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Unformatted text preview: Lecture 23 Manifold Hydraulic Design
I. Introduction
• Manifolds in trickle irrigation systems often have multiple pipe sizes to:
1. reduce pipe costs
2. reduce pressure variations •
•
•
• In small irrigation systems the reduction in pipe cost may not be significant,
not to mention that it is also easier to install a system with fewer pipe sizes
Manifold design is normally subsequent to lateral design, but it can be part of
an iterative process (i.e. design the laterals, design the manifold, adjust the
lateral design, etc.)
The allowable head variation in the manifold, for manifolds as subunits, is
given by the allowable subunit head variation (Eq. 20.14) and the calculated
lateral head variation, ∆Hl
This simple relationship is given in Eq. 23.1: ( ∆Hm )a = ∆Hs − ∆Hl
•
•
• (437) Eq. 23.1 simply says that the allowable subunit head variation is shared by
the laterals and manifold
Recall that a starting design point can be to have ∆Hl = ½∆Hs, and ∆Hm =
½∆Hs, but this half and half proportion can be adjusted during the design
iterations
The lateral pressure variation, ∆Hl, is equal to the maximum pressure minus
the minimum pressure, which is true for singledirection laterals and
uphill+downhill pairs, if Hn’ is the same both uphill and downhill II. Allowable Head Variation
•
•
• • Equation 20.14 (page 502 in the textbook) gives the allowable pressure head
variation in a “subunit”
This equation is an approximation of the true allowable head variation,
because this equation is applied before the laterals and manifold are
designed
After designing the laterals and manifold,
the actual head variation and expected
EU can be recalculated
Consider a linear friction loss gradient (no
multiple outlets) on flat ground:
In this case, the average head is Sprinkle & Trickle Irrigation Lectures Page 253 Merkley & Allen equal to Hn plus half the difference in the maximum and minimum heads: ( H max − H n = 2 H a − H n
• ) (438) 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, ( H max − H n = 4 H a − H 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/(10063) = 2.7 and, ( H max − H n = 2.7 H a − H n
•
•
•
• ) (440) 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
dualsize laterals (or manifolds), the coefficient might be approximately 2.7
The value of 2.5 used in Eq. 20.14 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. 20.14 is written as follows: ( ∆Hs = 2.5 H a − H n
• (439) ) (441) After the design process, the final value of ∆Hs may be different, but if it is
much different the deviation should be somehow justified Merkley & Allen Page 254 Sprinkle & Trickle Irrigation Lectures 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 1.5  2.0 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. Semigraphical
2. Hydraulic grade line (HGL)
3. Economic pipe sizing (as in Chapter 8 of the textbook) SemiGraphical Design Procedure
•
•
•
•
•
• The graphical method uses “standard” head loss curves for different pipe
sizes and different flow rates with equallyspaced 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. 23.2 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 3.8
3.6
3.4
3.2 Friction Head Loss (ft) 3.0
2.8
2.6
2.4
2.2
2.0
1.8
1.6
1.4
1.2 1.25 inch
1.50 inch
2.00 inch
2.50 inch
3.00 inch
4.00 inch 1.0
0.8
0.6
0.4
0.2
0.0
0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 Flow Rate (gpm )
• The following steps illustrate the graphical design procedure:
Step 1: flow direction (∆Hm)a 1 0 manifold flow rate ∆Em So Qm xd
Merkley & Allen Page 256 Sprinkle & Trickle Irrigation Lectures Step 2:
flow direction (∆Hm)a 1 0 ∆Em So Qm manifold flow rate xd
Step 3: flow direction (∆Hm)a 1 0 manifold flow rate ∆Em So Qm xd Sprinkle & Trickle Irrigation Lectures Page 257 Merkley & Allen Step 4:
flow direction (∆Hm)a 1 0 ∆Em So Qm manifold flow rate xd Step 5:
flow direction (∆Hm)a 1 0 manifold flow rate ∆Em So Qm xd Merkley & Allen Page 258 Sprinkle & Trickle Irrigation Lectures Step 6: flow direction (∆Hm)a 1 0 ∆Em So Qm manifold flow rate xd
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.
DarcyWeisbach, HazenWilliams), 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 •
• 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): Hm = Hl + k hf + 0.5∆Em (442) where k = 0.75 for singlediameter manifolds; k = 0.63 for dual pipe size
laterals; or k ≈ 0.5 for three or more pipe sizes (tapered manifolds); and ∆El
is negative for downwardsloping 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, Hl
The parameter ∆El 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
•
• 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 •
• 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 D1
•
• D2 D3>0.5D1 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 lowpressure 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 (Hn)uphill equal to
(Hn)downhill
If average friction loss slopes are equal for both uphill and downhill manifold
branches (assuming similar diameters will carry similar flow rates):
Downhill side: ( ∆Hm )a = hfd − ∆E ⎛
⎜ x⎞
= hfd − Y∆E
L⎟
⎝⎠ (443) L−x⎞
⎟ = hfu + (1 − Y)∆E
⎝L⎠ (444) Uphill side: ( ∆Hm )a = hfu + ∆E ⎛
⎜ 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
(445) hfu
h
= fd
L−x
x where Jbar is the average friction loss gradient from the mainline to the end
of the manifold (Jbar is essentially the same as JF)
Sprinkle & Trickle Irrigation Lectures Page 261 Merkley & Allen Then, hf d = J x (446) hfu = J (L − x )
and, then, ( ∆Hm )a = J x − Y∆E
( ∆Hm )a = J (L − x ) + (1 − Y) ∆E ( ∆Hm )a + Y∆E
x =J ( ∆Hm )a − (1 − Y) ∆E
L−x • (448) =J Equating both Jbar values, ( ∆Hm )a + Y∆E ( ∆Hm )a − (1 − Y) ∆E
x
• = L−x Y
or, •
•
• (449) Dividing by L and rearranging (to get Eq. 23.3), ( ∆Hm )a + Y∆E ( ∆Hm )a − (1 − Y) ∆E • (447) = 1− Y ∆E
2Y − 1
=
( ∆Hm )a 2Y(1 − Y) (450) (451) 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 (∆Hm)a = ∆Hs  ∆Hl
Remember that ∆Hs ≈ 2.5(Ha – Hn), where Ha is for the average emitter and
Hn is for the desired EU and νs
Equation 23.3 can be solved by isolating one of the values for Y on the left
hand side, such that: ⎛ 2Y − 1 ⎞ ⎛ ( ∆Hm ) ⎞
a
Y = 1− ⎜
⎟⎜
⎜ ∆E ⎟
⎟
⎜ 2Y ⎟
⎠
⎝
⎠⎝ (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 •
•
• Note that 0 ≤ Y ≤ 1, so the solution is already wellbracketed
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. NewtonRaphson) can also be used to solve the
equation for Y VII. Selection of 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 hf, ∆E, and (∆Hm)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, Sm, and the manifold length, do the following: (a) Construct an economic pipe size table where Qs = Qm
(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) ⎛ Qbeg − Qend ⎞
LD = L ⎜
⎟
Qm
⎝
⎠ (453) where Qbeg is the flow rate at the beginning of diameter “D” in the EPST (lps
or gpm); Qend 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 Qm 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):
a
a
a
a
FLK ⎛ Q1 Qa − Q1 Q3 − Qa Qa − Q3 ⎞
2+ 4
2
hf =
+
⎜ c+
⎟
c
100 Qm ⎜ D1
Dc
D3
Dc ⎟
2
4
⎝
⎠ (454) where,
a=
c= b+1 (for the Blasius equation, a = 2.75)
4.75 for the Blasius equation (as seen previously) Sprinkle & Trickle Irrigation Lectures Page 263 Merkley & Allen Q1 =
Q2 =
Q3 =
Q4 =
F= Q at the beginning of the smallest pipe diameter
Q at the beginning of the next larger pipe diameter
Q at the beginning of the third largest pipe diameter in the manifold
Q at the beginning of the largest pipe diameter in the manifold
multiple outlet pipe loss factor
•
• L=
D=
K=
K=
hf =
•
•
• For the HazenWilliams equation, F equals 1/(1.852+1) = 0.35
For the DarcyWeisbach equation, F equals 1/(2+1) = 0.33 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
0.133 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:
a
a
a
a
a
FK Qm−1 ⎛ x1 x a − x1 x 3 − x a x a − x 3 ⎞
2+ 4
2
hf =
+
⎜ c+
⎟
c
100 La −1 ⎜ D1
Dc
D3
Dc ⎟
2
4
⎝
⎠ where, • (455) x1 = length of the smallest pipe size
x2 = length of the next smaller pipe size
x3 = length of the third largest pipe size
x4 = 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), ∆Hm = hf + S xu (456) For s < 0 (downhill branch of the manifold), ⎛ 0.36 ⎞
∆Hm = hf + S ⎜ 1 −
xd
n⎟
⎝
⎠ Merkley & Allen Page 264 (457) Sprinkle & Trickle Irrigation Lectures 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 ∆Hm < 1.1 (∆Hm)a, then the pipe sizing is all right. Go to step (g) of this
procedure. Otherwise, do one or more of the following eight adjustments:
B B B B B B (1) Increase the pipe diameters selected for the manifold
• Do this proportionately by reselecting diameters from the EPST using a
larger Qs (to increase the energy “penalty” and recompute a new
EPST). This will artificially increase the breakeven flow rates in the
table (chart).
The new flow rates to use in redoing the EPST can be estimated for s >
0 as follows:
B • B 1/ b ⎛
⎞
hf
old
= Qs ⎜
⎟
⎜ ( ∆Hm ) − ∆Em ⎟
a
⎝
⎠ Qnew
s (458) and for s < 0 as:
1/ b Qnew
s ⎛
⎞
⎜
⎟
hf
old ⎜
⎟
= Qs
⎛ 0.36 ⎞ ⎟
⎜ ∆H
⎜ ( m )a − ∆El ⎜ 1 − n ⎟ ⎟
⎝
⎠⎠
⎝ (459) • The above two equations are used to change the flow rates to compute
the EPST
• The value of Qm remains the same
• The elevation change along each manifold (uphill or downhill branches)
is ∆El = sL/100
(2) Decrease Sm
• This will make the laterals shorter, Qm will decrease, and ∆Hl may
decrease
• This alternative may or may not help in the design process
B B B B B (3) Reduce the target EU
• This will increase ∆Hs
B Sprinkle & Trickle Irrigation Lectures B B B B Page 265 Merkley & Allen (4) Decrease ∆Hl (use larger pipe sizes)
• This will increase the cost of the pipes
B B (5) Increase Ha
• This will increase ∆Hs
• This alternative will cost money and or energy
B B B B (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 (Np)
• This will reduce the value of νs
B B B B (8) If Ns > 1, increase Ta per station
• Try operating two or more stations simultaneously
B • B B B Now go back to Step (b) and repeat the process. (g) Compute the manifold inlet head, Hm = Hl + khf + 0.5∆Em
where, •
• (460) 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 noncritical manifolds, or where ∆Hm < (∆Hm)a, decrease Qs (or just
design using another sizing method) in the Economic Pipe Selection
Table to dissipate excess head
For nonrectangular subunits, adjust F using a shape factor:
B B B B B B Fs = 0.38S1.25 + 0.62
f B B (461) where Sf = Qlc/Qla; Qlc is the lateral discharge at the end of the manifold
and Qla is the average lateral discharge along the manifold. Then,
B B B B B B B B B B ⎛ JL ⎞
hf = Fs F ⎜
⎟
⎝ 100 ⎠ (462) IX. Manifold Pipe Sizing by the “HGL” Method
•
• This is the “Hydraulic Grade Line” method
Same as the semigraphical method, but performed numerically Merkley & Allen Page 266 Sprinkle & Trickle Irrigation Lectures (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, D1
B •
•
• 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 So; 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 D1
Assume that Ql is constant along the manifold…
See the following figure, based on the length of the downstream part of
the manifold, xd
Some manifolds will only have a downhill part – others will have both
uphill and downhill parts
B • B B B B B • B B B H flow direction (∆Hm)a hf cu
rv
e •
• ss D1 = ??? fr 0
0 i on
ict lo 1
manifold flow rate ∆Em So Qm xd
Sprinkle & Trickle Irrigation Lectures Page 267 Merkley & Allen • 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: H = ( ∆Hm )a + ∆Em − hf + JFL
100 (463) where, using the HazenWilliams equation,
1.852 ⎛Q⎞
J = K⎜ ⎟
⎝C⎠ F= D−4.87 for 0 ≤ Q ≤ Qm (464) 1
1
0.852
+
+
2.852 2N
6N2 ⎛ x ⎞⎛ Q ⎞
N = ⎜ d ⎟⎜
⎟
⎝ Sl ⎠ ⎝ Qm ⎠ (465) for N > 0 (466) where N is the number of outlets (laterals) from the location of “Q” in the
manifold to the closed end ⎛Q⎞
L = xd ⎜
⎟
⎝ Qm ⎠ (467) For Q in lps and D in cm, K = 16.42(10)6
P • P The total head loss in the downhill side of the manifold is:
1.852 JFx
⎛Q ⎞
hf = hf hf d = 0.01K ⎜ m ⎟
100
⎝C⎠ D−4.87Fhf x d (468) where Fhf is defined as F above, except with N = xd/Sl.
B • B B B B B 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 dJ 1.852KQ0.852
=
dQ
C1.852D4.87
dF
xd ⎛ 1
0.852 ⎞
=−
⎜+
⎟
dQ
3N ⎟
SlQmN2 ⎜ 2
⎝
⎠ (471) dL
x
=d
dQ Qm
•
• (470) (472) Note that dH/dQ ≠ J
The ground surface (assuming a constant slope, So) is defined by:
B B ⎛Q⎞
H = SoL = So x d ⎜
⎟
⎝ Qm ⎠ (473) dH So x d
=
dQ
Qm (474) and, • Combine the two equations defining H (this makes the friction loss curve
just touch the ground surface): ⎛Q⎞
JFL
So x d ⎜
⎟ = ( ∆Hm )a + ∆Em − hf +
100
⎝ Qm ⎠
• Solve the above equation for the inside diameter, D: ⎡
⎛S x Q
⎞⎤
100C1.852 ⎜ o d − ( ∆Hm )a − ∆Em ⎟ ⎥
⎢
⎝ Qm
⎠⎥
D=⎢
1.852
1.852
⎢
⎥
KQ
FL − Qm Fhf x d
⎢
⎥
⎢
⎥
⎣
⎦ ( • (475) −0.205 ) (476) Set the slope of the friction loss curve equal to Soxd/Qm,
B B B B So x d
1⎛
dJ
dF
dL ⎞
=
+ JL
+ JF
⎜ FL
⎟
Qm
100 ⎝ dQ
dQ
dQ ⎠
Sprinkle & Trickle Irrigation Lectures Page 269 B B (477) Merkley & Allen •
•
• 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 Line
B • Now calculate the equation of the line through the origin and tangent to
the friction loss curve for D1
Let St be the slope of the tangent line
B • B B B ⎛Q⎞
H = StL = St x d ⎜
⎟
⎝ Qm ⎠ (479) ⎛Q⎞
JFL
St x d ⎜
⎟ = ( ∆Hm )a + ∆El − hf +
100
⎝ Qm ⎠ (480) then, • Set the slope of the friction loss curve equal to Stxd/Qm,
B B B B B B St x d
1⎛
dJ
dF
dL ⎞
=
+ JL
+ JF
⎜ FL
⎟
Qm 100 ⎝ dQ
dQ
dQ ⎠
•
• (481) Combine the above two equations to eliminate St, and
solve for Q (which is different than the Q in Eq. 476)
Calculate the slope, St, directly
B B B B Smaller (Downstream) Pipe Sizes
B • Then take the next smaller pipe size, D2, and make its
friction loss curve tangent to the same line (slope = St);
B B B H = H0 + JFL
100 B (482) where H0 is a vertical offset to make the friction loss curve tangent to the
St line, emanating from the origin
B B B B Merkley & Allen Page 270 Sprinkle & Trickle Irrigation Lectures • Equating heads and solving for H0,
B B ⎛ Q ⎞ JFL
H0 = St x d ⎜
⎟−
⎝ Qm ⎠ 100
• (483) Again, set the slope of the friction loss curve equal to St,
B B St x d
1⎛
dJ
dF
dL ⎞
=
+ JL
+ JF
⎜ FL
⎟
Qm 100 ⎝ dQ
dQ
dQ ⎠
•
•
• (484) Solve the above equation for Q, then solve directly for H0
Now you have the equation for the next friction loss curve
Determine the intersection with the D1 friction loss curve to set the length
for size D1; this is done by equating the H values for the respective
equations and solving for Q at the intersection:
B B B B B B −4.87
−4.87
(Dbig − Dsmall ) = 0 1.852 FLK ⎛ Q ⎞
Hbig − Hsmall +
⎜⎟
100 ⎝ C ⎠ (485) where, for the first pipe size (D1):
B B Hbig = ( ∆Hm )a + ∆El − hf (486) and for the second pipe size (D2):
B B Hsmall = H0 (487) and F & L are as defined in Eqs. 437 to 439.
• Then, the length of pipe D1 is equal to:
B B ⎛
Q⎞
LD1 = x d ⎜ 1 −
⎟
⎝ Qm ⎠
• (488) Continue this process until you have three or four pipe sizes, or until you
get to a pipe size that has D < ½D1
B Sprinkle & Trickle Irrigation Lectures B Page 271 Merkley & Allen Comments about the HGL Method
B •
•
• The above equation development could also be done using the DarcyWeisbach 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 5Sl
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, Hm
Below is a screen shot from a computer program that uses the HGL
method for manifold pipe sizing
B • B B • Merkley & Allen Page 272 B Sprinkle & Trickle Irrigation Lectures Sprinkle & Trickle Irrigation Lectures Page 273 Merkley & Allen Merkley & Allen Page 274 Sprinkle & Trickle Irrigation Lectures ...
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 Fall '03
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