Fluids experiments.

[monty]

This is aimed to have a discussion to better understand fluids in game and maybe make something amazing from it, or maybe just have a deeper understanding and better conceptualization of the topic.

I am declaring beforehand that what is to come might not be easily understandable(due to language issues or my lack in ability to express), but i will try and add graphs as and when possible. So if nothing else, they will help give a general idea.

I will start off with the basic understanding of fluids. This is detailed read and if you are only interested in result, skip to SUMMERY post directly(yet to add)

Introduction

As far as now, 12.20, fluids have a bunch of properties, but their effect can majorly be seen in these 3 properties

>>Energy
>>Flow
>>Pressure

amazingly enough none of these 3 are directly intractable.
>>energy is a function of temperature
>>Flow is a function of pressure difference and energy
>>Pressure is a function of volume of pipe content

So basically all fluids properties can majorly be studied keeping the variations in these 2 things

1>>current temperature
2>>current volume

There are ways to do these changes, but firstly lets focus on the properties alone rather than their cause .

>>firstly, increasing/changing temperature has a direct effect on the flow.
(taking water as fluid)
The relation flow to energy >>0.59 gives flow==0.59 energy content.

To get its results, we experiment with 3 temperatures,
1>>15 degrees
2>>100 degrees
3>>some intermediate temperature.>> this was a tricky part(mostly left undone).

When experimenting with flow, it can be seen as an extension of pressure.(more like pressure equalizing property)

It can vary greatly, but at every step will have some relation with temperature/pressure

At this point we will keep temperature constant and only vary pressure and note results.

Flow variation

The one general property that all fluids have influencing this field is pressure to flow ratio.

its denoted by P/F in this content.
(taking water)
P/F ==.4

From here we get a relation in pressure and flow.

Note>> Flow is nothing but ability to diffuse pressure. I see it not as fluid moving but fluid diffusing.

It can be seen as fluid moving towards the desired direction, but it can also be seen as VACUUM moving backwards.

The difference is that they are actually inversely related. However, when transporting fluid, i have come to realize that seeing it as fluid moving forward is a rather useless attempt, as ultimately we want to eliminate the gap.

If the gap reaches the initiation point, then that would mean that fluid is going into the system effectively.

SO FOR COMPRESSION PURPOSE , THE VACUUM IS SEEN AS ANOTHER FLUID, that is constantly being used by every fluid within the game and is generated in Fuel consuming entities.

I know it doesn't make much sense now, but see it as oil blocking water in a process. As we move along , its benefits will become evident .

Pressure

@XKnight
Fluid mechanics

Pressure can be seen as two parts. I can relate to the comment in this post, but i find it a little DIFFERENT in understanding , so lets share both of them.

First i am going to express it in the interactive form for understanding , and then relate to the experiments.

The pressure Pnet can be divided into 2 parts,

Pnet = P1 +P2

P1 = the volume ratio pressure of the pipe/tank/ fluid body.

This is a direct ratio between the volume of the body and the volume of the fluid in it
(ratio of fluid amount to total amount>>2500 for vanilla tank).

This can also be seen as primary pressure. Things with same primary pressure will not have any flow among them. EQUI-POTENTIAL vessels wont share any fluids among themselves. So a pipe with 1% content (1 unit of fluid/water) will not share any fluid with a tank with 1% fluid (25 units). The same goes for other pipes.


NOTE>> THINGS WITH SAME PRESSURE CAN HAVE DIFFERENT FLOW RATE. MORE OVER THEY CAN BE CONNECTED AND STILL MAINTAIN DIFFERENT FLOW RATE.

>>so 2 pipes with different volume/amount capacity can be joined such that they they supply 2 different sources at two different points, but don't exchange fluids, and fill them at different rate.

Whats more to add is that as long as the path of fluid delivery is bounded at ends, even if SOME of the middle section is replaced, same result can be obtained.(this will be covered in greater detail later)

The second component of pressure is its flow component.
P2 is actually that component of pressure which develops due to the nature of fluid, nature of pipe , volume/content of pipe.

This is NOT REAL pressure. And even though it changes the primary pressure, all flow related calculations are done on the P1 ( primary pressure)

It can basically be seen as pressure inertia. It is a very important aspect of pressure. Although it can be treated as Flow rate, it sometimes very dynamically controls and varies the pressure.

To give a general idea, its what causes the flow fluctuations and controls the flow rate. Smaller pipes and low viscosity or high P/F have higher P2 , where as Higher viscosity or lower P/F have higher P1.


General difference caused due to the different pressures.

let P(1/2) = P1/P2

Fluids with higher P(1/2), tends to equalize quickly, have higher pressure gradient range, and very low effective pumping length.

Side note>>

Effective pumping length is that length of pipe for which pump just gets utilized to 100% (if length is lower than this, pumping is wasted.)

Fluids with moderate P(1/2) have normal tendency to equalize, (will equalize normally without pumps) if pumper to a very large pressure gradient, they tend to create pressure energy waves, These waves causes fluctuating fluid flow through the pipe section. The have moderate pressure gradient range and have high effective pumping length.

To give a general idea the eff pumping low can be as low as 2 pipe segments, to 1 pipe segments (3 is the expected average)(these are not extreme cases, they are the normal values)

where as water at 0.5 pump and FULL fluid consumption has a effective pumping length of about 65+ segments.

The next in line are fluids with low P(1/2) ratio.
Let me start by saying that they are unplayable fluids for more than one reasons. They Almost never equalize, they cause heavy fluctuations , and god forbid if you use pump on them, as their eff range is not even in hundreds , its in the order of 1000s (that is a s at the end). Though they have a very low pressure gradient, that is almost never an issue as they have an insane flow rate.

Although they are totally useless as fluids, they can be used in some machines to act as fluid splitters (like belt splitters).

They have an IMPULSE type of pressure, so they can even enter those crafting machines that dont allow (these)fluids in them( and choke them).

But because of this property they can act as a pipe splitter, as they push the incoming fluid out in the direction of their flow and oscillate within the pipe section.
However they have a tendency to escape if the flow gets disrupted. I wanted to use it but with my level of coding it currently cant be done.

You will only encounter the second type, and first type in some cases.


However changing the pipe diameter or using heavy pumps can make liquid change their properties or change their class all together.
This will help as class 1 fluids are very hard to transport, hence it convenient to lower their viscous property.

[monty]

This post is where we start the experiment after the previous segment.

The main part flow, will be discussed here.

over view

Flow is , as said before, the diffusion of fluid . Here vacuum is also treated as fluid.

The three stages of fluid flow are,
1)Initial placement
2)Steady pressure
3) Steady flow

All of them will be discussed to cover the entire fluid flow segment.

brief into on them.

Initial placement aims at the flow nature as soon as a pipe section has been placed. It majorly deals with flow over large pipes created by robots or, massive expansion of a line. The major issue faced here is exhaustion of one line at the expense of other, saturation at one place and starvation at another within same line, or the most common bottle necking.

The steady pressure approach is an approach where different setup are used and its ensured that the pressure gradient along the way is constant. Its major application is in continuous feed lines with high competition for competition of resources. The aim is to have a predefined ratio set for different process, ensuring that under consumption or over consumption at one place doesnt disrupts the flow. Fluids like oil, petroleum gas.(sulfuric acid with mods)

The steady pressure line is the line which has study outlet.It isnt concerned with the individual demand and generally used with the energy segment , with small consumption in water handling. The idea is that maximum/controlled amount of fluid is transferred from source to destination, and the flow rate itself might change along the way(boiler segment)(turbine segment). Its effect can be seen in late factory rather than early ones, as at that time, water heating reaches saturation , and transportation starts to lag.

initiation phase

When placing pipes, it takes time to fill them with liquid. The relation between time taken to fill to segment and flow can vary over a vast range.

Initially when the player places an off shore pump(at the start), it takes almost no time to fully fill the assembly, (which is generally a steam engine).

But in later stages, when lines are joined within an active system with huge demand or high flow rate,(both are not same) it may take very long to equalize the pressure of the pipe segments. the initial setup looks something like this.

For when there is an existing flow rate.

itit.png (409.52 KiB) Viewed 6490 times

The existing flow will absorb the now supply of fluid and change the pressure of the segments. the actual change can vary with the requirement of the product .

Sometimes it can take well over 1 hr to reach the balance point when removing the setup will have a considerable impact on the flow rate. When faced with an existing flow current, its advised to not add cycle with low production rate or delay time, as they tend to further split the flow into more branches and starves the already struggling supply line.

For when there is an existing demand

init2.png (422.22 KiB) Viewed 6490 times

This acts like a open point with demand for fluid but no flow. Common example of this is the turbines (primarily through boiler section). In this case we have the fluid needed but we can make it reach the required destination. Most common mistake sometimes done here is addition of pumps.
Although pumps help PUSH the liquid, they also act as a break point in the path, making it (EFFECTIVELY) take longer for the supply flow to stabilize.

By effectively, its stated that these segments needs some kind of processing, and if things are rushed too frequently, though the availability of fluid at the end point, point of application(in case of recipe) increases. the quality (boiler) or threshold (production) cant be reached at the satisfactory level.

Also the amount of pumps needed also increases with length, and can become unmanageable if the flow changes, as they dont allow for dynamic change in volume flow rate over considerable degree.


The best way to equalize a flow in initiation can be found by understanding the flow fluctuation within the segment.

A more approachable manner would be to study relative pressure along the path and along time.

This can be divided into 2 sections,
>>Pressure difference study (P1 study along path)

>>Pressure fluctuations along the path ( P2 study along path, with time)

P1 study

init p diff.png (561.94 KiB) Viewed 6490 times

The initial pressure difference will built to allow an initial flow, but subsequent stable flow can take some time due to the variable pressure difference along the path.

HERE EACH UNIT DEFINES 10 pipes.

The initial straight ling signify the initial flow , setup right after the introduction of the fluid source.The later constant pressure difference signifies initial constant pressure flow and stable processing. After that relatively stable pressure difference is obtained as flow initiates, but after flow quickly dissipates with length.

THIS IS PRESSURE DIFFERENCE, NOT PRESSURE>>Pressure difference defines flow, pressure the current volume/amount of fluid.
After the range of .10, the flow is basically into stagnation phase.

To avoid it, its essential to initiate a proxy path, which is used to induce an initial pressure difference. This pressure difference can then be fed /slowly merged with the new /production(boiler) path. The result can save you anywhere from 1 to 8 hrs of equalizing (taking the requirement for 200 MJ heat capacity delivered) .

The final flow looks like this

init p diff fin.png (422.22 KiB) Viewed 6490 times

Notice how the flow INCREASES AFTER THE BOILER SECTION.
This is due to the extra energy gained. Adding it along the proxy line and feeding it small amount of fluid initiates this step. Exit this line at the end of the turbine segment(opens at the last turbine). This then is branched as the flow is increased, increasing branches as we get more working fluid in the flow.

The final dip is due to turbines. As there is nothing after them, once they fill up, the energy grid(demand for fluid inside the turbine )decides the flow rate. It may fluctuate a little, but the maxima generally lies above 12 ,in 13 and 15 range


P2 study

init p fluct.png (733.04 KiB) Viewed 6490 times

The fluctuation in the flow rate varies with time over a given segment of pipe and varies with flow.Simply put its ratio of pressure difference induced along the pipe.The flow has its own pressure gradient/difference. When we introduce new fluid with it, the Amount of the fluid changes, which changes the flow rate from the point on wards. The change is generally very bad. It almost always acts as a bottle neck, stopping the flow coming from before , while sometimes jamming the network.

It is experienced when an existing flow overlaps with the the new flow. This is the case of consumption line. Here the outlet /exit amount is to be the highest, as to avoid bottle neck. Here there is no concept of storage. Transport the fluid from point 1 to point 2 in minimum time type of problem .


This is what a super smooth flow looks like. It has maximum transportation along the given path (BALANCED FOR FLUCTUATIONS)
It can be obtained only within the EFFECTIVE PUMPING LENGTH/RANGE (Some very late designs use this)(use this for continuous production)

init p fluct ss.png (422.22 KiB) Viewed 6490 times

The corresponding pressure along the pipe.

init p fluct ssg.png (422.22 KiB) Viewed 6490 times

This is what generally can be obtained with some level of fluctuation but good base supply.Sometimes needs pumps.

init p fluct s.png (422.22 KiB) Viewed 6490 times

The pressure along the pipe.

init p fluct sg.png (422.22 KiB) Viewed 6490 times

The basic idea is to create a EQUI POTENTIAL line along some length. This takes care of the fluctuation, and in case clogging occurs, the fluid has an escape path.

[monty]

The general pipe discussion

Steady pressure

This is the steady pressure approach of pipes .It consists of of a predefined flow that has a fixed pressure gradient.

In other words, regardless of what pipes or containers are used, as long as the initiation and termination point are not disturbed, they will have a uniform dip in pressure.

The major advantage of this is that you done have to monitor each branch, as all branches have the same pressure as the main branch. Also different flow rate can be obtained along the length, without disrupting the flow in individual branch.

Since it has the same range of pressure difference, so if any branch is being considered, or any section of pipe is considered, all other branches and pipes have similar gradients. This is the pump extensive branch and heavily relays on the pumps for flow control.

In this different size pipes have different flow rate. The pipe used here can easily be used within the effective range, without worrying the flow rate or loss of performance.

Also since the gradient is predefined, adding pump will NEVER have any ADVERSE effects. Using pumps can be rather effective way to control both flow and consumption rate.

Very effective method for random demand driven process.

Built

This is what a general constant pressure looks like

co-p.png (1.06 MiB) Viewed 6477 times

Notice the pump right outside the tanks. They ensure that no matter the range of the fluid in the tank, they will always have UPPER LIMIT and a RELATIVE lower limit for the flow .

This is an example built. But any process that has reached lower saturation can be considered as a constant pressure process.
(saturation limit will be discussed soon)

In a typical factory(generally) any process that can reach 0 fluid in the pipe will have a tendency to be constant flow, where as the one that can reach max volume tends to be constant pressure process.

Most players use pumps for these to ramp up the flow, but they can also be used to set up a proxy flow, as they have a characteristic pressure gradient, but no fixed flow . So when high flow pipes need balancing, they are a good option to setup a basic pathway.

co-p2.png (1.41 MiB) Viewed 6477 times

Notice the pipes(Connectors) joining different lines. They dont transfer any liquid along lines . But in case a new setup has to be made, then they fill in the bare minimum to set the flow and then they again act as BUFFER LINES. These connectors act as a passive pumping mechanism in case of flow disruption(which is vary rare in this setup)

Data

The constant pressure flow only depends upon the exit condition and the pump condition. The pump condition defines upper limit of the flow/pressure, whereas,the exit defines lower limit.

Relation between any pump and line can be found simply by multiplying the volume ratio of pump with the volume of line to be found.

So if line 1 has 10 max amount, and 6 amount in its 51th pipe,

then line 2 with 20 max amount will have 12 amount in its 51th pipe.

If line 1 has 2 pumps, one pumping at 0.5 and other at 3, then as long as pump ratio is 1, both will have same volume in the Nth pipe after the pump.

Pump ratio is volume of fluid in pump to vol of pump.
It defines the effective of pump. Will be discussed later in detail.

If pump ratio is not 1, say its 0.01 , then the Nth pipe content will be 0.01*(amount at pump ratio 1)


These are generally converging fluid settiing.

Graph 1

cp1.png (422.22 KiB) Viewed 6477 times

This represents Same kind of pipe with different pumps, having different capacity. X-axis(length of pipe(1 unit=10 pipes) Y-axis (pressure of pipe)(this is not pressure difference, but pressure. It defines the amount of fluid in pipe))

Max volume of pipe =15
Series 1>>pumping power = 3
Series 2>>pumping power = 1.5
Series 3>>pumping power = 0.5

Graph 2

cp2.png (422.22 KiB) Viewed 6477 times

Represents the pressure in different pipes with SAME pump. All pipes have same pump, pump with power =3.
Look at the relative straight line, it signifies that the pressure is consistent. Any line drawn parallel to Y-axis gives equi potential zone, area with no transfer of fluid.
Graph 3

cp3.png (422.22 KiB) Viewed 6477 times

Among all the flow, this is the most unstable, and even it has relatively constant pressure difference.

The initial dip is the pressure excess due to pump. Pump doesnt behaves like the pipe and hence it has different rate of pressure change. This is largest(maximum slope)in smaller pipes and smaller in larger pipes.

[monty]

The general pipe discussion.

This section aims to define the nature of steady flow in pipes. This can help have a better understanding of the fluid flow and fluid amount.

STEADY Flow

Many times we confuse the two together, but they are very different from each other.

Unlike steady pressure, PUMPS, GENERALLY CANT/SHOULD'NT BE USED IN STEADY FLOW, as they tend to reduce the flow rate of the system.

The most confusing part is that even when the content of the pipe is very low, they can have a much larger flow rate than another pipe WITH SAME RATIO(not amount)

So 1%pipe 1 (10 max)can transfer more liquid than 1% volume pipe 3(50 max).
Infact, as the volume increases, the the flow rate drastically decreases, EVEN AT SAME RATIO

This goes against the common pipe spilling notion. It was stated that pipes behave like small tanks that will start to spill when reached a certain level and that rate depends upon the amount in container(the pressure concept)

However once a flow has been established,(equilibrium stage has been reached), such that the last pipe has obtained the desired amount of fluid needed for flow, and any further addition of fluid will not increase the amount of fluid in the pipes(as that would change the pressure gradient, disrupting the fluid flow.)

This is generally confused with an empty or stagnated pipe, but it actually has a much larger flow rate then that could be obtained with a pump, and adding pump actually LOWER'S THE FLOW RATE.

These are generally divergent curves, with a same initial condition and variable final condition.

Built

This is what a typical steady flow looks like




They are either one or both side opened flow networks, that dont depend on the final state of the process. They generally have a very good production rate and can have a
VERY HIGH VOLUME AT THE production side and much lower volume at the consumption side. They also dont have a steady rate of pressure fall.

The max pressure drop varies with pipe, outlet demand etc.

These are best seen in power production side, where the input is constant but the output may be variable.

>>>>Tanks are added to show the water content in various pipes

st-fl2.png (1.67 MiB) Viewed 6474 times

This is another example where the value well before final pipe has low amount, but it has higher flow then that can be obtained with pumps.

DATA

Unlike Steady pressure, the pipes here dont follow any one to one relation. All pipes have their own upper limit and lower limit.

stf2.png (926.49 KiB) Viewed 6470 times

Along the Y-axis is the ratio of content of each pipe.

These can be saperated into 2

1)Pipe above saturation limit
2)pipe below saturation limit

Pipe above saturation limit have reached their maximum rate flow for the current length and adding pumps to them will increase their flow by increasing the net PRESSURE GRADIENT.

pipe below their saturation have yet not completely exhausted their pressure gradient.They can still expand. IF A PUMP BELOW THEIR REMAINING GRADIENT IS USED, ALL OF THIS EXTRA GRADIENT WILL BE LOST.

If a pump above their gradient is used, the work done by pump is much lesser than their expected value.

For convenience sake lets take below saturation GOOD PIPE and above BAD PIPE


Good pipes use much lower head then bad pipes to transport fluid over the same range . In essence, they need much lower head/pressure gradient to gain the same flow rate. So they can deliver (say 50 units of fluid/sec) exactly same amount of fluid over much longer path , or much more fluid for same path.


For bad pipes

sfbp4.png (592.64 KiB) Viewed 6470 times

This is the range of the BAD pipe. Expanding from same point(production point) , they expand to the inlet point(consumption point).
Y-axis RELATIVE VOLUME X-axis Distance from inlet.(1 unit = 10 pipes)

sfbp3.png (876.87 KiB) Viewed 6465 times

This represents the different gradient for different processes.
They cover large area under the curve, covering large amount head.
Series 4 has range of .8 + at inlet and .1- at outlet.

sfbp2.png (528.97 KiB) Viewed 6470 times

This represent the relative flow rate of the pipe

The SATURATION CURVE

sfbp1.png (735.81 KiB) Viewed 6470 times

This represents the gradient used in the process while converting the pressure to flow. The max amount can be 1(100%).
At 100% entire amount of pressure has been used and is converted into flow.
But this will not happen practically, as for this the volume of the first/producer at 100% and the last/consumer unit at 0%

Although this seems reasonable, to make it practical, we need a VERY LONG PIPE, having very low flow rate. (more like making it into a reversible process).
Practical values can reach at the order of 99%, however for normal fluids, a value of about 80%+ is well into saturation limit ,so using pumps is recommended, as the flow is well below the 0.5 power pump.

NOW ABOUT THE GRAPH

Read this graph from right to left.
Y-axis is relative volume, X-axis is the process. So these are 5 different processes,
process 5 has minimum head utilization.

>>head utilization==pressure gradient== initial pressure -final pressure==(initial-final volume)/max volume

Pumps can be used to gain head, but MAY lead to flow loss(discussed later)


Good pipe

stf1.png (579.65 KiB) Viewed 6470 times

They have a relatively lower inlet and higher outlet.

sfgp1.png (421.76 KiB) Viewed 6465 times

Notice their relative volume/pressure, It ranges much lower than that of their predecessor. They cover much lower area for the same length.

sfgp2.png (648.97 KiB) Viewed 6465 times

The relative slope is much lower than their counter part. Also a smooth transaction ensures maximum flow rate.

sfgp3.png (422.22 KiB) Viewed 6465 times

Notice the head used here is much lower than their counterparts. So this pipe uses up to 63 of its net head to transfer fluid over the same section that other pipe(bad one)uses 99% to.

This transport more fluid and can transport fluid at the same rate for much longer distance.

[monty]

Pumping discussion.

In this section pumps and their effects are being studied. It will also define saturation limit for different pipe segments, and where and how pumps can be used to deliver maximum flow.

Pump usage

Pumps are used to raise the effective PRESSURE GRADIENT along the path of the length. Every pump acts as a sink for the pipe before it and a source for the pipe after.

However effective pumping requires that the pump is being used in its effective pumping length. This ensures that maximum pumping can be done and maximum PRESSURE GRADIENT CAN BE OBTAINED.

Built

This will explain the different approach in pumping and concept of saturation.

This is a steady flow identical pipe arrangement. At this setup, they all have reached saturation.

pu-5.png (2.07 MiB) Viewed 6440 times

>>How to find if a pipe is saturated or not.

The plot of pressure gradient/ difference (difference in pressure) with length of pipe defines flow of the pipe. Things with greater slope have higher pressure gradient/difference then those with lower slope. Each pipe has a maximum slope that it can have to support the flow.

This can be found by flowing section of pipe with fluid till the NET GRADIENT IS ABOUT 95% OF maximum gradient.

>>note pressure== amount over net amount. So 10 to 5 in a pipe with max volume and 50 to 25 in larger volume have same pressure.
>>also, along this range they will have same pressure gradient. So pressure difference the relative difference of volume in pipe sections.
>>For larger pipes this length is about 20 pipes, smaller ones can have it in range of 100+.

If the net gradient at 95% however has very low flow. Flow rate of 85 to 88% can be used for all practical , applicable flows.

If the change in gradient after adding the pump is lower than the gradient at 85%, then there is a flow loss. However, of the change in gradient is higher than 85% , then more flow can be obtained.

In this setup there are 50 pipe segments. After every 10 pipe segments there is a pipe extension built to find the relative pressure at that point.All pumps and pipes are identical.

pu-1.png (2.74 MiB) Viewed 6440 times

The first pump is built in the 11 to 20 section of the pipe assembly . Hence segment 2
The first pump is built in the 21 to 30 section of the pipe assembly . Hence segment 3
The first pump is built in the 31 to 40 section of the pipe assembly . Hence segment 4


Note that positioning the pumps differently has different effects on their performance.

Case 1

pu-3.png (1.57 MiB) Viewed 6440 times

In this case the pump is closer to the source then sink. The relative volume of the pump is 100%, meaning its below its effective pumping length.

This means that the pump acts as a source for the rest of the pipe and no greater pressure can be reached.The outlet pressure of pump is at the outlet pressure of the source. The pressure gradient of this pump setup can be divided into two parts

dP net = dP in part before the pump + dP after the pump.

The initial 20 segments now experience a much greater fall in pressure, (has larger pressure gradient then ) then the original pipe,This depends upon the pumping power of the pump. The greater pumping power pump will have much higher pressure gradient then its counter part.

The later 30 segments also get a boost in the flow, but this depends on the pipe flow, and doesn't depends on the pump power at all.

Effectively this setup behave in the same manner as pipe would with its pipe length of 30 units. That's all the pump does. It gets more flow rate rate for the new length of pipe.

Case 2

pu-4.png (1.5 MiB) Viewed 6440 times

This is the most effective use of pump. This uses the pump AT THEIR EFFECTIVE PUMPING LENGTH.

The volume of the pump is just below 100%.
(if it was moved 1 segment back then this would have 100% volume)

The gradient in this section is also maximum, and the outlet pressure is very close to the source pressure.
>>If relative volume is 95%, then outlet pressure =95% of source pressure

The net gradient of pressure in this section is the maximum. This also tends to lie in the middle of the source sink setup.

This reduces the pipe effective length by maximum .

Effective pipe length = pipe length for 100% source pressure.

L eff = L1 + L2

L1 = length after the pump
L2 is the extrapolated length before the pump.

>>
If the pump was assumed to be a pipe segment, Then adding the pressure gradient in this till the max pressure is reached is L2

Example, let the pressure gradient (pressure difference ) between 2 consecutive pipes is 0.1 and the pressure of pump is 9.5 (max pressure 10),

then L2 = (10-9.5)*0.1 = 5 .
So if pump was assumed to be a pipe ,at (adding) 5 pipes before the pipe maximum pressure can be reached.


In this case L2 is generally very small.
Case 3

pu-2.png (1.32 MiB) Viewed 6440 times

This is the late pump addition. It seems to have similar effect as Case 1.

In this segment, the effective pressure gradient is increased on both ends, but the outlet pressure is much lower compared to the inlet pressure.

The effect of this is similar to Case 1.

This is when a pump is used AFTER ITS EFFECTIVE PUMPING LENGTH. Here the pump provides maximum pressure gradient it can to the inlet section, and increases the
pressure, however,more often than not it creates a bottle neck.

It should only be used as last resort, and even then it will lower the flow efficiency and is not a solution. It disrupts future flow to gain immediate flow addition.

They also have a very large L2 in their effective length, to makeup for their head loss.

data

The flow measurement graph.Pressure vs pipe length

SERIES 1 >> CASE 1
SERIES 2 >>CASE 2
SERIES 3 >>CASE 3
SERIES 4 >>no pumps

Flow at outlet

SERIES 1 >> CASE 1>>203
SERIES 2 >>CASE 2>>261
SERIES 3 >>CASE 3>>182
SERIES 4 >>no pumps>>130

Pump1.png (37.63 KiB) Viewed 6432 times

The slope defines the flow for the length.
SERIES 4 acts as the defining flow rate curve.
For flow rate,calculate the slope leading into outlet(slope in second half)

SERIES 3 raises the pressure in the 4th segment. It gets more slope then the base slope.
SERIES 1 raises the pressure in the 2nd segment. It gets more slope then the SERIES 3.

SERIES 2 raises the pressure in the 3nd segment. It gets greatest slope .

Pump volume defines the point where effective pumping length occurs. Pumps gives maximum output for 99% of effective pressure.

For flow comparison look at graph in the steady flow segment

[monty]

Summery 1

This is the conclusion drawn from all above discussion

Fluid properties

Pressure and flow.

Outside the name, there is no such thing as pressure in the game.

The thing called pressure is actually volumetric ratio of a pipe.

This ratio cant be more than 1.

It difference is called pressure difference or pressure gradient.
ALTHOUGH this can be divided into any given numbers, making the difference between 2 pipes very small, its practical number depends on the fluid type being used.

Fluids with higher (P/F) ratio can have much smaller divisions to sustain a flow then fluids with larger ratio.

Pump doesn't affects the pressure in any way at all. All pump does is it REMOVES THE EFFECT OF TRAVELING THROUGH PIPES.


So a small pump basically reduces the number of pipes traveled by the fluid.It acts like an underground underground pipe, only difference, unlike underground ,it doesn't counts itself.


The flow ultimately depends only on the relative volumetric ratio (pressure gradient) of connecting pipes, which only depends on(P/V) ratio.
Changing the size of the pipe also changes the (P/V), making the fluid effectively behave differently.

Take extreme cases, very large volume, fluid will never leave the pipe,
Very small case, fluid never fills the pipe (as the number never stabilizes ).


Type of flow and gradient in next part.

Flow

Flow has 2 phases,

1)initial unstable phase
2)steady state

flow dev.png (33.42 KiB) Viewed 6404 times

When the pipe is first placed , it has variable flow and pressure gradient.
However as time passes and flow develops , this stabilizes to give a constant flow ( uniform pressure gradient).

Series 1 as we put it, series 4 when stable. Generally ,Lower(P/V) Stabilizes quicker then higher ones, but after a certain limit, they will have fluctuations in the flow, making it have a oscillate nature.

In graph that ca be visualized as half sine wave traveling on the Series 4.(superimpose it with very small sine wave).

Series 4 has constant and maximum flow across the ends.

To stabilize, it can either be left alone or be superimposed with a existing flow, slowly adding in fluid at controlled rate.(making the new source act like a pump).
Done properly, it can easily stabilize and gain good flow much quicker then if left to stabilize by itself.

Flow range

All flow has a minimum and maximum range. The maximum flow is at 0 pipe length.

0 pipe length can be created by supplying right at the point of requirement. However its pointless as at that stage its not the flow but the production rate that matters.
But if you want to find this, create a recipe that requires very large amount of fluid, but its pointless anyways.


However , the things that are not pointless is that the maximum exit rate is also capped.

All fluids will leave(get consumed) at no more than 740 to 750 times their average gradient.

So if you want to calculate the stagnation amount to get a flow, its this amount.
No matter how close or far or frequent the consumption is, this amount of fluid will not be consumed(as long s the flow is there(new fluid is being produced constantly)(max pressure ratio is 1 at producer end))

So if the pipe gradient is 0.17, that is two connecting pipes have this much difference in their relative volume, then 0.17*(740,750) == about 125.5(,127.5)

so if you add a storage tank at the last fluid , then it must hold this much (127.5)for flow.

Now if you attach a source directly to a sink, keeping one storage tank between them, then they store 1.4K fluid for the flow.

The flow gradient in this case comes out to be ~1.9, which is almost 2, which is also greater then 1. So a source actually acts as a negative pressure.
(this is not incorrect, as there is no such thing as pressure)(the source has a 1 as maxima, whereas sinks have -1 as maxima)(so basically 1.9 is actually 95% of maximum head developed)
Don't see it as double volume, that will give wrong results.Its a special case in which a flow can maintain its speed above the threshold.

The lower limit can be very low. So for practical reasons we will take it at 95%, and slow process at 85%. of the total head gradient.

So taking 0.1 water/fluid in outlet tank (0.1/2500 for pipe) ,the pressure gradient is about 0.00135

For 1000 pipes, the threshold is about 8 ,the gradient is 0.108

This is the pressure difference in 10 pipes. for one pipe divide by 10.

This is the smallest slope that can be obtained for flow observable in the game. Simulation will give result below this too, but got 60 ticks per sec, you wont notice anything.



So the most common range goes from 1 unit of pipe to 120 units of pipe (This is the flow range in the current pipe)

It is different for different pipes and different fluids, but it can be calculated by relation method.
This is an approx method, but it provides quite accurate results within the range of 10 to 60 pipes segment.(below and above the difference becomes large)

It uses the steady flow approach.
Measure the change in head (pressure) for steady flow(flow without pumps, corners, intersection) for 10 pipe length.
Get the ratio of this with the flow of known pipe(10 volume pipe)
Rest of the data can be found by multiplying this number with the known properties of the fluid.

pump

Pump are a length contraction entity.It basically subtracts the number of pipes in the segment. So a pump which is applied to 30 pipes, gives 10 pipe reduction, then the pipes behave like they would as 20 pipes.

The main difference between them and underground pipe is the priority of removal. The underground pipes remove the pipes Between them , whereas the pump removes pipes linked to them .

So the pump with the minimum power will remove 1 pipe,(itself).The number of pipes removed also depends on the fluid type. Basically calculate the relative property of the fluid by approx. method given above, and multiply it with that ratio. So if a pump removes 10 pipes in vanilla pipes, and the multiplier is 2 or 1/2(depending on how u take ratio), then it will have 5 pipes removal effect (the ratio of 2 means property of being calculated pipe/property of known pipe)

The more the power of the pump(pumping power), the more pipes it can remove/substitute.

Using multiple pumps right after each other will however not always have a good result. Pumps may not count themselves when calculating the flow, but they do act as a source and sink system.

At the low pressure side they act as sink, whereas at high pressure side they act as source.

The rate flow is capped by the sink amount and the source head.

If the relative volume of the pump is 1,(100%), then its used before its EFFECTIVE PUMPING LENGTH. It will experience a loss in flow if the volume and power of pump is not enough to maintain the flow. Since it has 100% fluid content, it experiences no loss of flow due to sink starvation.

If its content at lower than 100%(lower than 95%), then there is a sink starvation. in this case the flow reduces due to lack of fluid available.

At 100%,(or just lower than 100%) pump acts at their effective length. They have the least loss of flow in this case. Though both losses act at this point, they tend to be greatly minimized .As there is very low sink starvation, and very low head gradient loss(excess pressure loss).

PUMP POWER.

Pump power is also not a random number. using maximum pump power may be a safe bet, but dont assume that it will definitely increase your flow.Also adding lower power pump can reduce the pressure and flow rate.

A pump power defines the amount of pipes it can replace, or pressure of these pipes under the pressure gradient curve.
Basically a higher power pump can provide flow that could only be sustained in the shorter pipes.

Best way is to compare the pressure gradient with that of pipes and find the equivalent flow.

Pipes

The most common conclusion that people draw from the pipes are that LARGER VOLUME PIPES ARE actually BAD pipes for good flow rate.

The game has opposite relation. In game, the larger volume pipes are actually very useful pipes.

They can be used to built a flow in a new setup. Larger pipes equalize quicker than smaller pipes, and since they have much lower flow rate even at same pressure gradient,they can be used to setup a very large pipe connection system.

They might have low flow rate, but since pressure gradient doesn't needs the pipes to be full, or even half, they can setup a flow over much larger range than ordinary pipes, as smaller pipes quickly fill in the other end, removing the flow.

They don't transport as much, but are great way to overcome bottle necking and flow disruption. Adding fluid through them will have lower effect on the existing flow.

Graphs

These are the graph for various processes.

1)Pressure gradient in pipes along the length .Y-axis relative volume(10=100%) X-axis, length of path(1 = 10 pipes).

pipe fr.png (19.14 KiB) Viewed 6404 times

The slope defines the gradient and flow. Larger slope has more flow rate.

2) Pressure gradient with exit flow rate.(max. rate of consumption of fluid).

pipe frs.png (30.41 KiB) Viewed 6404 times

.

The small slant line at the end defines the rate of fluid consumption. This is not part of flow. Depends on consumption rate and pressure gradient.

3)Relative pumping effect (has various pumps and the pressure gradient along path)

Pump1.png (37.63 KiB) Viewed 6404 times

4)Effective flow rate of these pumps.

Best case.

fp2.png (41.9 KiB) Viewed 6404 times

In this the slope is approaching series 2.Hence this pumping will have an effective flow that which is observed in pipe length of 20 and below.

intermediate case

fp1.png (40.05 KiB) Viewed 6404 times

fp3.png (32.42 KiB) Viewed 6404 times

They have a flow in between series 2 and 3, approaching series 3. This will have an effective flow of this region. the greater slope ensures more flow in case upper pump(pump before its effective pumping length).

Worst case

fp4.png (38.83 KiB) Viewed 6404 times

Here the pump has a slope on the order or series 5, and at points its even crossing it. This will actually DECREASE the flow of the pipe in all segments.(within this range)

For a pump to have flow rate to have better flow and improve the PRESSURE, its slope should be more than that of the section. Simply put, it should provide more pressure gradient then the pipe without it so that flow and pressure can be increased. Using pumps in section outside of this range lowers the flow and may cause clogging.

Derived conclusion. (applicable only on this case, NOT general)

a)None of the pumps should be used below pipe length 20.
b)Only BEST CASE PUMP AT 20-30 range
c)Intermediate used in range 30-40.
d)worst case pump effective in range above 50, and since it's actually overshooting the last series, use it above 60 pipe length.

using them at this MINIMUM range has no losses, and we gain flow ,but below this there is a permanent loss in flow.


Pumps can also be increased to increase the flow rate too. But its rather difficult as the lower end tends to get starved of fluid. However if its not starved, using pumps, in series, (multiple lower pump to feed a higher pump(to avoid starving))can start a higher flow rate. It is however still caped by the gradient of the pump.

>> side note, never store fluid in tanks by storing it to a tank, rather place it along the path. Storing things to tanks is not a good way for low fluctuation.

In case of higher fluctuations however, a secondary buffer path can be made, with tank on one end and pipe on another. this way pipe will provide fast flow, and tank provide fluctuation resistance. (use pipe and tank in pair, originating from a same point, meeting back at same point before splitting).
Although tanks at later part of the pipes store much lower amount of fluid, it must be placed to ensure rapid drop in flow.

This was the basic conclusion that one can come to after a bit of experimenting.

maybe it can be used to create mods/in-game mechanisms for different flow and thermodynamic cycle involving different pressure.

I hope it helps .

[BlakeMW]

All pump does is it REMOVES THE EFFECT OF TRAVELING THROUGH PIPES.

That might explain why when you connect 1 pump to a string of 10 boilers, you can end up with the 5 boilers at the far end of the string consuming the liquid, and the 5 at the near end of the string (closest to the pump) being starved: the pump teleports the liquid as far as it can, and the liquid then works backwards from there (Note: This only seems to happen with certain orientations - I think when the liquid is pumped rightwards and downwards)

[monty]

Speaking in simple language, a pump is a set of consumer and producer

It will consume any amount of resource/fluid that it can to fill up its producer.
Its producer adds the pumping pressure to the already available pressure.

So having pumping power above 1 is useless, as the pipe(tank or anything else) right next to it can only store max of 1:1 fluid.(or 100% of its max volume)
The only use of it(if you can call it use) is to fill up a consumer from a tank rapidly(but for this the only thing between them should be the pump)(and it doesnt works other way around)


Regarding the pipe, the maximum difference can be seen as having a pipe full at one end and empty at another.flow would develop and depend upon the difference in two pipes,

If there are very large number of pipes, the difference is small, so flow is less.
However if there are very few pipes, difference is large.(larger flow,so larger amount of liquid is transferred )

(one way to stimulate this is to setup an off shore pump, pumping 60 liquid/ sec, and a generator consuming 1 (or more) fluid per tick)
(if you vary their distance , you can see how flow very)

What happens in your case, or any other case can be explained like this

effect

usually for some flow (say 60 (liquid/fluid)/sec )it takes say 30 pipes,
If you place a pump on the 15th pipe, the its equivalent to shifting consumer closer. This makes pipe length smaller,(15) and there is more difference between each pipe pressure(fluid content ratio).This was the consumer's side effect.
At the producer side, the pump has more fluid ratio (content)than the 15th pipe. So it acts like a pipe which constantly maintains this ratio. This makes the difference between the pump and sink(/consumer/generator) rise

>>lets say in equilibrium the 15th pipe had 5(out of 10) volume, and end had 0.01(the difference is 4.99)
when you add pump, this 15th pipe becomes say 7(or 10), then the difference also increases (6 or more)and flow increases.

The net flow is minimum of the two separate flows.

The most a pump can increase the pipe pressure is to 100%, (or when its volume is full). If used before this, then although the rate of flow at the inlet end rises, the rate at the outlet caps the flow rate. If used after 100% point(volume of pump less than 100%), the rate at producer end(in pump direction ) is max ,but not enough fluid is being supplied to the pump to keep itself at this volume.

>>about the boiler problem

boiler

entity like boilers effectively work on the STEADY VOLUME in them(not exactly, but proportionally).

When you put a pump right next to a boiler(/pipe) ,the consumer side pump is supposed to have 0 volume, so the point before should have just greater than 0(if at 100% mark),and 0 or no volume(if used after 100% mark). If used before 100% mark, it will still have some volume in it.

All boilers on the receiving side of the pump have lower volume now,(so place them after the pump).Although the flow increases, the boiler gets to heat lower amount of fluid now.(and lower amount of fluid in pipes remains).

The reason you don't notice it on the far end is because the residue amount of fluid in the pipe gets heated and then the flow replaces it, but at the near end, this volume is too low and the boiler stays idle before it gets replenished,as it cant consume all of it.

So before placing your pump,one should calculate the amount of energy the boiler can provide, then find out the minimum volume of fluid that is needed to store this energy.

But since when the flow changes, the boilers before also have an increased chance to PRE HEAT the water,so this is not easy/advised approach.
The rate of heating first decreases, then increases, and then decreases again, until it reaches to the point that the entire energy is used.

Lets say the boiler provides enough energy to completely heat 3 liquid/fluid in one sec.
If there is almost 0 fluid, then boiler fully heats all of it, and then remains idle.(since boiler adds equal heat per tick, heat lost is lost forever, meaning it wont add more temperature at a later tick)
If there is exactly 3 fluid, then its used at 100%, while no more heating can be done by subsequent boilers.
if it has more than 3 fluids, then some energy will be left for the later boilers to add.

Due to this there are two variables you have to consider,
1,heat added per boiler
2 minimum volume that one boiler must have(at lower energy)


This complex problem can be solved in an effective manner. And that is parallel heating.

All parallel boilers have exactly the same amount of fluid, but this fluid now gets replenished slower than it would in series.

So rather than finding the fluid in each boiler, you just need to add more boilers parallel to each other.The only reason(in my opinion )people use series is to use small inserter setup. But boilers take much longer than it takes a inserter to feed the fuel.

Unlike series in parallel you have only one parameter, temperature. If any one boiler in a parallel setup reaches 95+ temperature, then just add one (or another parallel connection of much lower number) boiler in their series, and you get fully heated fluid and maximum utility of boilers at same time.

And since the flow only varies between the number of pipes between the producer and source, it has much faster flow then the series.

I hope you find it useful

[BlakeMW]

Oops I actually meant "steam engines" not "boilers". When you take a single small pump (which provides enough water to run 5 steam engines), then connect that to 10 steam engines, the 5 steam engines furthest from the pump consume the water, and the 5 closest to the pump consume no water (assuming the electricity grid is under 100% load). This only seems to happen when the water is pumped to the right or downwards, otherwise the 5 closest steam engines consume the water and the 5 furthest ones consume no water. The fact that water can skip over a bunch of steam engines is pretty weird and it's high level of dependence on orientation is also very weird.

It's pretty clear in this image just from the steam:

steam engines

In this case the 5 engines closest to the pump run at about 10%, the 6th runs at about 50% and the last 4 run at 100%

With a string of 30 engines, the engine closest to the pump runs at about 10%, this gradually decreases to about 5% for the 27th engine, the 28th runs at about 60%, and the 29th and 30th run at 100%.

For reference this is what it looks like when the string goes in the other direction:


No surprises here! The 5 steam engines closest to the pump consume all the water and the rest consume none, just what you would expect.

[Fatmice]

Nothing weird, pipes are updated leftward and upward flow first, then westward and downward flow. Within these directions, they are updated by their position within the pipe tables.

Your example clearly shows how pipes behave.