# Perforated Pipe Distributor Sizing Calculations

Perforated Pipe Distributors have been discussed many times on “Cheresources”. How to design a perforated pipe distributor also known as a sparger has been a frequent question on the forum. Some general replies without providing in-depth methodology of sizing a distributor can be seen in the queries raised.

Perry’s Handbook (8th Edition) has a brief sub-section on perforated pipe distributors in Section 6, Fluid & Particle Dynamics which I had gone through critically but which was not to my satisfaction.

Since I do have a penchant of finding and developing engineering calculations, I was continuously on the look-out for something related to perforated pipe distributors. Last week I struck gold, when I found a company design manual providing detailed calculations for perforated pipe distributors. I had a critical look at it and found it to be better than anything I had found and read earlier related to perforated pipe distributors. I could even develop an excel workbook for perforated pipe distributor from this very informative design procedure.

Today’s blog entry is meant to provide the stepwise calculations for a perforated pipe distributor including the design equations. Both liquid and gas pipe distributors are covered. Gas pipe distributors follow the same design steps as that for liquid pipe distributors except for some minor variations in the design procedure. Both Metric units and USC units have been provided in the methodology.

Let us straight away get to the steps for sizing a Perforated Pipe Liquid distributor:

Step 1:
Initially set the pipe size of the pipe distributor, same as the pipe size feeding the pipe distributor

Step 2:
Calculate the Reynolds number, Rei, of the inlet stream to the pipe distributor using the following equation:

Metric Units:
Rei = 1.27*Q*ρ / (d*μ)

USC Units:
Rei = 50.6*Q*ρ / (d*μ)

where:
Q = Volumetric flow Rate, liters/s (gpm)
ρ = Liquid Density, kg/m3 (lb/ft3)
d = inside diameter of pipe, mm (inch)
μ = Liquid Viscosity, Pa.s (cP)

Step 3:
Find the fanning friction factor f (dimensionless), for the given flow regime. For turbulent flow some values for fanning friction factor based on pipe size are provided in the attached table.

Step 4:
Calculate the Kinetic Energy per unit volume of the inlet stream, Ek, kPa (psi) from the following equations:

Metric Units:
Ek = 810*α*ρ*Q2 / (d4)

USC Units:
Ek = 1.8*10-5*α*ρ*Q2 / (d4)

where:
Ek = Kinetic energy per unit volume of the inlet stream, kpa (psi)
α = velocity correction factor (use α = 1.1 for turbulent flow and 2.0 for laminar flow)

Step 5:
Calculate the pressure change ΔPp along the distributor pipe due to friction and momentum recovery from the following equations:

Metric Units:
ΔPp = ((4000*f*L*J/α*d) – 1)*Ek

USC Units:
ΔPp = ((48.0*f*L*J/α*d) – 1)*Ek

where:
f = fanning friction factor, dimensionless
L = Length of perforated distributor pipe, m (ft)
J = dimensionless factor (Use J = 0.35 as an initial value)

Step 6:
Find the required pressure drop, ΔPo across the distributor holes by multiplying the greater of Ek or ΔPp by 10. If the calculated value of ΔPo is less than 1.75 kPa (0.25 psi) make it equal to at least 1.75 kPa (0.25 psi).

Step 7:
Calculate the required total area of the pipe distributor holes, Ao, using the following equations:

Metric Units:
Ao = 22.3*(Q / C)*sqroot (ρ/ΔPo)

USC Units:
Ao = 3.32*10-3*(Q / C)*sqroot (ρ/ΔPo)

where:
Ao = Total required hole area, mm2 (in2)
C = flow coefficient, dimensionless (as a first value consider C = 0.60)

Step 8 (Guidelines for choosing hole diameter and hole-to-hole linear distance):
a. Minimum hole diameter ≈ 1/2-in. (13 mm) to avoid plugging and to limit the number of holes to a reasonable value. In very clean service, smaller holes may be considered, but in severely fouling service, 1/2-in. (13 mm) holes may be too small.
b. Maximum hole diameter = 0.2 times inside diameter of distributor.
c. The ratio of hole diameter, do, to inside pipe diameter, di, should be between 0.15 and 0.20 when the criterion ΔPo = 10 Ek is used. If it is necessary to use do /di < 0.10, then make ΔPo = 100 Ek.
d. To provide sufficient pipe strength, the minimum distance (edge-to-edge) between adjacent holes should approximately equal the hole diameter.
e. Within the limitations imposed by the above requirements, a larger number of small holes are preferred over a smaller number of large holes.
f. If slots are used instead of holes, the slot width should be at least 1/2-in. (13 mm).

Step 9:
The value of Rei / n should be greater than 4000. If it is not, then a new flow coefficient value "C" should be calculated from the attached chart. Instead of Re shown on the x-axis of the chart use Rei / n for reading the flow coefficient of the chart.

Step 10:
Using the calculated number of holes, find the factor "J" from attached chart and compare this with the assumed value of 0.35. If this revised value of J affects the value of ΔPo by more than 10%, substitute the revised value of J in equation given in Step 5 and repeat the steps starting from calculation of ΔPp.

Perforated Pipe Gas Distributor:

Step 1:
Initially set the pipe size of the pipe distributor, same as the pipe size feeding the pipe distributor

Step 2:
Calculate the Reynolds number, Rei, of the inlet gas stream to the pipe distributor using the following equation:

Metric Units:
Re = 1270*W*ρ / (d*μ)

USC Units:
Re = 6310*W*ρ / (d*μ)

where:
W = gas flow Rate, kg/s (lb/h)
ρ = Liquid Density, kg/m3 (lb/ft3)
d = inside diameter of pipe, mm (inch)
μ = Liquid Viscosity, Pa.s (cP)

Step 3:
Find the fanning friction factor f (dimensionless), for the given flow regime. For turbulent flow some values for fanning friction factor based on pipe size are provided in the attached table.

Step 4:
Calculate the Kinetic Energy per unit volume of the inlet stream, Ek, kPa (psi) from the following equations:

Metric Units:
Ek = 8.10*108*α*W2 / (ρ*d4)

USC Units:
Ek = 0.28*α*W2 / (ρ*d4)

where:
Ek = Kinetic energy per unit volume of the inlet stream, kpa (psi)
α = velocity correction factor (use α = 1.1 for turbulent flow and 2.0 for laminar flow)

Step 5:
Calculate the pressure change ΔPp along the distributor pipe due to friction and momentum recovery from the following equations:

Metric Units:
ΔPp = ((4000*f*L*J/α*d) – 1)*Ek

USC Units:
ΔPp = ((48.0*f*L*J/α*d) – 1)*Ek

where:
f = fanning friction factor, dimensionless
L = Length of perforated distributor pipe, m (ft)
J = dimensionless factor (Use J = 0.35 as an initial value)

Step 6:
Find the required pressure drop, ΔPo across the distributor holes by multiplying the greater of Ek or ΔPp by 10. If the calculated value of ΔPo is less than 1.75 kPa (0.25 psi) make it equal to at least 1.75 kPa (0.25 psi).

Step 7:
Calculate the required total area of the pipe distributor holes, Ao, using the following equations:

Metric Units:
Ao = 2.24*104*(W/C*Y)*(1 / sqroot (ρ*ΔPo))

USC Units:
Ao = 2.24*104*(W/C*Y)*(1 / sqroot (ρ*ΔPo))

where:
Ao = Total required hole area, mm2 (in2)
C = flow coefficient, dimensionless (as a first value consider C = 0.60)
Y = Gas expansion factor, dimensionless

Y is calculated as follows:

Y = 1 - (0.41 + 0.35*β4)*ΔPo/(k*P) for ΔPo/P <0.37 -------(i)

Y = Y0.37 - 0.37*( (ΔPo/P) - 0.37) for ΔPo/P >0.37 --------(ii)

where:
P = Pressure at the inlet of the gas distributor, kPa (abs) (psia)
k = ratio of specific heats, Cp / Cv
β = ratio of hole to the perforated pipe inside diameter (specified earlier as a value between 0.15 to 0.20)
Y0.37 = value of Y calculated using eqn (i) with ΔPo / P equal to 0.37

Steps 8,9 & 10: These remain the same as for Perforated Pipe Liquid Distributors.

This has been a rather detailed description on how to size a perforated pipe distributor and I am hoping that readers and members of "Cheresources" find it useful and can build a excel workbook using the equations and method provided. Please do refer the attachments while reading the text of this blog entry.

Looking forward to comments from the knowledgeable forum members.

Regards,
Ankur.

sandy343

Hi sir,

i need your suggestions on, whether can i follow the above method to calculate number of holes in each of the branch in distributor of sparger pipe. My aim is to see that pressure drop of steam is equal till the last branch, so that steam is not rushed in to few branches. i assume this equal pressure drop across each hole in each branch shall make steam properly distributed across the sparger and its branches and set of small hole in each branch.

This sparger pipe is burried in near saturated water by about 800 - 1000 mm. This is for deaerator in power plants

I am new to this site so unable to attach rough sketch.

Need your suggestion on the above issue.

thanking you

sandeep

Niyamat

Dear Sir,

I want to design the steam sparger for 18.88 bar pressure drop between inlet of sparger pipe to outlet of sparger pipe.

Using above method method pressure drop in step 6 is coming as ~0.8 bar(80KPa).

Pipe dimension is 150mm, steam flow rate is 17830 kg/hr,steam density is 5.5 kg/m3, inlet pressure is 19.88 bar.pipe length 1m.

Thanks,

Niyamat

ankur2061

Dear Sir,

I want to design the steam sparger for 18.88 bar pressure drop between inlet of sparger pipe to outlet of sparger pipe.

Using above method method pressure drop in step 6 is coming as ~0.8 bar(80KPa).

Pipe dimension is 150mm, steam flow rate is 17830 kg/hr,steam density is 5.5 kg/m3, inlet pressure is 19.88 bar.pipe length 1m.

Thanks,

Niyamat

Niyamat,

Please read my responses to the various posts / queries about pressure drop. You will be able to proceed further.

Regards,

Ankur

Dear Mr. Ankur

Thank you for your kind materials provided here.I am going to design a diffuser involves perforated pipe.My initial info are as below:

Di=203.2 mm

Do=12 mm

P=7 Bara (inlet fluid= Superheated steam T=655 K)

Based on equations provided here, required pressure drop,  across the distributor holes =15.71 Kpa(ΔPo) using multiplier 10 of Ek. In addition, for my design (Di/Do=0.059<0.1) so I should select 100 multiplier fo Ek, which pressure drop of holes would be 15.71 bar. these quantity is more than inlet pressure and is too big amount. I think using 100 multiplier for gas in mentioned condition creates undesirable results. i would appreciated if you let me to have your guidelines here.

ankur2061

Please check the calculation for Ek. Have you used the right units in the equation for the various variables? I am saying this because the pressure drop value of 15.71 kPa (ΔPo) looks very high. In the formula for Ek for gas distributor, W is kg/s, rho in kg/m3 (density of superheated steam) and d (inside dia of distributor pipe) in mm. Also alpha value to be used is 1.1. Check again and revert.

Regards,

Ankur

Dear ankur

My calculation is proceed via Ek =( 8.10*108*α*W2) / (ρ*d4)
as below:

W=30000 kg/hr=8.33333 Kg/s

ρ=2.31 kg/m3

d=203 mm

Ek=8.1*108*1.1*(8.3333^2)/(2.31*203^4)=15.7

it seems to be correct position.

ankur2061

Dear ankur

My calculation is proceed via Ek =( 8.10*108*α*W2) / (ρ*d4)
as below:

W=30000 kg/hr=8.33333 Kg/s

ρ=2.31 kg/m3

d=203 mm

Ek=8.1*108*1.1*(8.3333^2)/(2.31*203^4)=15.7

it seems to be correct position.

Increase Do to 32 mm (1.25 inch). 12 mm is too small for your case.

Regards,

Ankur

Dear ankur

My calculation is proceed via Ek =( 8.10*108*α*W2) / (ρ*d4)
as below:

W=30000 kg/hr=8.33333 Kg/s

ρ=2.31 kg/m3

d=203 mm

Ek=8.1*108*1.1*(8.3333^2)/(2.31*203^4)=15.7

it seems to be correct position.

Increase Do to 32 mm (1.25 inch). 12 mm is too small for your case.

Regards,

Ankur

Dear Ankur

Thank you for your attention. Furthermore, what is effect of increasing D0 from 12 mm to 32 mm on the Ek. again we have Ek=15.7 Kpas which is very high.

ankur2061

Dear Mohammed,

Now ratio of Do / Di (32 / 203) will become 0.157. So pressure drop ΔPo can be calculated as 10*Ek = 10*15.71 = 157.1 kPa =1.57 bar. For such high flow rate 30000 kg/h, this much pressure drop would probably be acceptable in the perforated pipe distributor. If this is not acceptable then you will have to increase the distributor pipe size Di from 8" (203 mm) to 10" (250 mm).

Regards,

Ankur

abizerjamali

Dear Mr. Ankur,

Could you please guide on sizing of header and lateral pipes of pipe arm distributors?

Thanks

Abizer

hjjinnie

Hi,

Thank you for these calculations! I was just wondering where you got the equations for Kinetic Energy in Step 4, for the pressure change in Step 5, and the total area of pipe distributor holes in Step 7 all for the perforated pipe gas distributor.

Cheers,

Lisa

hjjinnie

I am trying to determine the total area of pipe distributor holes for 150 ft long pipe with 3 in diameter for a soil vapor extraction well for air. I am using 1 scfm which results in a gas flow rate of 674.28 lb/hr and a pressure at inlet of 0.38371 psia (26 in of water). I am getting incredibly large required pressure drops and a negative Y... Any guidance will be much appreciated.

ankur2061

I am trying to determine the total area of pipe distributor holes for 150 ft long pipe with 3 in diameter for a soil vapor extraction well for air. I am using 1 scfm which results in a gas flow rate of 674.28 lb/hr and a pressure at inlet of 0.38371 psia (26 in of water). I am getting incredibly large required pressure drops and a negative Y... Any guidance will be much appreciated.

I have answered these questions before based on earlier comments and questions. You will have to patiently read through all the comments and pick up those comments which are relevant to you.

As far as origin of these equations is concerned they from the engineering design manual of a world class company.

Regards,

Ankur.

ramrecon

Can I ask if anyone has produced an excel worksheet from this method? If so I would be very interested in testing it out.

Best regards,

ajitgondhalekar

Dear Ankur,

In step 8, circular holes are are considered and limiting diameters are mentioned.

If slotted holes are to be provided, the interpolation should be done on area basis.

The calc. method does not mention anything about velocities (inlet, exit).

Can you guide me on the same.

moru007

Dear @ankur sir

I wanted design RIng Sparger for Amonia. Sparger Will be located at reactor bottom. Will this guideline work for ring sparger?  I Wanted compute

Hole Area and Diameter

Critical Weeping Velocity and Bubble Diameter

Since I havr Tried to design a/c to above guideline but my Pressure drop is coming very Less

moru007

Dear @ankur sir

I wanted design RIng Sparger for Amonia. Sparger Will be located at reactor bottom. Will this guideline work for ring sparger?  i Wanted compute

Hole Area and Diameter

Critical Weeping Velocity and Bubble

Santosloera

In step 9, Rei/n means Reynolds number divided by number of holes calculated ?

hbiglari

Dear @Ankur2061

First of all, thanks for the data that you shared.

I want to calculate the pressure drop of a perforated pipe with gas inside, using the mentioned calculation steps but I don't know how.

Ao computed from step 7 formula and number of holes calculates by dividing Ao per one hole area. I want to calculate vise versa. I mean, calculate the pressure drop of distributor pipe with specified hole diameter and number.

I will be grateful if you  help me.

EdinsonRoa

Mr. Ankur,

I need to calculate the pressure drop in a sparger or perforated tube. What equation i can use for it. I a existing sparger or perforated pipe.

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