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2 00 Pipe ID 3 inches 200,Perforation 4 holes every 6 inches. Unit Discharge Rate gpm Hole size inch,Flowrate in Pipe gpm. 0 10 20 30 40 50 60 70 80 90 100,Distance from End of Pipe ft. Unit Discharge Rate Flow rate in Pipe, Figure 3 Unit Discharge Rate and Flow Rate the Typical Practice. In order to uniformly distribute the injected liquid along the entire pipe length a pressurized. perforated pipe design is necessary of which both the sizing and number of the perforations need to. be reduced In an example illustrated in Figure 4 one inch perforation is drilled for every linear. foot of the pipe As seen in the results the perforated pipe is pressurized entrance pressure head is. 9 ft and a relative uniform distribution of liquid along the entire length is achieved between 2 2 and. 1 8 gpm for any given perforation The following sections will focus on the design of the. pressurized liquid injection pipes,Unit Discharge Rate gpm.
Flowrate in Pipe gpm,Total flowrate 200 gpm,Entrance Pressure 9 ft W C. Pipe ID 3 inches,Perforation 1 holes every 1 ft,Hole size inch. 0 10 20 30 40 50 60 70 80 90 100,Distance from End of Pipe ft. Unit Discharge Rate Flow rate in Pipe, Figure 4 Unit Discharge Rate and Flow Rate the Pressurized Design. DESIGN METHOLOGY,Design Equations, The unit discharge rate q from each of the perforations is governed by the size of the.
perforation and the static pressure at its respective location along the pipe. q BA 2 gP 11 79d 2 P 1 2 1,Where q flow rate per perforation gpm. B orifice coefficient assumed as 0 60,A area of orifice in2. g gravitational acceleration 32 2 ft s2,P pressure head over orifice water column in ft. d diameter of perforation inch, According to Bernoulli s equation total head at any given point in liquid under motion is the sum of. pressure velocity and elevation heads,Where h total head feet.
P pressure head feet,V velocity ft sec,g gravitational acceleration 32 2 ft s2. Z elevation head feet, Change of total head in pipes is primarily due to friction and other minor losses Since perforated. pipes are typically constructed with straight sections with limited number of joints minor losses are. generally considered negligible Therefore the friction loss along the pipe will determine the. change in total head Friction loss in pipes can be calculation using Hazen Williams equation as. h f 0 002082 L 4 8655 3,Where hf friction loss head feet. L length of pipe feet,C pipe friction factor 150 for HDPE pipes. Q flow rate in pipe gpm,D nominal pipe size inch, Due to discharge at perforations flow in perforated pipes varies along the pipe length Figure 5.
Flow in perforated pipes can be obtained by summing discharges from all of the downstream holes. Where Qi flow in the pipe before perforation i gpm. qj discharge rate at perforation j downstream of i gpm. Qn 1 Qn 2 Qn 3 Q3 Q2 Q1,Q Qn n n 1 n 2 n 3 3 2 1,qn qn 1 qn 2 qn 3 q3 q2 q1. Figure 5 Flow Rate along Perforated Pipe, Friction loss in each section between two perforations can be determined as. h f i 0 002082 L 5,C D 4 8655, Where L is the spacing between two adjacent perforations L can be calculated based on total. number of perforations n as, Based on the conservation of energy the total head can be calculated as. h Pi zi Pi 1 i 1 zi 1 h fi 7, For low velocity flow less than 5 ft sec the kinetic head is generally very low less than 0 4 ft and.
is typically neglected For horizontal placed pipes pressure at an upstream perforation can be. determined as,Pi 1 Pi h f i 8, The unit discharge rate at an upstream perforation can be calculated as. qi 1 11 79d 2,Pi h f i 11 79d 2,Pi 0 002082 L 9,C D 4 8655. The unit discharge rate at the end of the pipe q1 can be calculated as. q1 11 79d 2 P1 10,where P1 is the pressure at end of the pipe. Once the far end pressure value P1 and the far end discharge rate q1 are determined unit. discharge rate for all perforations can be obtained using Equations 4 and 9 The entrance. pressure and the total flow rate will be utilized in the pumping system calculations The above listed. procedures can be readily incorporated in spreadsheet programs However a trial and error process. may be required to match the pumping system requirements. Design Principles, The ratio of unit discharge rates between the first and the last perforations can be used to. quantify the uniformity of liquid distribution In other words if the ratio for a given perforated pipe. design is closer to unity the liquid is more evenly distributed As the examples illustrated in Figures. 3 and 4 a satisfactory ratio of 1 2 can be found in the pressurized pipe design whereas a ratio. greater than 10 000 which is clearly inadequate can be seen in the low pressure design. Note that the variation in the unit discharge rates is caused by the pressure change in the pipe. and the relative change of the discharge rate can be determined as. q n q1 Pn P1, Deriving from Equation 11 a correlation between the change in discharge rate and the change in.
pressure can be developed as,Pn q n q n,where q qn q1. The correlation between the change in pipe pressure and the change in unit discharge rates can be. established using Equation 12 see Figure 6,Change in Entrance Pressure. 0 5 10 15 20 25 30,Change in Unit Discharge Rate, Figure 6 Correlation between Change in Unit Discharge Rate and Change in Entrance Pressure. As previously discussed pressure change in pipe is primarily due to friction loss. P h f i 13, The total friction loss in perforated pipes can be estimated using Equation 14. Note that F is a correction factor and P is the friction loss calculated for a solid wall pipe. having same diameter length and total flow rate Equations 15 and 16 depict the determinations. for F and P respectively Note that the correlation shown in Equation 15 is established. based on an assumption that the change of unit discharge rate is less than 20. P 0 002082 L,C D 4 8655, As shown in Equation 15 the correction factor F is a function of the number of.
perforations along the pipe As the number of perforations increases the correction factor decreases. and ultimately levels off at a value of 0 36 Figure 7 For most design with more than 100 holes. along the pipe a correction factor F of 0 36 can be used. 0 50 100 150 200,Number of Hole on Perforated Pipe n. Figure 7 Friction Loss Correction Factor for Perforated Pipe. Finally by combining and rearranging Equations 14 and 16 the required pipe diameter can be. determined as,0 2055 0 3802,D 1 6193 17,Design Procedures. Uniform liquid distribution along the perforated liquid injection pipes can be achieved by. proper selection of pipe diameter size of perforations and spacing between perforations A. systematic procedure can be presented in a flowchart format as shown in Figure 8 Individual steps. will be discussed in detail in the following subsections. Pipe length L and linear discharge rate q,Calculation. Total flow rate Q,Pumping system,and entrance pressure. Change linear discharge rate q,Perforation diameter d and unit discharge rate q.
Number of perforations n and spacing L,Calculation Input. Pressure difference between first and last perforations Allowed variation. Eq 17 and Fig 7 for unite discharge rate,Calculation. Determine pipe diameter,Perforation diameter d spacing L. pipe diameter D and entrance pressure Pn,Figure 8 Design Procedure Flowchart. 1 Selecting input parameters, Length of the perforated pipe L is generally determined by the dimensions of the waste lift.
where the injection line is to be installed To avoid leachate outbreaks on refuse slopes the. injection lines should not be located within 50 ft of the exterior waste slope The injection lines. are typically spaced horizontally 50 to 150 ft with a vertical interval of 20 ft. The linear discharge rate q should also be pre selected The actual value is controlled by the. infiltration capacity of the waste Reinhart and Townsend 1998 suggested that injection rates. between 25 to 50 gpd ft are adequate To further promote lateral distribution and minimize. biological clogging intermittent liquid injection should also be considered Reinhart and. Townsend 1998 Generally speaking selecting linear discharge rate between 0 2 to 0 4 gpm ft. seems appropriate,2 Determining total flow rate,The total flow rate Q can be calculated as. Note that this total flow rate is identical to the entrance flow rate Qn. 3 Determining the entrance pressure, Based on the required flow rate the pumping and forcemain analyses can be conducted and. subsequently the entrance pressure can be determined Since the procedure is a common. practice for hydraulic engineers no detailed discussed will be provided herein Note that. however the entrance pressure should be less than 5 psi 11 5 ft of water column to avoid. excessive increase in pore pressure which may adversely impact the slope stability Bachus et. 4 Selecting size of perforations and calculating the unit discharge rate. As long as the clogging potential is avoided smaller perforation sizes are preferred for better. liquid distribution Unit discharge rate can be determined based on the entrance pressure and the. perforation size using Equation 1 See Figure 9 for typical correlations. Maximum Recommended Entrance Pressure 11 5 ft,Pressure ft. 0 2 4 6 8 10 12,Unit Discharge Rate gpm, Figure 9 Unit Discharge Rate vs Entrance Pressure for Different Sizes of Perforation. 5 Calculating number and spacing of perforations,Number of perforations n can be calculated as.
Spacing between perforations L can be calculated as. In most cases the number of perforations n should be greater than 50 i e q Q 2 and. spacing between perforations L should be less than 2 of the length of perforated section L. If these requirements are met the design procedure can continue Otherwise a new perforation. size shall be selected and Step 4 shall be repeated until all design requirements are met. 6 Selecting the allowable variation for unit discharge rate and calculating the corresponding. allowable pressure difference, Friction loss along the perforated pipe can be minimized but can not be completely eliminated. In other words some differences in the unit discharge rate will always exist A tolerable. variation should be pre determined for each project To maintain a reasonable pipe size the. tolerance q qn can be set between 10 and 20 The corresponding variance in pressure. between the two extreme ends of the perforated pipe can be calculated using Equation 12 or. Figure 6 Subsequently the allowable pressure drop P in the perforated pipe can be. calculated based on the entrance pressure,7 Determining pipe size. Size of the perforated pipe can be determined using Equation 17 or Figure 10 based on the. unit friction loss and total flow rate Unit friction loss can be calculated by dividing the. allowable pressure drop P by the length of perforated pipe L Note that the correction factor. F can be obtained from Figure 7 If the number of perforation is greater than 100 the value of. F can be assumed as 0 36, The diameter of the perforated pipe should be rounded to higher standard size If the result is not. satisfactory a new linear discharge rate can be selected and the entire design procedure can be. repeated The following example illustrates the use of the above mentioned design procedures. DESIGN EXAMPLE, A landfill plans to install several leachate recirculation lines on the active surface Based on. the geometry of the lift boundary three subsurface leachate injection lines will be installed Figure. 11 Leachate will be pumped from the storage facility through a forcemain into a control vault. located at the base of the northeastern slope Designated transmission lines will direct leachate from. the vault into the perforated pipes Only one line will be used during each injection event. 0 08 0 010,Unit Friction Loss,Unit Friction Loss,0 04 0 005.
D 2 in 0 003,0 02 D 6 in,D 3 in 0 002,D 4 in 0 001. 0 00 0 000,0 50 100 150 200 0 50 100 150 200 250 300 350 400. Flowrate in Pipe gpm Flowrate in Pipe gpm, Figure 10 Unit Friction Loss at Different Flow Rate. Leachate Leachate,Storage Transmission,Facility Control Lines Lift Boundary. ft 100 ft 100 ft 100 ft,Recirculation, Figure 11 Layout of the Proposed Leachate Recirculation System Example Problem.
Using the recommended procedures discussed earlier the following design can be formulated. 1 Selecting input parameters,Line Length Linear Discharge Rate. 1 600 0 15,2 300 0 30,3 150 0 60, Note that the selected linear discharge rates will result in similar total discharge rate for each. of the 3 injection lines,2 Determining total flow rate using Equation 18. Line Linear Discharge Rate Total Flow Rate,gpm ft gpm. 3 Determining the entrance pressure, To avoid excessive velocity and friction the loss flow rate will be controlled below 100.
gpm Note that the entrance immediately before the first perforation pressures listed below. were determined via separate forcemain analyses Differences in the calculated entrance. pressures are results of the different lengths in the transmission pipes between the control. vault and the perforated pipes,Line Entrance Pressure. Water column in ft, 4 Selecting size of perforations and calculating the unit discharge rate. A perforation size is pre selected as 3 16 inches in diameter With that the unit discharge. rates can be calculated using Equation 1 Results of the unit discharge rates are listed. Line Entrance Pressure Diameter of Unit Discharge Rate. Water column in ft Perforation inch gpm,1 2 5 3 16 0 66. 2 3 4 3 16 0 76,3 4 3 3 16 0 86,5 Calculating number and spacing of perforations. For Line 1 the number of perforations can be calculated as. Subsequently the spacing between perforations L can be determined as. For ease of construction the spacing is set to 4 5 ft which will result in a total of 134. perforations Same procedures can be repeated for Lines 2 and 3 Results for all three lines. are listed below, Line Length Total Flow Rate Unit Discharge Rate No of Spacing.
ft gpm gpm Perforations ft,1 600 90 0 66 135 4 5,2 300 90 0 76 121 2 5. 3 150 90 0 86 101 1 5, Note Spacing for the last two perforations at end of the pipe is 1 5 ft. 6 Selecting the allowable variation for unit discharge rate and calculating the corresponding. allowable pressure difference, The allowable variation in the unit discharge rate is pre selected as 20 With that the. allowable pressure drop can be calculated using Equation 12. Line Variation in Unit Entrance Pressure Allowed Pressure Drop. Discharge Rate Water column in ft ft,1 20 2 5 0 90. 2 20 3 4 1 22,3 20 4 3 1 55,7 Determine pipe size, Diameter of the pipe can be calculated using Equation 17 The correction factor F can be.
selected using Figure 6 Since the numbers of perforations are greater than 100 for all three. lines an F value of 0 36 will be used for the pipe sizing calculations for all lines. Line Length Total Flow Allowed No of Pipe Diameter Pipe Diameter. ft Rate Pressure Drop Perforations Calculated Selected. gpm ft inch inch,1 600 90 0 90 135 4 11 4,2 300 90 1 22 121 3 35 4. 3 150 90 1 55 101 2 77 3, Note that the pipe diameter can also be selected based on the unit friction loss and the total. flow rate using Figure 10,8 Results verification, Based on output of the design procedures i e pipe size perforation size and spacing. entrance pressure etc three simulations were executed using a spreadsheet program that. incorporates Equations 4 9 and 10 Results of the simulation illustrate the predicted. discharge rate at each of the perforations along the entire perforated sections see Figure 12. Further examining the results shown in Figure 12 reveals that the actual variations of unit. discharge flow rates changes between the first and the last perforations are 18 7 and. 10 for Lines 1 2 and 3 respectively All of which are less than the pre selected maximum. allowable variation 20 see Step 6 in the previous section Therefore the design is. verified as appropriate Otherwise different pipe sizing may be considered and the. procedures can be repeated until the result is successfully verified. Flow per Flow,Unit Discharge,0 100 200 300 400 500 600. Distance fromfrom distal,the end of ft,Line 1 Line 2 Line 3.
Figure 12 Predicted Discharge Flow Rate along the Perforated Pipes Example Problem. MAXIMUM PERFORATION LENGTH, There is a theoretical length limitation to the perforated section of any liquid injection pipe In. other words one set of design parameters i e pipe size perforation size and spacing allowable. variation in unit discharge rate and entrance pressure etc will not offer same performance when. different perforated lengths are used, To demonstrate this fact two design charts were developed and shown in Figures 13 and 14. Both charts assumed a 5 ft spacing between perforations and an entrance pressure of 5 ft of water. column Additionally both charts correlate the perforation size with the maximum pipe length and. the corresponding discharge flow rates for different pipe sizes The only difference between Figures. 13 and 14 is the allowable variation among the unit discharge rates a maximum variation of 10. and 20 were assigned in Figures 13 and 14 respectively.

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