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Pipe throughput: simple about complex things

How does the capacity of a pipe change depending on the diameter? What factors other than cross-section influence this parameter? Finally, how to calculate, even approximately, the permeability of a water pipeline with a known diameter? In this article I will try to give the most simple and accessible answers to these questions.

Our task is to learn how to calculate the optimal cross-section water pipes.

Why is this necessary?

Hydraulic calculation allows you to obtain optimal minimum water pipe diameter value.

On the one hand, there is always a catastrophic shortage of money during construction and repairs, and the price per linear meter of pipes increases nonlinearly with increasing diameter. On the other hand, an undersized water supply section will lead to an excessive drop in pressure at the end devices due to its hydraulic resistance.

When the flow rate is at the intermediate device, the pressure drop at the end device will lead to the fact that the water temperature with the cold water and hot water taps open will change sharply. As a result, you will either be doused with ice water or scalded with boiling water.

Restrictions

I will deliberately limit the scope of the problems under consideration to the water supply of a small private house. There are two reasons:

1. Gases and liquids of different viscosities behave completely differently when transported through a pipeline. Consideration of the behavior of natural and liquefied gas, oil and other media would increase the volume of this material several times and would take us far from my specialization - plumbing;
2. In the case of a large building with numerous plumbing fixtures, for the hydraulic calculation of the water supply it will be necessary to calculate the probability of simultaneous use of several water points. IN small house the calculation is performed for peak consumption by all available devices, which greatly simplifies the task.

Factors

Hydraulic calculation of a water supply system is a search for one of two quantities:

• Calculation of pipe capacity for a known cross-section;
• Calculation of the optimal diameter with a known planned flow rate.

In real conditions (when designing a water supply system), it is much more common to perform the second task.

Everyday logic dictates that the maximum water flow through a pipeline is determined by its diameter and inlet pressure. Alas, the reality is much more complicated. The fact is that the pipe has hydraulic resistance: Simply put, the flow is slowed down by friction against the walls. Moreover, the material and condition of the walls predictably influence the degree of braking.

Here full list Factors affecting the performance of a water pipe:

• Pressure at the beginning of the water supply (read - pressure in the line);
• Slope pipes (change in its height above the conditional ground level at the beginning and end);

• Material walls Polypropylene and polyethylene have much less roughness than steel and cast iron;
• Age pipes. Over time, steel becomes overgrown with rust and lime deposits, which not only increase roughness, but also reduce the internal clearance of the pipeline;

This does not apply to glass, plastic, copper, galvanized and metal-polymer pipes. Even after 50 years of operation they are in new condition. The exception is siltation of the water supply when there is a large amount of suspended matter and there are no filters at the inlet.

• Quantity and angle turns;
• Diameter changes water supply;
• Presence or absence welds, solder burrs and connecting fittings;

• Shut-off valves. Even full bore ball valves provide some resistance to flow movement.

Any calculation of pipeline capacity will be very approximate. Willy-nilly, we will have to use average coefficients typical for conditions close to ours.

Torricelli's Law

Evangelista Torricelli, who lived at the beginning of the 17th century, is known as a student of Galileo Galilei and the author of the very concept of atmospheric pressure. He also owns a formula describing the flow rate of water pouring out of a vessel through a hole of known dimensions.

For the Torricelli formula to work, you must:

1. So that we know the water pressure (the height of the water column above the hole);

One atmosphere under Earth's gravity is capable of raising a water column by 10 meters. Therefore, pressure in atmospheres is converted into pressure by simply multiplying by 10.

1. So that there is a hole significantly smaller than the diameter of the vessel, thus eliminating loss of pressure due to friction against the walls.

In practice, Torricelli's formula allows one to calculate the flow of water through a pipe with an internal cross-section of known dimensions at a known instantaneous pressure at the time of flow. Simply put: to use the formula, you need to install a pressure gauge in front of the tap or calculate the pressure drop in the water supply system at a known pressure in the line.

The formula itself looks like this: v^2=2gh. In it:

• v is the flow velocity at the outlet of the hole in meters per second;
• g is the acceleration of the fall (for our planet it is equal to 9.78 m/s^2);
• h is the pressure (the height of the water column above the hole).

How will this help in our task? And the fact that fluid flow through the hole(the same bandwidth) is equal to S*v, where S is the cross-sectional area of ​​the hole and v is the flow velocity from the above formula.

Captain Obviousness suggests: knowing the cross-sectional area, it is not difficult to determine the internal radius of the pipe. As you know, the area of ​​a circle is calculated as π*r^2, where π is taken to be rounded equal to 3.14159265.

In this case, Torricelli’s formula will look like v^2=2*9.78*20=391.2. The square root of 391.2 is rounded to 20. This means that water will pour out of the hole at a speed of 20 m/s.

We calculate the diameter of the hole through which the flow flows. Converting the diameter to SI units (meters), we get 3.14159265*0.01^2=0.0003141593. Now let’s calculate the water consumption: 20*0.0003141593=0.006283186, or 6.2 liters per second.

Back to reality

Dear reader, I would venture to guess that you do not have a pressure gauge installed in front of the mixer. Obviously, for a more accurate hydraulic calculation, some additional data is needed.

Typically, the calculation problem is solved in reverse: given the known water flow through the plumbing fixtures, the length of the water pipe and its material, a diameter is selected that ensures the pressure drop to acceptable values. The limiting factor is the flow rate.

Reference data

The normal flow rate for internal water supply systems is considered to be 0.7 - 1.5 m/s. Exceeding the last value leads to the appearance of hydraulic noise (primarily at bends and fittings).

Water consumption standards for plumbing fixtures are easy to find in regulatory documentation. In particular, they are given in the appendix to SNiP 2.04.01-85. To save the reader from lengthy searches, I will provide this table here.

The table shows data for mixers with aerators. Their absence equalizes the flow through the mixers of the sink, washbasin and shower with the flow through the mixer when setting the bath.

Let me remind you that if you want to calculate the water supply of a private house with your own hands, add up the water consumption for all installed devices. If these instructions are not followed, you will be in for surprises such as a sharp drop in temperature in the shower when you open the tap. hot water on .

If the building has a fire water supply, 2.5 l/s is added to the planned flow rate for each hydrant. For fire water supply, flow speed is limited to 3 m/s: In the event of a fire, hydraulic noise is the last thing that will irritate residents.

When calculating the pressure, it is usually assumed that at the device farthest from the input it should be at least 5 meters, which corresponds to a pressure of 0.5 kgf/cm2. Some plumbing fixtures (instantaneous water heaters, automatic filler valves) washing machines etc.) simply do not work if the pressure in the water supply is below 0.3 atmospheres. In addition, it is necessary to take into account hydraulic losses on the device itself.

On the picture - instantaneous water heater Atmor Basic. It turns on heating only at a pressure of 0.3 kgf/cm2 and above.

Flow, diameter, speed

Let me remind you that they are linked together by two formulas:

1. Q = SV. Water flow in cubic meters per second is equal to the cross-sectional area in square meters, multiplied by the flow speed in meters per second;
2. S = π r^2. The cross-sectional area is calculated as the product of pi and the square of the radius.

Where can I get the radius values ​​for the internal section?

• U steel pipes with a minimum error it is equal to half the remote control(conditional bore used to mark pipes);
• For polymer, metal-polymer, etc. the internal diameter is equal to the difference between the external one, which is used to mark the pipes, and twice the wall thickness (it is also usually present in the marking). The radius, accordingly, is half the internal diameter.

1. The internal diameter is 50-3*2=44 mm, or 0.044 meters;
2. The radius will be 0.044/2=0.022 meters;
3. The internal cross-sectional area will be equal to 3.1415*0.022^2=0.001520486 m2;
4. At a flow rate of 1.5 meters per second, the flow rate will be 1.5*0.001520486=0.002280729 m3/s, or 2.3 liters per second.

Loss of pressure

How to calculate how much pressure is lost in a water pipeline with known parameters?

The simplest formula for calculating the pressure drop is H = iL(1+K). What do the variables in it mean?

• H is the desired pressure drop in meters;
• i — hydraulic slope of a water pipe meter;
• L is the length of the water pipeline in meters;
• K— coefficient, which makes it possible to simplify the calculation of the pressure drop by shut-off valves And . It is tied to the purpose of the water supply network.

Where can I get the values ​​of these variables? Well, except for the length of the pipe, no one has canceled the tape measure yet.

Coefficient K is taken equal to:

With a hydraulic slope the picture is much more complicated. The resistance offered by a pipe to flow depends on:

• Internal section;
• Wall roughness;
• Flow rates.

A list of values ​​for 1000i (hydraulic slope per 1000 meters of water supply) can be found in Shevelev’s tables, which, in fact, serve for hydraulic calculations. The tables are too large for an article because they provide 1000i values ​​for all possible diameters, flow rates and materials, adjusted for service life.

Here is a small fragment of Shevelev’s table for plastic pipe size 25 mm.

The author of the tables gives pressure drop values ​​not for the internal section, but for standard sizes, which are used to mark pipes, adjusted for wall thickness. However, the tables were published in 1973, when the corresponding market segment had not yet been formed.
When calculating, keep in mind that for metal-plastic it is better to take values ​​corresponding to a pipe that is one step smaller.

Let's use this table to calculate the pressure drop on a polypropylene pipe with a diameter of 25 mm and a length of 45 meters. Let's agree that we are designing a water supply system for household purposes.

1. At a flow speed as close as possible to 1.5 m/s (1.38 m/s), the 1000i value will be equal to 142.8 meters;
2. The hydraulic slope of one meter of pipe will be equal to 142.8/1000=0.1428 meters;
3. The correction factor for domestic water supply systems is 0.3;
4. The formula as a whole will take the form H=0.1428*45(1+0.3)=8.3538 meters. This means that at the end of the water supply system, with a water flow rate of 0.45 l/s (the value from the left column of the table), the pressure will drop by 0.84 kgf/cm2 and at 3 atmospheres at the inlet it will be quite acceptable 2.16 kgf/cm2.

This value can be used to determine consumption according to Torricelli formula. The calculation method with an example is given in the corresponding section of the article.

In addition, in order to calculate the maximum flow rate through a water supply system with known characteristics, you can select in the “flow rate” column of Shevelev’s complete table a value at which the pressure at the end of the pipe does not fall below 0.5 atmosphere.

Conclusion

Dear reader, if the given instructions, despite being extremely simplified, still seem tedious to you, just use one of the many online calculators. As always, Additional information can be found in the video in this article. I would appreciate your additions, corrections and comments. Good luck, comrades!

July 31, 2016

If you want to express gratitude, add a clarification or objection, or ask the author something - add a comment or say thank you!

Water consumption in a stream is the volume of liquid passing through a cross section. The consumption unit is m3/s.

Calculation of water consumption should be carried out at the planning stage of the water supply system, since the main parameters of the water pipelines depend on this.

Water flow in the pipeline: factors

In order to independently calculate the water flow in the pipeline, you need to know the factors that ensure the passage of water in the pipeline.

The main ones are the degree of pressure in the water pipeline and the cross-sectional diameter of the pipe. But, knowing only these values, it will not be possible to accurately calculate water consumption, since it also depends on such indicators as:

1. Pipe length. This is all clear: the longer its length, the higher the degree of friction of water against its walls, so the flow of liquid slows down.
2. The material of the pipe walls is also an important factor on which the flow rate depends. Thus, the smooth walls of a polypropylene pipe provide the least resistance than steel.
3. The diameter of the pipeline - the smaller it is, the higher the resistance of the walls to fluid movement will be. The narrower the diameter, the more unfavorable it is to match the outer surface area to the inner volume.
4. Service life of the water supply system. We know that over the years they are exposed to corrosion, and cast iron deposits form on them. The friction force against the walls of such a pipe will be significantly higher. For example, the surface resistance of a rusty pipe is 200 times higher than that of a new steel pipe.
5. Changes in diameter in different sections of the water pipeline, turns, shut-off fittings or fittings significantly reduce the speed of water flow.

What quantities are used to calculate water flow?

The following quantities are used in the formulas:

• Q – total (annual) water consumption per person.
• N is the number of residents of the house.
• Q – daily flow rate.
• K is the consumption unevenness coefficient equal to 1.1-1.3 (SNiP 2.04.02-84).
• D – pipe diameter.
• V – water flow speed.

Formula for calculating water consumption

So, knowing the values, we get the following formula for water consumption:

1. For daily calculation – Q=Q×N/100
2. For hourly calculation – q=Q×K/24.
3. Calculation by diameter - q= ×d2/4 ×V.

An example of calculating water consumption for a household consumer

The house is equipped with: toilet, washbasin, bathtub, kitchen sink.

1. According to Appendix A, we take the flow rate per second:
   • Toilet - 0.1 l/sec.
   • Washbasin with mixer - 0.12 l/sec.
   • Bath - 0.25 l/sec.
   • Kitchen sink - 0.12 l/sec.
2. The amount of water consumed from all supply points will be:
   • 0.1+0.12+0.25+0.12 = 0.59 l/sec
3. According to the total flow rate (Appendix B), 0.59 l/sec corresponds to the calculated flow rate of 0.4 l/sec.

You can convert it to m3/hour by multiplying it by 3.6. Thus it turns out: 0.4 x 3.6 = 1.44 cubic meters / hour

Procedure for calculating water consumption

The entire calculation procedure is specified in the set of rules 30. 13330. 2012 SNiP 2.04.01-85 * “Internal water supply and sewerage”, updated edition.

If you are planning to start building a house, remodeling an apartment or installing plumbing structures, then information on how to calculate water consumption will be very helpful. Calculating water consumption will help not only determine the required volume of water for a particular room, but will also allow timely detection of a decrease in pressure in the pipeline. In addition, thanks to simple formulas, you can do all this yourself, without the help of specialists.

Laying a pipeline is not very difficult, but quite troublesome. One of the most complex problems this involves calculating the pipe capacity, which directly affects the efficiency and performance of the structure. This article will discuss how pipe capacity is calculated.

Throughput is one of the most important indicators of any pipe. Despite this, this indicator is rarely indicated in pipe markings, and there is little point in this, because the throughput capacity depends not only on the dimensions of the product, but also on the design of the pipeline. That is why this indicator has to be calculated independently.

Methods for calculating pipeline capacity

1. External diameter. This indicator is expressed in the distance from one side of the outer wall to the other side. In calculations, this parameter is designated Day. The outer diameter of the pipes is always indicated in the markings.
2. Nominal diameter. This value is defined as the diameter of the internal section, which is rounded to whole numbers. When calculating, the nominal diameter is displayed as Dn.

Calculation of pipe permeability can be carried out using one of the methods, which must be selected depending on the specific conditions of pipeline laying:

1. Physical calculations. IN in this case a pipe capacity formula is used to take into account each design indicator. The choice of formula is influenced by the type and purpose of the pipeline - for example, sewer systems have their own set of formulas, as do other types of structures.
2. Spreadsheet calculations. You can select the optimal cross-country ability using a table with approximate values, which is most often used for arranging wiring in an apartment. The values ​​indicated in the table are quite vague, but this does not prevent them from being used in calculations. The only drawback of the tabular method is that it calculates the throughput of the pipe depending on the diameter, but does not take into account changes in the latter due to deposits, therefore, for highways susceptible to build-up, such a calculation will not be possible. best choice. To get accurate results, you can use Shevelev’s table, which takes into account almost all factors affecting pipes. This table is perfect for installing highways on individual plots of land.
3. Calculation using programs. Many companies specializing in pipeline laying use in their activities computer programs, allowing you to accurately calculate not only the throughput of pipes, but also a lot of other indicators. For independent calculations, you can use online calculators, which, although they have a slightly larger error, are available free of charge. A good option A large shareware program is “TAScope”, and in the domestic space the most popular is “Hydrosystem”, which also takes into account the nuances of pipeline installation depending on the region.

Calculation of gas pipeline capacity

Designing a gas pipeline requires fairly high precision - gas has a very high compression ratio, due to which leaks are possible even through microcracks, not to mention serious ruptures. That is why correct calculation of the capacity of the pipe through which gas will be transported is very important.

If we are talking about gas transportation, then the throughput of pipelines, depending on the diameter, will be calculated using the following formula:

• Qmax = 0.67 DN2 * p,

Where p is the value of the working pressure in the pipeline, to which 0.10 MPa is added;

DN – the value of the nominal diameter of the pipe.

The above formula for calculating the capacity of a pipe by diameter allows you to create a system that will work in domestic conditions.

In industrial construction and when performing professional calculations, a different type of formula is used:

• Qmax = 196.386 DN2 * p/z*T,

Where z is the compression ratio of the transported medium;

T – temperature of the transported gas (K).

To avoid problems, professionals also have to take into account the climatic conditions in the region where it will pass when calculating the pipeline. If the outer diameter of the pipe is smaller than the gas pressure in the system, then the pipeline is very likely to be damaged during operation, resulting in loss of the transported substance and an increased risk of explosion in the weakened section of the pipe.

If necessary, you can determine the patency gas pipe using a table that describes the relationship between the most common pipe diameters and the operating pressure level in them. By and large, the tables have the same drawback that the pipeline capacity calculated by diameter has, namely, the inability to take into account the influence of external factors.

Calculation of sewer pipe capacity

When designing a sewer system, it is imperative to calculate the throughput of the pipeline, which directly depends on its type (sewage systems are either pressure or non-pressure). Hydraulic laws are used to carry out calculations. The calculations themselves can be carried out either using formulas or using appropriate tables.

For the hydraulic calculation of the sewer system, the following indicators are required:

• Pipe diameter – DN;
• The average speed of movement of substances is v;
• The magnitude of the hydraulic slope is I;
• Filling degree – h/DN.

As a rule, when carrying out calculations, only the last two parameters are calculated - the rest can then be determined without any problems. The magnitude of the hydraulic slope is usually equal to the slope of the ground, which will ensure the movement of wastewater at the speed necessary for self-cleaning of the system.

The speed and maximum filling level of domestic sewerage are determined from a table that can be written out as follows:

1. 150-250 mm - h/DN is 0.6 and speed is 0.7 m/s.
2. Diameter 300-400 mm - h/DN is 0.7, speed is 0.8 m/s.
3. Diameter 450-500 mm - h/DN is 0.75, speed is 0.9 m/s.
4. Diameter 600-800 mm - h/DN is 0.75, speed is 1 m/s.
5. Diameter 900+ mm - h/DN is 0.8, speed – 1.15 m/s.

For a product with a small cross-section, there are standard indicators for the minimum pipeline slope:

• With a diameter of 150 mm, the slope should not be less than 0.008 mm;
• With a diameter of 200 mm, the slope should not be less than 0.007 mm.

To calculate the volume of wastewater, the following formula is used:

• q = a*v,

Where a is the open cross-sectional area of ​​the flow;

v – speed of wastewater transportation.

The speed of transport of a substance can be determined using the following formula:

• v= C√R*i,

where R is the value of the hydraulic radius,

C – wetting coefficient;

i is the degree of slope of the structure.

From the previous formula we can derive the following, which will allow us to determine the value of the hydraulic slope:

• i=v2/C2*R.

To calculate the wetting coefficient, a formula of the following form is used:

• С=(1/n)*R1/6,

Where n is a coefficient that takes into account the degree of roughness, which varies from 0.012 to 0.015 (depending on the material of the pipe).

The R value is usually equated to the usual radius, but this is only relevant if the pipe is completely filled.

For other situations, a simple formula is used:

• R=A/P,

Where A is the cross-sectional area of ​​the water flow,

P is the length of the inner part of the pipe in direct contact with the liquid.

Tabular calculation of sewer pipes

You can also determine the permeability of sewer system pipes using tables, and the calculations will directly depend on the type of system:

1. Gravity sewerage. To calculate free-flow sewer systems, tables are used that contain all the necessary indicators. Knowing the diameter of the pipes being installed, you can select all other parameters depending on it and substitute them into the formula (read also: " "). In addition, the table indicates the volume of liquid passing through the pipe, which always coincides with the patency of the pipeline. If necessary, you can use the Lukin tables, which indicate the throughput of all pipes with a diameter in the range from 50 to 2000 mm.
2. Pressure sewer. Determining the throughput in this type of system using tables is somewhat simpler - it is enough to know the maximum degree of filling of the pipeline and the average speed of liquid transportation. Read also: "".

Bandwidth table polypropylene pipes allows you to find out all the parameters necessary for arranging the system.

Calculation of water supply capacity

Water pipes are most often used in private construction. In any case, the water supply system is subject to a serious load, so calculating the pipeline capacity is mandatory, because it allows you to create the most comfortable operating conditions for the future structure.

To determine the permeability of water pipes, you can use their diameter (read also: " "). Of course, this indicator is not the basis for calculating cross-country ability, but its influence cannot be excluded. The increase in the internal diameter of the pipe is directly proportional to its permeability - that is, a thick pipe almost does not interfere with the movement of water and is less susceptible to the accumulation of various deposits.

However, there are other indicators that also need to be taken into account. For example, a very important factor is the coefficient of friction of the fluid on the inside of the pipe (for different materials there are eigenvalues). It is also worth considering the length of the entire pipeline and the pressure difference at the beginning of the system and at the outlet. An important parameter is the number of different adapters present in the design of the water supply system.

The throughput of polypropylene water pipes can be calculated depending on several parameters using the tabular method. One of them is a calculation in which the main indicator is water temperature. As the temperature in the system increases, the fluid expands, causing friction to increase. To determine the permeability of the pipeline, you need to use the appropriate table. There is also a table that allows you to determine the permeability in the pipes depending on the water pressure.

The most accurate calculation of water based on pipe capacity can be made using the Shevelev tables. In addition to accuracy and large number standard values, these tables contain formulas that allow you to calculate any system. This material fully describes all situations related to hydraulic calculations, which is why most professionals in this field most often use the Shevelev tables.

The main parameters taken into account in these tables are:

• External and internal diameters;
• Pipeline wall thickness;
• System operation period;
• Total length of the highway;
• Functional purpose systems.

Conclusion

Pipe capacity calculations can be performed different ways. Choice the best way calculation depends on a large number of factors - from pipe sizes to purpose and type of system. In each case, there are more and less accurate calculation options, so both a professional who specializes in laying pipelines and an owner who decides to lay a pipeline at home can find the right one.

In enterprises, as well as in apartments and houses in general, it is consumed a large number of water. The numbers are huge, but can they say anything other than the fact of a certain expense? Yes they can. Namely, water flow can help calculate the diameter of the pipe. These are seemingly unrelated parameters, but in fact the relationship is obvious.

After all, the throughput of a water supply system depends on many factors. A significant place in this list is occupied by the diameter of the pipes, as well as the pressure in the system. Let's look into this issue deeper.

Factors influencing the passage of water through a pipe

Water flow through the pipe round section having a hole depends on the size of this hole. Thus, the larger it is, the more water will pass through the pipe in a certain period of time. However, do not forget about pressure. After all, you can give an example. A meter-long column will push water through a centimeter-long hole in much less time per unit of time than a column with a height of several tens of meters. It is obvious. Therefore, water flow will reach its maximum at the maximum internal cross-section of the product, as well as at maximum pressure.

Diameter calculation

If you need to get certain consumption water at the outlet of the water supply system, then you cannot do without calculating the diameter of the pipe. After all, this indicator, along with the others, affects the throughput indicator.

Of course, there are special tables that are available on the Internet and in specialized literature that allow you to bypass the calculations, focusing on certain parameters. However, you should not expect high accuracy from such data; the error will still be present, even if all factors are taken into account. Therefore, the best way to get accurate results is to do your own calculations.

To do this you will need the following data:

• Water consumption consumption.
• Pressure loss from the source point to the point of consumption.

Water consumption does not have to be calculated - there is a digital standard. You can take the data on the mixer, which states that about 0.25 liters are consumed per second. This figure can be used for calculations.

An important parameter for obtaining accurate data is the pressure loss in the area. As is known, the pressure pressure in standard water supply risers ranges from 1 to 0.6 atmospheres. The average is 1.5-3 atm. The parameter depends on the number of floors in the house. But this does not mean that the higher the house, the higher the pressure in the system. In very tall buildings (more than 16 floors), dividing the system into floors is sometimes used to normalize the pressure.

Regarding head loss, this figure can be calculated using pressure gauges at the source point and before the consumption point.

If, however, knowledge and patience are not enough for independent calculations, then you can use tabular data. And even if they have certain errors, the data will be quite accurate for certain conditions. And then it will be very simple and quick to determine the diameter of the pipe based on water flow. This means that the water supply system will be calculated correctly, which will allow you to obtain an amount of liquid that will satisfy your needs.