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Unformatted text preview: Sprinkle & Trickle Irrigation Lectures Page 241 Merkley & Allen Lecture 22 Numerical Solution for Manifold Location I. Introduction In the previous lecture it was seen how the optimal manifold location can be determined semi-graphically using a set of non-dimensional curves for the uphill and downhill laterals This location can also be determined numerically In the following, equations are developed to solve for the unknown length of the uphill lateral, x u , without resorting to a graphical solution . Definition of Minimum Lateral Head In the uphill lateral, the minimum head is at the closed end of the lateral (furthest uphill location in the subunit) This minimum head is equal to: II n l fu u h ' h h x S = (394) where h n is the minimum head (m); h l is the lateral inlet head (m); h fu is the total friction loss in the uphill lateral (m); x u is the length of the uphill lateral (m); and S is the slope of the ground surface (m/m) Note that S must be a positive value x m (h ) fd 2 (h ) fd 1 x u h fu manifold location h n h n In the downhill lateral, the minimum head may be anywhere from the inlet to the outlet, depending on the lateral hydraulics and the ground slope The minimum head in the downhill lateral is equal to: ( ) ( ) n l fd fd m 1 2 h ' h h h x S = + + (395) Merkley & Allen Page 242 Sprinkle & Trickle Irrigation Lectures where (h fu ) 1 is the total friction loss in the downhill lateral (m); (h fu ) 2 is the friction loss from the closed end of the downhill lateral to the location of minimum head (m); and x m is the distance from the manifold (lateral inlet) to the location of minimum head in the downhill lateral (m) Combining Eqs. 1 and 2: ( ) ( ) ( ) fu u m fd fd 1 2 h S x x h h + + + (396) III. Location of Minimum Head in Downhill Lateral = The location of minimum head is where the slope of the ground surface, S, equals the friction loss gradient, J: S J' = (397) where both S and J are in m/m, and S is value of S) he friction loss gradient in the downhill positive (you can take the absolute Using the Hazen-Williams equation, t lateral (at the location where S = J) is: ( ) + 1.852 S f = 10 4.87 a u m e e e e q L x x J' 1.212(10) D S 3,600S C (398) the distance from the manifold to the location of minimum head in D is the lateral inside diameter (mm); The value of 3,600 is to convert q a units from lph to lps Note that x d = L - x u , where x d is the length of the downhill lateral Note that q a (L - x u - x m )/(3,600 S e ) is the flow rate in the lateral, in lps, at the location of minimum head, x m meters downhill from the manifold Combining the above two equations, and solving for x...
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This note was uploaded on 03/01/2012 for the course BIE 6110 taught by Professor Sprinkle during the Fall '03 term at Utah State University.
- Fall '03