# Manifolds in trickle irrigation systems often have multiple pipe sizes to: 1. reduce pipe costs 2. reduce pressure variations ( )

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2 equal to H n plus half the difference in the maximum and minimum heads: ( ) H H = 2 H H max n a n Consider a sloping friction loss gradient (multiple outlets) on flat ground: In this case, the average head occurs after about ¾ of the total head loss (due to friction) occurs, beginning from the lateral inlet. Then, (438) ( ) H H = 4 H H (439) max n a n For a sloping friction loss gradient (multiple outlets) on flat ground with dual pipe sizes, about 63% of the friction head loss occurs from the lateral inlet to the location of average pressure. Then 100/(100-63) = 2.7 and, ( ) H H = 2.7 H H (440) max n a n In summary, an averaging is performed to skew the coefficient toward the minimum value of 2, recognizing that the maximum is about 4, and that for dual-size laterals (or manifolds), the coefficient might be approximately 2.7 The value of 2.5 used in Eq is such a weighted average With three or four pipe sizes the friction loss gradient in the manifold will approach the slope of the ground, which may be linear Thus, as an initial estimate for determining allowable subunit pressure variation for a given design value of EU, Eq is written as follows: s ( a ) H = 2.5 H H n (441) After the design process, the final value of H s may be different, but if it is much different the deviation should be somehow justified Merkley & Allen Page 254 Sprinkle & Trickle Irrigation Lectures

3 III. Pipe Sizing in Manifolds Ideally, a manifold design considers all of the following criteria: 1. economic balance between pipe cost (present) and pumping costs (future) 2. allowable pressure variation in the manifold and subunit 3. pipe flow velocity limits (about m/s) From sprinkler system design, we already know of various pipe sizing methods These methods can also be applied to the design of manifolds However, the difference with trickle manifolds is that instead of one or two pipe sizes, we may be using three or four sizes The manifold design procedures described in the textbook are: 1. Semi-graphical 2. Hydraulic grade line (HGL) 3. Economic pipe sizing (as in Chapter 8 of the textbook) Semi-Graphical Design Procedure The graphical method uses standard head loss curves for different pipe sizes and different flow rates with equally-spaced multiple outlets, each outlet with the same discharge The curves all intersect at the origin (corresponding to the downstream closed end of a pipe) Below is a sample of the kind of curves given in Fig of the textbook Instead of the standard curves, specific curves for each design case could be custom developed and plotted as necessary in spreadsheets The steps to complete a graphical design are outlined in the textbook The graphical procedure is helpful in understanding the hydraulic design of multiple pipe size manifolds, but may not be as expedient as fully numerical procedures Sprinkle & Trickle Irrigation Lectures Page 255 Merkley & Allen

4 Friction Head Loss (ft) inch inch inch inch inch inch Flow Rate (gpm) The following steps illustrate the graphical design procedure: Step 1: flow direction ( H m ) a 1 0 manifold flow rate Q m S o E m x d Merkley & Allen Page 256 Sprinkle & Trickle Irrigation Lectures

5 Step 2: flow direction ( H m ) a 1 0 manifold flow rate Q m S o E m x d Step 3: flow direction ( H m ) a 1 0 manifold flow rate Q m S o E m x d Sprinkle & Trickle Irrigation Lectures Page 257 Merkley & Allen

6 Step 4: flow direction ( H m ) a 1 0 manifold flow rate Q m S o E m x d Step 5: flow direction ( H m ) a 1 0 manifold flow rate Q m S o E m x d Merkley & Allen Page 258 Sprinkle & Trickle Irrigation Lectures

7 Step 6: flow direction ( H m ) a 1 0 manifold flow rate Q m S o E m x d HGL Design Procedure The HGL procedure is very similar to the graphical procedure, except that it is applied numerically, without the need for graphs Nevertheless, it is useful to graph the resulting hydraulic curves to check for errors or infeasibilities The first (upstream) head loss curve starts from a fixed point: maximum discharge in the manifold and upper limit on head variation Equations for friction loss curves of different pipe diameters are known (e.g. Darcy-Weisbach, Hazen-Williams), and these can be equated to each other to determine intersection points, that is, points at which the pipe size would change in the manifold design But, before equating head loss equations, the curves must be vertically shifted so they just intersect with the ground slope curve (or the tangent to the first, upstream, curve, emanating from the origin) The vertical shifting can be done graphically or numerically Economic Design Procedure The economic design procedure is essentially the same as that given in Chapter 8 of the textbook Sprinkle & Trickle Irrigation Lectures Page 259 Merkley & Allen

8 The manifold has multiple outlets (laterals or headers), and the section flow rate changes between each outlet The system flow rate would be the flow rate entering the manifold IV. Manifold Inlet Pressure Head After completing the manifold pipe sizing, the required manifold inlet pressure head can be determined (Eq. 23.4): H = H + kh E (442) where k = 0.75 for single-diameter manifolds; k = 0.63 for dual pipe size laterals; or k 0.5 for three or more pipe sizes (tapered manifolds); and E l is negative for downward-sloping manifolds As with lateral design, the friction loss curves must be shifted up to provide for the required average pressure In the case of manifolds, we would like the average pressure to be equal to the calculated lateral inlet head, H l The parameter E l is the elevation difference along one portion of the manifold (either uphill or downhill), with positive values for uphill slopes and negative values for downhill slopes V. Manifold Design m l f m Manifolds should usually extend both ways from the mainline to reduce the system cost, provided that the ground slope in the direction of the manifolds is less than about 3% (same as for laterals, as in the previous lectures) As shown in the sample layout (plan view) below, manifolds are typically orthogonal to the mainline, and laterals are orthogonal to the manifolds Merkley & Allen Page 260 Sprinkle & Trickle Irrigation Lectures

9 Manifolds usually are made up of 2 to 4 pipe diameters, tapered (telescoping) down toward the downstream end For tapered manifolds, the smallest of the pipe diameters (at the downstream end) should be greater than about ½ the largest diameter (at the upstream end) to help avoid clogging during flushing of the manifold D 1 D 2 D>0 3.5D 1 The maximum average flow velocity in each pipe segment should be less than about 2 m/s Water hammer is not much of a concern, primarily because the manifold has multiple outlets (which rapidly attenuates a high- or low-pressure wave), but the friction loss increases exponentially with flow velocity VI. Trickle Mainline Location The objective is the same as for pairs of laterals: make (H n ) uphill equal to (H n ) dow nhill If average friction loss slopes are equal for both uphill and downhill manifold branches (assuming similar diameters will carry similar flow rates): Downhill side: ( x Hm) a = hfd E hfd Y E L = Uphill side: L x ( Hm) = hfu + E = h fu + (1 Y) E a L (443) (444) where x is the length of downhill manifold (m or ft); L is the total length of the manifold (m or ft); Y equals x/l; and E is the absolute elevation difference of the uphill and downhill portions of the manifold (m or ft) Note that in the above, E is an absolute value (always positive) Then, the average uphill and downhill friction loss slopes are equal: Juphill = Jdownhill hfu h (445) = fd L x x where J-bar is the average friction loss gradient from the mainline to the end of the manifold (J-bar is essentially the same as JF) Sprinkle & Trickle Irrigation Lectures Page 261 Merkley & Allen

10 Then, and, then, ( ) m a ( ) m a hfd = Jx hfu = J(L x) H = Jx Y E H = J(L x) + (1 Y) E ( ) Hm + Y E a = J x = L x ( ) H m (1 Y) E a J (446) (447) (448) Equating both J-bar values, ( ) ( ) H m + a Y E m = H a (1 Y) E x L x (449) Dividing by L and rearranging (to get Eq. 23.3), or, ( ) ( ) H m + Y E H m (1 Y) E a = a Y 1 Y ( ) m a (450) E 2Y 1 = (451) H 2Y(1 Y) Equation 23.3 is used to determine the lengths of the uphill and downhill portions of the manifold You can solve for Y (and x), given E and ( H m ) a = H s - H l Remember that H s 2.5(H a H n ), where Ha is for the average emitter and H n is for the desired EU and ν s Equation 23.3 can be solved by isolating one of the values for Y on the left hand side, such that: 2Y 1 ( Hm ) Y 1 a 2Y E (452) and assuming an initial value for Y (e.g. Y = 0.6), plugging it into the right side of the equation, then iterating to arrive at a solution Merkley & Allen Page 262 Sprinkle & Trickle Irrigation Lectures

11 Note that 0 Y 1, so the solution is already well-bracketed Note that in the trivial case where E = 0, then Y = 0.5 (don t apply the above equation, just use your intuition!) A numerical method (e.g. Newton-Raphson) can also be used to solve the equation for Y V II. Selection o f Manifold Pipe Sizes The selection of manifold pipe sizes is a function of: 1. Economics, where pipe costs are balanced with energy costs 2. Balancing h f, E, and ( H m ) a to obtain the desired EU 3. Velocity constraints VIII. Manifold Pipe Sizing by Economic Selection Method This method is similar to that used for mainlines of sprinkler systems Given the manifold spacing, S m, and the manifold length, do the following: (a) Construct an economic pipe size table where Q s = Q m (b) Select appropriate pipe diameters and corresponding Q values at locations where the diameters will change (c) Determine the lengths of each diameter of pipe (where the Q in the manifold section equals a breakeven Q from the Economic Pipe Size Table (EPST) L D Qbeg Qend = L Qm (453) where Q beg is the flow rate at the beginning of diameter D in the EPST (lps or gpm); Q end is the flow rate at the end of diameter D in the EPST, which is the breakeven flow rate of the next larger pipe size) (lps or gpm); L is the total length of the manifold (m or ft); and Q m is the manifold inflow rate (lps or gpm). (see Eq. 23.7) (d) Determine the total friction loss along the manifold (see Eq. 23.8a): h a a a a a a a FLK Q1 Q2 Q1 Q3 Q2 Q4 Q3 f = Q c c c c m D1 D2 D3 D4 (454) where, a = b+1 (for the Blasius equation, a = 2.75) c = 4.75 for the Blasius equation (as seen previously) Sprinkle & Trickle Irrigation Lectures Page 263 Merkley & Allen

12 Q 1 = Q at the beginning of the smallest pipe diameter Q 2 = Q at the beginning of the next larger pipe diameter Q 3 = Q at the beginning of the third largest pipe diameter in the manifold Q 4 = Q at the beginning of the largest pipe diameter in the manifold F = multiple outlet pipe loss factor For the Hazen-Williams equation, F equals 1/( ) = 0.35 For the Darcy-Weisbach equation, F equals 1/(2+1) = 0.33 L = D = K = K = h f = the total length of the manifold inside diameter of the pipe 7.89(10) 7 for D in mm, Q in lps, and length in m for D in inches, Q in gpm, and length in ft friction head loss The above equation is for four pipe sizes; if there are less than four sizes, the extra terms are eliminated from the equation An alternative would be to use Eq. 23.8b (for known pipe lengths), or evaluate the friction loss using a computer program or a spreadsheet to calculate the losses section by section along the manifold Eq. 23.8b is written for manifold design as follows: h a 1 a a a a a a a FKQm x1 x2 x1 x3 x2 x4 x3 f = a 1 c c c c 100L D 1 D2 D3 D4 (455) where, x 1 = length of the smallest pipe size x 2 = length of the next smaller pipe size x 3 = length of the third largest pipe size x 4 = length of the largest pipe size Again, there may be up to four different pipe sizes in the manifold, but in many cases there will be less than four sizes (e) For s 0 (uphill branch of the manifold), H = h + Sx For s < 0 (downhill branch of the manifold), m f u (456) 0.36 Hm = hf + S 1 x n d (457) Merkley & Allen Page 264 Sprinkle & Trickle Irrigation Lectures

13 < (to remains will may where n is the number of different pipe sizes used in the branch; and S is the ground slope in the direction of the manifold (m/m) The above equation estimates the location of minimum pressure in the downhill part of the manifold (f) if HBmB 1.1 ( HBmB)BaB, then the pipe sizing is all right. Go to step (g) of this procedure. Otherwise, do one or more of the following eight adjustments: (1) Increase the pipe diameters selected for the manifold Do this proportionately by reselecting diameters from the EPST using a larger QBsB increase the energy penalty and recompute a new EPST). This will artificially increase the break-even flow rates in the table (chart). The new flow rates to use in re-doing the EPST can be estimated for s > 0 as follows: Q h = E m new old f s Qs ( Hm) a 1/ b (458) and for s < 0 as: Q new old f s = Qs h 0.36 Hm E a l 1 n ( ) 1/ b (459) The above two equations are used to change the flow rates to compute the EPST The value of QBmB the same The elevation change along each manifold (uphill or downhill branches) is El = sl/100 (2) Decrease SBmB This will make the laterals shorter, QBmB decrease, and HBlB decrease This alternative may or may not help in the design process (3) Reduce the target EU This will increase HBsB Sprinkle & Trickle Irrigation Lectures Page 265 Merkley & Allen

14 > (use = per < (or (4) Decrease HBlB larger pipe sizes) This will increase the cost of the pipes (5) Increase HBaB This will increase HBsB This alternative will cost money and or energy (6) Reduce the manufacturer s coefficient of variation This will require more expensive emitters and raise the system cost (7) Increase the number of emitters per tree (NBpB) This will reduce the value of νbsb (8) If NBsB 1, increase TBaB station Try operating two or more stations simultaneously Now go back to Step (b) and repeat the process. (g) Compute the manifold inlet head, Hm = Hl + khf Em (460) where, k = 0.75 for a single size of manifold pipe k = 0.63 for two pipe sizes k = 0.50 for three or more sizes For non-critical manifolds, or where HBmB ( HBmB)BaB, decrease QBsB just design using another sizing method) in the Economic Pipe Selection Table to dissipate excess head For non-rectangular subunits, adjust F using a shape factor: s 1.25 f F = 0.38S (461) where SBfB QBlcB/QBlaB; QBlcB is the lateral discharge at the end of the manifold and QBlaB is the average lateral discharge along the manifold. Then, JL = (462) hf FsF 100 IX. Manifold Pipe Sizing by the HGL Method This is the Hydraulic Grade Line method Same as the semi-graphical method, but performed numerically Merkley & Allen Page 266 Sprinkle & Trickle Irrigation Lectures

15 is (a) Uphill Side of the Manifold Get the smallest allowable pipe diameter and use only the one diameter for this part of the manifold (b) Downhill Side of the Manifold Largest Pipe Size, DB1B First, determine the minimum pipe diameter for the first pipe in the downhill side of the manifold, which of course will be the largest of the pipe sizes that will be used This can be accomplished by finding the inside pipe diameter, D, that will give a friction loss curve tangent to the ground slope To do this, it is necessary to: (1) have the slope of the friction loss curve equal to SBoB; and, (2) have the H values equal at this location (make them just touch at a point) These two requirements can be satisfied by applying two equations, whereby the two unknowns will be Q and DB1B Assume that QBlB constant along the manifold See the following figure, based on the length of the downstream part of the manifold, xbdb Some manifolds will only have a downhill part others will have both uphill and downhill parts H flow direction h f D =??? 1 friction loss curve ( H m ) a 0 0 manifold flow rate Q m 1 S o E m x d Sprinkle & Trickle Irrigation Lectures Page 267 Merkley & Allen

16 For the above figure, where the right side is the mainline location and the left side is the downstream closed end of the manifold, the friction loss curve is defined as: JFL H= ( Hm) + Em hf + a 100 (463) where, using the Hazen-Williams equation, Q 4.87 J= K D for 0 Q Q C m (464) F = N 6N (465) 2 xd Q N= for N> 0 S Q l m (466) where N is the number of outlets (laterals) from the location of Q in the manifold to the closed end Q L = xd (467) Qm 6 For Q in lps and D in cm, K = 16.42(10)P P The total head loss in the downhill side of the manifold is: JhfFhfxd Qm 4.87 f hf d h = = 0.01K D F x 100 C (468) where FBhfB is defined as F above, except with N = xbdb/sblb. The slope of the friction loss curve is: dh 1 dj df dl = FL + JL + JF dq 100 dq dq dq (469) where, Merkley & Allen Page 268 Sprinkle & Trickle Irrigation Lectures

17 KQ = (470) dj dq C D df x d = dq 2 SQ l mn + 2 3N (471) dl dq x = d (472) Qm Note that dh/dq J The ground surface (assuming a constant slope, SBoB) is defined by: and, H S L S x Q = o = o d Qm dh dq S x (473) = o d (474) Qm Combine the two equations defining H (this makes the friction loss curve just touch the ground surface): Q JFL Sx o d = ( Hm) + E a m hf + Qm 100 (475) Solve the above equation for the inside diameter, D: SxQ 100C o d ( Hm) Em = Q a m D K( Q FL Q ) m Fhfxd (476) Set the slope of the friction loss curve equal to SBoBxBdB/QBmB, Sx o d 1 dj df dl = FL + JL + JF Q 100 dq dq dq m (477) Sprinkle & Trickle Irrigation Lectures Page 269 Merkley & Allen

18 SBtB line, be is Combine the above two equations so that the only unknown is Q (note: D appears in the J & dj/dq terms of the above equation) Solve for Q by iteration; the pipe inside diameter, D, will be known as part of the solution for Q The calculated value of D is the minimum inside pipe diameter, so find the nearest available pipe size that is larger than or equal to D: D1 D & minimize(d1 D) (478) Slope of the Tangent LineB Now calculate the equation of the line through the origin and tangent to the friction loss curve for DB1B Let SBtB the slope of the tangent line then, Q = t = t d Qm H SL S x Q JFL Sx t d = ( Hm) E a + l hf + Qm 100 (479) (480) Set the slope of the friction loss curve equal to SBtBxBdB/QBmB, Sx t d 1 dj df dl = FL + JL + JF Q 100 dq dq dq m (481) Combine the above two equations to eliminate SBtB, and solve for Q (which is different than the Q in Eq. 476) Calculate the slope, SBtB, directly Smaller (Downstream) Pipe SizesB Then take the next smaller pipe size, DB2B, and make its friction loss curve tangent to the same line (slope = SBtB); JFL H= H0 + (482) 100 where HB0B a vertical offset to make the friction loss curve tangent to the emanating from the origin Merkley & Allen Page 270 Sprinkle & Trickle Irrigation Lectures

19 is friction Equating heads and solving for HB0B, H Q JFL = S x Qm t d (483) Again, set the slope of the friction loss curve equal to SBtB, Sx t d 1 dj df dl = FL + JL + JF Q 100 dq dq dq m (484) Solve the above equation for Q, then solve directly for HB0B Now you have the equation for the next friction loss curve Determine the intersection with the DB1B loss curve to set the length for size DB1B; this is done by equating the H values for the respective equations and solving for Q at the intersection: ( ) FLK Q Hbig Hsmall + Dbig Dsmall = C (485) where, for the first pipe size (DB1B): ( ) H = H + E h (486) big m a l f and for the second pipe size (DB2B): and F & L are as defined in Eqs. 437 to 439. Then, the length of pipe DB1B H small = H0 (487) equal to: = Q LD1 xd 1 Q m (488) Continue this process until you have three or four pipe sizes, or until you get to a pipe size that has D < ½DB1B Sprinkle & Trickle Irrigation Lectures Page 271 Merkley & Allen

20 Comments about the HGL MethodB The above equation development could also be done using the Darcy- Weisbach equation Specify a minimum length for each pipe size in the manifold so that the design is not something ridiculous (i.e. don t just blindly perform calculations, but look at what you have) For example, the minimum allowable pipe length might be something like 5SBlB Note that the friction loss curves must be shifted vertically upward to provide the correct average (or minimum, if pressure regulators are used) pressure head in the manifold; this shifting process determines the required manifold inlet pressure head, HBmB Below is a screen shot from a computer program that uses the HGL method for manifold pipe sizing Merkley & Allen Page 272 Sprinkle & Trickle Irrigation Lectures

21 Sprinkle & Trickle Irrigation Lectures Page 273 Merkley & Allen

22 Merkley & Allen Page 274 Sprinkle & Trickle Irrigation Lectures

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