depth of the fluid times two, because there are two <br />sides of the channel, or 6 feet, The hydraulic radius is therefore 4,5/6 = ,0,75 feet The slope is usually <br />taken as the drop in the channel expressed in feetlfoot A channel with I foot of fall in I ()() feet has a slope <br />of 1%, required to he expressed as 0.01 ftIft in the equation, <br /> <br />For simple configurations with readily defined parameters, computing the flow for a given set of conditions <br />can he quite easy, For example, the above rectangular channel flowing half full, Assume it is concrete <br />lined with a Manning's n of 0,013, and a slope of 0.0034. TII1e flow is: <br /> <br />, , <br />1.486 ; ;- _ <br />Q = 0.013 (45)(0,75) (0,0034) = 24.8 d;s <br /> <br />While solving for the flow, or determining the capacity, in a particular channel is a relatively simple exer- <br />cise, the more common need in engineering is designing a cbannel for a givc:n flow, This task is somewhat <br />more difficult due to the different factors involved. <br /> <br />In equation (I), the area and the hydraulic radius are both dependant upon the channel configuration. The <br />fact that the hydraulic radius is raised to the 2/3 power makes solving the equation for channel parameters <br />very cwuhersome, For example. in a rectangular channel, A = boy and R = iVP or: <br /> <br />R=J!L <br />b+2y <br /> <br />(2) <br /> <br />Page 3 <br />Grunhome & O'Mara, Inc. <br />