Final Double Pipe

Double- Pipe Heat Exchanger

PERFORMANCE OF A DOUBLE-PIPE HEAT

EXCHANGER

INTRODUCTION

Modern manufacturing industries employ processes that require heating and

cooling. From the preparation of the raw materials, to their processing, to the

conditioning of the final products into sellable items and even down to the treatment

of process effluents, heat transfer mechanisms are always applied. Most of the

time, heating and cooling are done using heat exchangers and a double-pipe heat

exchanger is one of the commonly used type. Being such a vital industrial tool, it is

of great importance that chemical engineering students learn the basic concepts

and theories especially the operation of a double-pipe heat exchanger. The

fundamental concepts applied will enable the students to analyze and design other

types of heat exchanger.

OBJECTIVES

1. To familiarize the students with the characteristics, parameters and problems

involved in the operation of a double-pipe heat exchanger when operated

using countercurrent or co-current flow.

2. To determine and compare measured and calculated mean temperature

difference between hot and cold water in both countercurrent and co-current

flow.

3. To compare experimental overall heat transfer coefficient obtained using data

from direct measurements with the theoretical overall heat transfer

coefficients calculated using available empirical equations.

Unit Operations Laboratory Page 1


THEORY

Although there are several ways of transferring heat between fluids, the most

common is the use of a heat-exchanger wherein the hot fluid and cold fluid are

separated by a solid boundary. Different types of heat exchangers have been

developed. The simplest type is a double-pipe heat exchanger. This consists

essentially of two concentric pipes with one fluid flowing through the inside of the

inner pipe while the other fluid moves co-currently in the annular space. This type of

heat exchanger, however, is not recommended for processes that require very large

heating surfaces.

The heat transfer analysis of a double-pipe heat exchanger deals with the

application of several equations that relate the different parameters involved.

Consider the heat exchanger,

Where:

mh = Mass flow rate of hot fluid, lbm/hr

mc = mass flow rate of cold fluid, lbm/hr

Tc = temperature of cold fluid, °F

Th = temperature of hot fluid, °F

**subscript 1 refers to entrance conditions, 2 refers to exit conditions

To determine the rate of heat loss by the hot fluid or the heat gained by the cold

fluid, we apply a steady overall energy balance between the two ends of the heat

exchanger. On the basis of 1 lbm/sec of fluid flowing, we have,



W + JQ = ΔZ( ggc ) + v2

2αgc + JΔH (1)

Where: W = shaft work

ΔZ( ggc ) = mechanical potential energy

v2

2α gc = mechanical kinetic energy

α = kinetic energy velocity correction factor

(α = 1.0 for turbulent flow; 0.5 for laminar flow)

Since no shaft work W, is involved, ΔZ( ggc ) and v2

2α gc, are small compared with

the thermal energy transfer. Then for one fluid, the equation reduces to,

Q = ΔH = (H2 – H1) (2)

If no change in phase involved,

ΔH = CpΔT (3)

Therefore, the rates of heat transfer for the cold and hot fluids are respectively,

qc = mcCpc(Tc2 – Tc1) (4)

qh = mhCph(Th1 – Th2) (5)

If heat losses to the surroundings are neglected,

qc = qh or (6)

mcCpc(Tc2 – Tc1)= mhCph(Th1 – Th2) (7)

To relate the heat transfer rate with the size of the heat exchanger, we apply the

transfer around the differential element of length, dL. Thus,

dq = U1(Th – Tc)dA = Uo(Th – Tc)dAo (8)



Where: U = Overall heat transfer coefficient, Btu/hr-ft2·°F

A = heat transfer area, ft2

ΔT = temperature driving force, °F = (Th – Tc)

**subscript 1 refers to the inside of the heating surface and

subscript o refers to the outside of the heating surface

For double-pipe heat exchangers, the overall heat transfer coefficient is almost

constant along the length of the heat exchanger and the driving potential ΔT may

be considered almost linear with q so that Equation (7) can be integrated to give,

q = UiAiΔTln = UoAoΔTln (9)

where: ΔTln = Logarithmic mean temperature difference

logarithmic mean temperature difference is defined by the

equation,

ΔTln = ΔT 1−ΔT 2

lnΔT 1ΔT 2

(10)

Where: ΔT1 = Temperature approach in one end

ΔT2 = Temperature approach in the other end

The ΔTln is fairly accurate if the ΔT is linear with q or L. however, in most situations,

this relationship is not always true. Let us compare therefore the log mean

temperature difference as defined by equation (9) and the arithmetic mean

temperature difference, ΔTo defined by,

ΔTo = ΔT 1+ΔT 2

2 (11)

With the true mean temperature difference, ΔTm which is obtained directly from

equation (7) by expressing ΔT in terms of L,



q = 2πUD∫0

L

ΔT dL = 2πUDL(ΔT)tm (12)

therefore,

(ΔT)tm = ∫0

L

ΔT dL

L

(13)

Equation (11) is evaluated using graphical or numerical integration by plotting

values of ΔT against exchanger length and getting the area under the curve. These

are then divided by the total length of the exchanger.

It is given that the experimental overall heat transfer coefficient may be calculated

based on equation (8) by determining the rate of heat transfer by direct

measurements. To determine theoretical overall heat transfer coefficient, express U i

or Uo in terms of the individual transfer coefficients by considering resistances

involved when heat travels from the hot to the cold fluid. Such a relationship,

assuming relatively clean surface, is given by:

1UoAo

= 1UiAi

= 1hiAi

+ XmkmA

+ 1hoAo

(14)

Where: xm =Thickness of the tube wall

km = Thermal conductivity of the metal

A = Average heat transfer area

If Uo is desired, equation (12) simplifies to

1Uo

= 1ho

+ XmDokmD

+ DhiDi

(15)

If Ui is desired, we get



1Uo

= 1hi

+ XmDikmD

+ DihoDo

(16)

Since the values of the xm, Do, and km can easily be obtained from available data, the

problem now boils down to the evaluation of the individual heat transfer coefficients.

This involves the choice of a particular empirical equation based on several factors

such as mechanism of heat transfer, character of flow, geometry of the system type

of fluid involved, etc.

Since most of the conditions in this experiment can be set, the equations for h may

be limited to only several choices. Based on mechanism, we can limit it to forced

convection by using flow rates that yield turbulent flow. This will eliminate the

effects of natural convection. Based on geometry, we are limited to horizontal tubes

with fluids flowing inside the conduits, circular and annular. Based on the type of

fluid, we are limited to usng hot and cold water.

In general, for forced convection in turbulent flow, (NRE > 10,000), k may be

calculated considering the effect of tube length by

( hCpG )(Cpμ

k )3

( μμ )0 .14

= 0 .023¿¿ (17)

Where the properties Cp, μ, k are evaluated based on the arithmetic mean bulk

temperature of the fluid defined by,

Tave = T 1+T 22

(18)

The viscosity, based on the wall temperature, μw will have to be determined by

estimating Tw by iterative calculation using individual resistances evaluated by first

neglecting the effect of μw.



If the effect of the tube length can be ignored, (L/D > 60) and the (μw/μ)0.14 is

approximately equal to 1, the simpler Dittus-Boelter Equation (Foust 13-77), given

by

NNu = 0.023(NRe)0.8(NPr)n (19)

May be applied, where n= 0.4 where the fluid is heated and 0.3 when it is being

cooled. Here, the dimensionless numbers are defined as

NNu = hDk

Nusselts’s Number

NRe = DVρμ

=DGμ

Reynold’s Number

NPr = Cpμk

Prandtl Number

Another equation which is limited to water based temperature range of 40°F to 220°

F, turbulent flow, may be used. This is given by

h = 150 (1 + .011 T) V 0 .8

( D )0 .5¿

¿ (20)

where: T = Arithmetic temperature of fluid, °F

D’ = Tube diameter, inches

Equations (15), (16) and (17) are used to determine both h i and ho. to get hi, the

corresponding inside diameter of the tube is used for D. to get ho, the D is replaced

by the equivalent diameter, De, which is four times the hydraulic radius RH, defined

to be the ratio of the cross-sectional area of the annular space to the wetted

perimeter. For an annular space,

RH = 4 (Di j2−Do t2)

π ¿¿ = 14

¿ (21)

Where: Dij = inside diameter of jacket (outer tube)



Dot = outside diameter of inner tube

It is possible that flow with Reynold’s number less than 10,000 will be encountered.

In this case, Equations (15),(16) and (17) are no longer valid. For NRe = 2100 and for

fluids of moderate velocity.

hiaDk

=1 .75NGr 1/3 = 1.75 (mCp

L )0 .33

(22)

For NRe between 2100 and 10,000, Figure 9-22 (MC) will have to be used. Also, if the

flow is laminar, the effect of natural convection should not be discounted. This effect

can be accounted for by multiplying h ia (computed from equation (19) or figure 9-22)

by the factor

Ǿn = 2.25(1+0 .010Ng r0 .33)

logNRe(23)

NGr = DeρtβgcΔT

μt 2(24)

Where: De = equivalent diameter

β = coefficient of thermal expansion, °F-1

f = subscript indicating that fluid properties should be based on

Tf = Tw+T2

EQUIPMENT



Figure 1. Side view of Double-pipe Heat Exchanger

Equipment Description

The double-pipe heat exchanger set-up as shown in the previous figure consists

essentially of concentric pipes welded in series. The inner is made of brass with an

inside diameter of 0.625 inch and an outside diameter of 0.815 inch. The outer tube

made of standard 1 ¼ steel pipe. The unit is composed of 12 sections in series. Each

section is approximately 50 inches long. Hot water, which comes from the nearby

tubular heat exchanger, is passed through the inner pipe and the cold water, coming

from the supply main is passed through the annular space between the tubes.

Valves are provided for reversing the direction of the cold stream to obtain either

countercurrent or co-current flow. Valves on both lines are also provided to control

the flow rates of the streams. Each section is provided with thermometer wells,

which contain small amount of oil, to measure the temperature of the streams at



appropriate points along the heat exchanger. At the exit ends of the pipes, weighing

tanks with calibrated levels are provided for measurement of flow rates.

PROCEDURE

It is important that this experiment should be performed with proper coordination

with Experiment B2, Performance of a Tubular Heat Exchanger, since the hot water

used in this experiment is the hot water discharged from the tubular exchanger. Any

valve movement in Experiment B2 will affect the temperature and flow rate of the

hot water. Therefore, each run for both experiments should start and end

simultaneously.

1. Familiarizing yourself with the parts and operation of the equipment,

especially the use of the valves provided in the lines. Place the thermometers

at the appropriate wells provided.

2. Open the supply valve for cold water, check whether water is flowing out the

measuring tanks, if not, checks exit valves. Pressure gauge provided should

indicate a constant reading. Adjust this valve to have a feel of the range of

flow rates to be used. Approximately determine the setting so as to get six

different flow rates later for each run. The exit valves in the measuring tanks

should be open to drain the liquid to avoid overflowing when flow is not being

measured.

3. Adjust the four valves in the cold water line to get either co-current or

countercurrent flow. This is done by fully opening or closing two opposite

valves. Trace the direction of flow from inlet to exit to determine this.

4. If hot water is already available, allow this to flow through the lines by fully

opening the exit valves.

Note: you should not move any valve along the hot water line without the

consent of the people operating the tubular exchanger nor they should move

anything without you knowing it. The flow rate of the hot water is usually at

their control, so regular consultation is advised.



5. If flow rates have been established, prepare to continue the run by regularly

checking the temperature indicated by the thermometers at regular intervals

of time to determine whether steady conditions have already been

established and by measuring the flow rates of the two streams. The flow rate

is measured by closing the first exit valve for the water level to pass between

pre-selected points in the level gauge. The more time you spend in the

measurement, the better. The volumetric flow rate is obtained by dividing the

volume of water collected by the time interval.

6. If reasonable steady state conditions have been established, record all

temperature readings and flow rates i.e., no significant changes are observed,

and the run is completed.

7. Proceed with another run by adjusting the flow rate of the cold fluid and/or

the flow rate of the hot fluid. Each run should last approximately 20 minutes.

8. Perform a total of six runs; three countercurrent and three co-current flows.

9. Tabulate all data collected, measure the length of each section accurately,

check diameter of tubes, etc.

DATA SHEET

A. CO-Current Flow Operation

Trial 1

Well Number 1st Reading 2nd Reading 3rd ReadingTH (°C) TC (°C) TH (°C) TC (°C) TH

(°C)TC (°C)

1 37 37 37 37 37 372 39.8 37 40 37 40 373 40.5 36 40.9 36.5 41 36.754 41.5 35.5 42 36 42 365 43 34 44 34.25 44 34.256 45.5 32 46 32.5 46 32.757 49 30 49.5 50 50 30

Flow Rate (kg/s) 0.266667

0.33333

0.3 0.366667

0.3 0.366667



Trial 2

Well Number 1st Reading 2nd Reading 3rd ReadingTH (°C) TC (°C) TH (°C) TC (°C) TH (°C) TC (°C)

1 33 33 32.5 32.5 33 332 43 33 45.5 32.5 45 33.53 46.5 32 46 32 46 324 49 35 48.5 34.5 50.25 34.55 53 37 53 37 54 32.56 53.5 36.5 53.5 36 54.5 327 54 36 54 35.5 55.5 31

Flow Rate (kg/s) 0.25 0.366667 0.258333 0.375 0.25 0.366667

B. Countercurrent Flow Operation

Trial 1

Well Number 1st Reading 2nd Reading 3rd ReadingTH (°C) TC (°C) TH (°C) TC (°C) TH (°C) TC (°C)

1 38.5 39.5 38.5 38.5 38.5 392 38 29 38 29 38.5 293 41 31 40 30.5 40.5 314 43 33 42 32.5 42.5 32.55 46 34 45 34 45.5 346 48 36 47 36.5 47.5 367 50.5 38 49.5 37.5 50.5 38

Flow Rate (kg/s) 0.272222 0.355556 0.283333 0.366667 0.283333 0.366667

Trial 2

Well Number 1st Reading 2nd Reading 3rd Reading

TH (°C) TC (°C) TH (°C) TC (°C) TH (°C) TC (°C)1 42 42 42 42.5 42 422 45 42.5 45 42.5 46 42.53 46 40.5 46 40.5 46.5 40.54 48 39.5 48 39.5 47 395 50 38 49 38 49 386 50.5 37.5 49.5 37 49.5 37.5

50.5 51 37 50 36.5 51 37Flow Rate (kg/s) 0.25 0.366667 0.258333 0.375 0.25 0.366667



ANALYSES AND CALCULATIONS

1. Plot for each run the temperature of the hot and cold fluid versus the length

of the heat exchanger indicating whether it is countercurrent flow or co-

current flow. Also, in the same graph, plot ΔT versus length. Present these

figures (1) to (6). Did you get linear behavior? Explain.

2. Using the terminal temperatures for each run, calculate the logarithmic mean

and arithmetic mean temperature differences. Based on the plot of T versus L

as given in Figures (1) to (6), calculate the true mean temperature difference

by graphical integration. Calculate also the percentage deviation of ΔTa from

ΔTtm. Tabulate the results and present as Table 1. Explain the results you got

as to the validity of the various temperature differences you obtained.

3. Calculate the heat gained by the cold fluid, qc, and the heat lost, qh. Compare

the two by solving for the difference. Tabulate the results and present this as

Table 2.

4. Using qh as the basis, calculate for the experimental Ui, by calculating first A,

and using Tln in Equation (2). Tabulate the results and present this as Table 3.

5. Calculate the theoretical Ui by first solving hi and ho using appropriate

empirical formulas. Summarize the results by preparing a table indicating the

run number, average bulk temperature, Reynolds number, Prandtl number, h

and theoretical U. also compare h obtained using Equations (14) and (15).

Present this as Table 4.

6. Calculate the percentage difference between the experimental and the

theoretical Ui. Present this as Table 5.

7. Using only the date from one run each for co-current and countercurrent flow,

calculate h using equations (13), (14), and (15). Compare by tabulating the

results. Present this as Table 6.

GUIDE QUESTIONS

1. Based on your findings, discuss the applicability of the arithmetic mean and

logarithmic temperature difference in double pipe heat exchanger

calculations. What affects accuracy?



In computation for the temperature difference, a little variation has been

observed. The logarithmic mean temperature difference records a value of

several decimal places, which can be considered as more accurate than of the

arithmetic mean temperature difference. In a double pipe heat exchanger,

logarithmic mean difference should be used instead of arithmetic mean

difference, although a small deviations exist considering an accuracy of the

value, the former hold true. Accuracy of the measurement might due to

parallax error relative to the reader of the of the thermometer in each well on

the double pipe heat exchanger. The condition of the atmosphere or the

surroundings might intervene as well.

The behavior of a heat exchanger in variable regime can be described by a

two parameter model with a time lag and a time constant. In many studies,

the analytical calculation based on the energy balance permitted to express

the time constant in various configurations of the device operating. However,

the time lag is only experimentally determined. An empirical method for the

prediction of this parameter when a double pipe heat exchanger is submitted

to a flow rate step at the entrance.

2. Give your comments as to the validity of the theoretical and experimental

overall heat transfer coefficients you obtained.

Certain possibilities can be considered as to how the heat gained by the cold

fluid differs from the heat lost by the hot fluid, the wall resistance of the tube,

the length the fluid travels in the heat exchanger and the type of the

materials used for the pipe system.

The overall heat transfer coefficient can also be calculated by the view of

thermal resistance. The wall is split in areas of thermal resistance where

the heat transfer between the fluid and the wall is one resistance

the wall itself is one resistance



the transfer between the wall and the second fluid is a thermal

resistance

3. What are the problems you encountered in the operation of the double-pipe

heat exchanger? How did you overcome these problems and what

recommendations can you give to streamline or improve the use of such

experiment?

The distance between the sheets in the spiral channels are maintained by

using spacer studs that were welded prior to rolling. Once the main spiral

pack has been rolled, alternate top and bottom edges are welded and each

end closed by a gasketed flat or conical cover bolted to the body. This

ensures no mixing of the two fluids will occur. If a leakage happens, it will be

from the periphery cover to the atmosphere, or to a passage containing the

same fluid.

4. Give the physical significance of NRe, NNu and NPr in relation to heat transfer

characteristics.

Reynolds Number, Nusselt, and Prandtl Numbers are significant in the

calculations and widely applicable in the heat exchange principle. NRe

determines the type of flow regime in the heat exchanger equipment as well

as in the pipeline. The flow of the fluid or the velocity affects the temperature

in somewhat considerable amount. The laminar or turbulence behavior of the

fluid also accounts to the film resistance of the fluid and thus needed to be

determined. NNu or the Nusselt number is a dimensionless quantity, which is

define as the ratio of the tube diameter to the equivalent thickness of the

laminar layer. Further, Nusselt number is the resulting correlation on the ratio

of the total heat transfer by molecular and turbulent transport to heat transfer

by molecular transport alone. The physical significance of the Prandtl number

appears that it is the ratio of the velocity to the thermal diffusivity, it is

therefore a measure of the magnitude of the momentum, diffusivity relative

to that of the thermal diffusivity. Its numerical value depends on the

temperature and pressure of the fluid, and therefore it is a true property.



Low-Reynold’s Number turbulent flow, and laminar non-Newtonian flow. Heat

exchaner configurations and materials were examined, as were compact and

noncompact versions and heat transfer and fouling.

The Prandtl number effects on heat transfer are categorized into two

perspectives: fin perspective and array perspective. The fin perspective

Prandtl number effects explain the dependence of the periodic fully

developed Nusselt number on Prandtl number. The array perspective is

analogous to the thermal entry length perspective in duct flow. Array

perspective Prandtl number effects yield higher Nusselt numbers in the

entrance region of the offset fin array.

Nusselt numbers are measured in three counterflow tube-in-shell heat

exchangers with flow rates and temperatures representative of thermosyphon

operation in solar water heating systems. Mixed convection heat transfer

correlations for these tube-in-shell heat exchangers were previously

developed in Dahl and Davidson (1998) from data obtained in carefully

controlled experiments with uniform heat flux at the tube walls. The data

presented in this paper confirm that the uniform heat flux correlations apply

under more realistic conditions. Water flows in the shell and 50 percent

ethylene glycol circulates in the tubes. Actual Nusselt numbers are within 15

percent of the values predicted for a constant heat flux boundary condition.

The data reconfirm the importance of mixed convection in determining heat

transfer rates. Under most operating conditions, natural convection heat

transfer accounts for more than half of the total heat transfer rate.

5. Discuss briefly the relative merits of countercurrent and co-current flow of

fluids for the transfer of heat?

Countercurrent exchange along with Concurrent exchange comprise the

mechanisms used to transfer some property of a fluid from one flowing

current of fluid to another across a semipermeable membrane or thermally-

conductive material between them. The property transferred could


http://en.wikipedia.org/wiki/Fluid


be heat, concentration of a chemical substance, or others. Countercurrent

exchange is a key concept in chemical engineering thermodynamics and

manufacturing processes, for example in extracting sucrose from sugar

beet roots.

Concurrent Flow – In this exchange system, the two fluids flow in the

same direction. As the diagram shows, a concurrent exchange system has

a variable gradient over the length of the exchanger. With equal flows in

the two tubes, this method of exchange is only capable of moving half of

the property from one flow to the other, no matter how long the exchanger

is. If each stream changes its property to be 50% closer to that of the

opposite stream's inlet condition, exchange will stop because at that point

equilibrium is reached, and the gradient has declined to zero. In the case

of unequal flows, the equilibrium condition will occur somewhat closer to

the conditions of the stream with the higher flow.


http://en.wikipedia.org/wiki/Sugar_beet

http://en.wikipedia.org/wiki/Sugar_beet

http://en.wikipedia.org/wiki/Sucrose

http://en.wikipedia.org/wiki/Thermodynamics

http://en.wikipedia.org/wiki/Chemical_engineering

http://en.wikipedia.org/wiki/Chemical_substance

http://en.wikipedia.org/wiki/Concentration

http://en.wikipedia.org/wiki/Heat

http://en.wikipedia.org/wiki/File:Exchangerflow.svg


Countercurrent Flow - By contrast, when the two flows move in opposite

directions, the system can maintain a nearly constant gradient between

the two flows over their entire length. With a sufficiently long length and a

sufficiently low flow rate this can result in almost all of the property being

transferred. However, note that nearly complete transfer is only possible if

the two flows are, in some sense, "equal". If we are talking about mass

transfer, then this means equal flowrates of solvent or solution, depending

on how the concentrations are expressed. For heat transfer, then the

product of the average specific heat capacity (on a mass basis, averaged

over the temperature range involved) and the mass flow rate must be the

same for each stream. If the two flows are not equal (for example if heat is

being transferred from water to air or vice-versa), then conservation of

mass or energy requires that the streams leave with concentrations or

temperatures that differ from those indicated in the diagram.

6. Give a summary of your findings and conclusions and give recommendations,

if any.

The experiment presents the results of an experimental study of shell-side

heat transfer and flow resistance performance of multi-tube type of double-

tube heat exchanger units, which is a double-pipe heat exchanger with

smooth or roughen tubes and a segmental baffled one with smooth tubes,

using water and crude oil (a mixture of oil and water) as working fluids. The

experimental results indicate that the double-tube heat exchanger with a

spiral groove tube bundle provides superior shell-side heat transfer and

pressure drop characteristics. Double-tube heat exchanger is installed for

heating crude oil in a solar energy system.

1. Plot of Temperature vs Length of Pipe


Length of the heat exchanger pipe

Tem

per

atur

e,o

C

Plot of Temperature vs Length of pipe


2. Computing for the Logarithmic Mean Temperature Difference

Where: ΔT1 = Tleaving temperature , hot fluid –Tentering temperature, cold fluid

ΔT2 = Tentering temperature, hot fluid –Tleaving temperature, cold fluid

LMTD = 6.6955 0C

3. Computing for the Arithmetic Mean Temperature Difference

AMTD = 6.70 0C


Tem

pera

ture

, C


4. Comparison of LMTD and AMTD for Counter-current Flow

LMTD AMTD

Flow 1 6.6955 6.70

Flow 2 6.4499 6.450

Flow 3 6.1434 6.150

Flow 4 5.8994 5.90

Flow 5 6.2467 6.25

Flow 6 6.2467 6.25

5. Plot of Temperature vs Length of Pipe

6. Computing for the Logarithmic Mean Temperature Difference

Where: ΔT1 = Tleaving temperature , hot fluid –Tentering temperature, cold fluid

ΔT2 = Tentering temperature, hot fluid –Tleaving temperature, cold fluid


Length of the heat exchanger pipe

Plot of Temperature vs Length of pipe


LMTD = 10.3718 0C

Computing for the Arithmetic Mean Temperature Difference

40 27 5 38 29 5

2

. . + AMTD =

AMTD = 10.500

7. Comparison of LMTD and AMTD for Counter-current Flow

LMTD AMTD

Flow 1 10.3718 10.50

Flow 2 8.6084 7.5

Flow 3 5.4389 5.5

Flow 4 3.6995 3.75

Flow 5 2.4663 2.5

Flow 6 ∞ 2.0


Documents

Final Double Pipe