Determination of water flow by pipe diameter and pressure. Pipe capacity: simple about the complex

In some cases, one has to face the need to calculate the flow of water through a pipe. This indicator indicates how much water the pipe can pass, measured in m³ / s.

• For organizations that have not put the meter on the water, the charge is based on the patency of the pipe. It is important to know how accurately these data are calculated, for what and at what rate you have to pay. Individuals this does not apply, for them, in the absence of a meter, the number of registered people is multiplied by the water consumption of 1 person according to sanitary standards. This is a fairly large volume, and with modern tariffs it is much more profitable to install a meter. In the same way, in our time it is often more profitable to heat the water yourself with a column than to pay utilities for their hot water.
• Calculation of pipe permeability plays a huge role when designing a house, when bringing communications to the house .

It is important to make sure that each branch of the water supply can receive its share from the main pipe, even during peak water consumption hours. Plumbing was created for comfort, convenience, and ease of work for a person.

If every evening water will practically not reach the inhabitants of the upper floors, what kind of comfort can we talk about? How can you drink tea, wash dishes, swim? And everyone drinks tea and bathes, so the volume of water that the pipe could provide was distributed over the lower floors. This problem can play a very bad role in fire fighting. If firefighters connect to the central pipe, and there is no pressure in it.

Sometimes calculating the flow of water through a pipe can come in handy if, after repairing the water supply by unfortunate masters, replacing part of the pipes, the pressure has dropped significantly.

Hydrodynamic calculations are not an easy task, usually carried out by qualified specialists. But, let's say you are engaged in private construction, designing your cozy spacious house.

How to calculate the flow of water through the pipe yourself?

It would seem that it is enough to know the diameter of the pipe hole in order to get, maybe, rounded, but generally fair figures. Alas, this is very little. Other factors can change the result of calculations at times. What affects the maximum flow of water through the pipe?

1. Pipe section. obvious factor. Starting point of hydrodynamic calculations.
2. Pipe pressure. With increasing pressure, a pipe with the same cross section passes through more water.
3. Bends, turns, change in diameter, branching block the flow of water through the pipe. Different variants to varying degrees.
4. Pipe length. Longer pipes will carry less water per unit of time than shorter ones. The whole secret is in the force of friction. Just as it delays the movement of objects familiar to us (cars, bicycles, sleds, etc.), the force of friction impedes the flow of water.
5. A pipe with a smaller diameter has more area of ​​water contact with the pipe surface in relation to the volume of water flow. And from each point of contact there is a force of friction. Just like in longer pipes, in narrower pipes the speed of water movement becomes less.
6. Pipe material. Obviously, the degree of roughness of the material affects the magnitude of the friction force. Modern plastic materials(polypropylene, PVC, metal-plastic, etc.) are very slippery compared to traditional steel and allow water to move faster.
7. Duration of pipe operation. Lime deposits, rust greatly impair the throughput of the water supply. This is the most tricky factor, because the degree of clogging of the pipe, its new internal relief and the coefficient of friction is very difficult to calculate with mathematical accuracy. Fortunately, water flow calculations are most often required for new construction and fresh, unused materials. And on the other hand, this system will be connected to already existing, existing communications for many years. And how will she behave herself in 10, 20, 50 years? Newest technologies greatly improved this situation. plastic pipes do not rust, their surface practically does not deteriorate over time.

Calculation of water flow through a tap

The volume of fluid flowing out is found by multiplying the cross section of the pipe opening S by the outflow velocity V. The cross section is the area of ​​a certain part of the volumetric figure, in this case, the area of ​​a circle. It is found according to the formula S = πR2. R will be the radius of the pipe opening, not to be confused with the radius of the pipe. π is a constant value, the ratio of a circle's circumference to its diameter, approximately 3.14.

The flow rate is found by the Torricelli formula: . Where g is the acceleration free fall, on planet Earth is approximately 9.8 m/s. h is the height of the water column above the hole.

Example

Let us calculate the water flow through a tap with a hole with a diameter of 0.01 m and a column height of 10 m.

Hole cross section \u003d πR2 \u003d 3.14 x 0.012 \u003d 3.14 x 0.0001 \u003d 0.000314 m².

Outflow velocity = √2gh = √2 x 9.8 x 10 = √196 = 14 m/s.

Water consumption \u003d SV \u003d 0.000314 x 14 \u003d 0.004396 m³ / s.

In terms of liters, it turns out that 4.396 liters per second can flow out of a given pipe.

This characteristic depends on several factors. First of all, this is the diameter of the pipe, as well as the type of liquid, and other indicators.

For hydraulic calculation of the pipeline, you can use the pipeline hydraulic calculation calculator.

When calculating any systems based on the circulation of fluid through pipes, it becomes necessary exact definition pipe capacity. This is a metric value that characterizes the amount of fluid flowing through pipes in a certain period of time. This indicator is directly related to the material from which the pipes are made.

If we take, for example, plastic pipes, then they differ in almost the same throughput throughout the entire period of operation. Plastic, unlike metal, is not prone to corrosion, so a gradual increase in deposits is not observed in it.

As for metal pipes, their throughput decreases year after year. Due to the appearance of rust, material detachment occurs inside the pipes. This leads to surface roughness and the formation of even more deposits. This process occurs especially quickly in pipes with hot water.

The following is a table of approximate values ​​\u200b\u200bwhich was created to facilitate the determination of the throughput of pipes for intra-apartment wiring. This table does not take into account the reduction in throughput due to the appearance of sediment buildup inside the pipe.

Pipe capacity table for liquids, gas, steam.

Most often, ordinary water is used as a coolant. The rate of decrease in throughput in pipes depends on its quality. The higher the quality of the coolant, the longer the pipeline made of any material (steel, cast iron, copper or plastic) will last.

Calculation of pipe throughput.

For accurate and professional calculations, you must use the following indicators:

• The material from which pipes and other elements of the system are made;
• Pipeline length
• Number of water consumption points (for water supply system)

The most popular calculation methods:

1. Formula. A rather complicated formula, which is understandable only to professionals, takes into account several values ​​at once. The main parameters that are taken into account are the material of the pipes (surface roughness) and their slope.

2. Table. This is an easier way by which anyone can determine the throughput of the pipeline. An example is the engineering table of F. Shevelev, by which you can find out the throughput based on the pipe material.

3. Computer program. One of these programs can be easily found and downloaded on the Internet. It is designed specifically to determine the throughput for pipes of any circuit. In order to find out the value, it is necessary to enter the initial data into the program, such as material, pipe length, coolant quality, etc.

It should be said that the latter method, although it is the most accurate, is not suitable for calculating simple household systems. It is quite complex and requires knowledge of the values ​​of a variety of indicators. To calculate a simple system in a private house, it is better to use tables.

An example of calculating the throughput of the pipeline.

Pipeline length - important indicator when calculating throughput The length of the backbone has a significant impact on throughput performance. The more distance the water travels, the less pressure it creates in the pipes, which means that the flow rate decreases.

Here are some examples. Based on tables developed by engineers for these purposes.

Bandwidth pipes:

• 0.182 t/h at 15 mm diameter
• 0.65 t/h with pipe diameter 25 mm
• 4 t/h at 50 mm diameter

As can be seen from the examples given, larger diameter increases the flow rate. If the diameter is increased by 2 times, then the throughput will also increase. This dependence must be taken into account when installing any liquid system, whether it be water supply, sewerage or heat supply. This is especially true for heating systems, since in most cases they are closed, and the heat supply in the building depends on the uniform circulation of the liquid.

Water flow parameters:

1. The value of the pipe diameter, which also determines the further throughput.
2. The size of the pipe walls, which will then determine the internal pressure in the system.

The only thing that does not affect consumption is the length of communications.

If the diameter is known, the calculation can be carried out according to the following data:

1. Structural material for pipe construction.
2. Technology affecting the pipeline assembly process.

Characteristics affect the pressure inside the water supply system and determine the flow of water.

If you are looking for an answer to the question of how to determine the flow of water, then you must learn two calculation formulas that determine the parameters of use.

1. The formula for daily calculation is Q=ΣQ×N/100. Where ΣQ is the annual daily water use per 1 inhabitant, and N is the number of inhabitants in the building.
2. The formula for calculating per hour is q=Q×K/24. Where Q is the daily calculation, and K is the ratio according to SNiP, uneven consumption (1.1-1.3).

These simple calculations can help determine the expense, which will show the needs and requirements of this house. There are tables that can be used in calculating the liquid.

Reference data in the calculation of water

When using tables, you should calculate all the taps, bathtubs and water heaters in the house. Table SNiP 2.04.02-84.

Standard consumption rates:

• 60 liters - 1 person.
• 160 liters - for 1 person, if the house has better plumbing.
• 230 liters - for 1 person, in a house where high-quality plumbing and a bathroom are installed.
• 350 liters - for 1 person with running water, built-in appliances, bathroom, toilet.

Why calculate water according to SNiP?

How to determine the flow of water for each day is not the most requested information among ordinary residents of the house, but pipeline installers need this information even less. And for the most part, they need to know what the diameter of the connection is, and what pressure it maintains in the system.

But in order to determine these indicators, you need to know how much water is needed in the pipeline.

The formula to help determine the pipe diameter and fluid flow rate:

The standard liquid velocity in a headless system is 0.7 m/s and 1.9 m/s. And the speed from external source, for example, a boiler, is determined by the source passport. When the diameter is known, the flow rate in communications is determined.

Water head loss calculation

The loss of water flow is calculated taking into account the pressure drop using one formula:

In the formula, L - denotes the length of the connection, and λ - friction loss, ρ - malleability.

The friction index varies from the following values:

• the level of roughness of the coating;
• obstacle in the equipment at the locking points;
• fluid flow rate;
• pipeline length.

Ease of calculation

Knowing pressure loss, fluid velocity in pipes and volume required water how to determine the flow of water and the size of the pipeline becomes much clearer. But in order to get rid of long calculations, you can use a special table.

Where D is the diameter of the pipe, q is the consumption of water, and V is the speed of the water, i is the course. To determine the values, they must be found in the table and connected in a straight line. Also determine the flow rate and diameter, while taking into account the slope and speed. Therefore, the easiest way to calculate is to use tables and graphs.

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Pipe capacity: simple about the complex

How does the throughput of a pipe vary with diameter? What factors, besides the cross section, affect this parameter? Finally, how to calculate, albeit approximately, the permeability of a water supply system with a known diameter? In the article I will try to give the most simple and accessible answers to these questions.

Our task is to learn how to count optimal cross section water pipes.

Why is it needed

Hydraulic calculation allows you to get the optimal minimum the diameter of the pipeline.

On the one hand, money during construction and repair is always sorely lacking, and the price running meter pipes grows non-linearly with increasing diameter. On the other hand, an underestimated section of the water supply will lead to an excessive drop in pressure at the end devices due to its hydraulic resistance.

With a flow rate 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 dramatically. 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 tasks under consideration to the plumbing 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 lead us far away from my specialization - plumbing;
2. In the case of a large building with numerous plumbing fixtures for the hydraulic calculation of the water supply system, it will be necessary to calculate the probability of the simultaneous use of several points of water intake. AT 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 the throughput of a pipe with a known cross section;
• Calculation of the optimal diameter with a known planned flow rate.

In real conditions (when designing a water supply system), the second task is much more often necessary.

Household logic suggests that the maximum flow of water 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 slows down due to friction against the walls. Moreover, the material and condition of the walls predictably affect the degree of braking.

Here is a complete list of factors that affect the performance of a water pipe:

• Pressure at the beginning of the water supply (read - pressure in the route);
• bias 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 the roughness, but also reduce the internal clearance of the pipeline;

This does not apply to glass, plastic, copper, galvanized and metal-polymer pipes. They are in like new condition even after 50 years of operation. The exception is the silting of the water supply when in large numbers suspended solids and the absence of inlet filters.

• Quantity and Angle turns;
• Diameter changes plumbing;
• Presence or absence welds, burr from soldering and connecting fittings;

• Shut-off valves. Even full bore Ball Valves provide some resistance to flow.

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

Law of Torricelli

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

For the Torricelli formula to work, it is necessary:

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

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

1. For the hole to be significantly smaller than the diameter of the vessel, thus eliminating the loss of pressure due to friction against the walls.

In practice, Torricelli's formula allows you to calculate the flow of water through a pipe with an internal section of known dimensions at a known instantaneous head during flow. Simply put: to use the formula, you need to install a pressure gauge in front of the tap or calculate the pressure drop on the water supply 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 orifice, in meters per second;
• g is the acceleration of fall (for our planet it is equal to 9.78 m/s^2);
• h - head (height of the water column above the hole).

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

Captain Evidence suggests: knowing the cross-sectional area, it is easy to determine the inner radius of the pipe. As you know, the area of ​​a circle is calculated as π*r^2, where π is rounded 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 stream flows. Converting the diameter to SI units (meters), we get 3.14159265*0.01^2=0.0003141593. And now we calculate the water flow: 20 * 0.0003141593 \u003d 0.006283186, or 6.2 liters per second.

Back to reality

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

Usually, the calculation problem is solved from the opposite: with known water flow through 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 flow rate for internal water pipes is considered to be 0.7 - 1.5 m / s. Exceeding the latter value leads to the appearance of hydraulic noise (primarily at bends and fittings).

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

The table shows data for mixers with aerators. Their absence equalizes the flow through the sink, washbasin and shower faucets with the flow through the faucet when taking a bath.

Let me remind you that if you want to calculate the water supply of a private house with your own hands, sum up the water consumption for all installed appliances. If this instruction is not followed, surprises will await you, such as a sharp drop in the temperature in the shower when the tap is opened. hot water on .

If there is a fire water supply in the building, 2.5 l / s for each hydrant is added to the planned flow. For fire water supply, the flow velocity is limited to 3 m/s: in case of fire, hydraulic noise is the last thing that will unnerve the residents.

When calculating the pressure, it is usually assumed that on the device extreme from the input it must be at least 5 meters, which corresponds to a pressure of 0.5 kgf / cm2. Part of plumbing fixtures (instantaneous water heaters, filling valves for automatic 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 the hydraulic losses on the device itself.

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

Flow rate, diameter, speed

Let me remind you that they are linked to each other by two formulas:

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

Where can I get the values ​​for the radius of the inner section?

• For steel pipes, it is, with a minimum error, equal to half of the control(conditional pass, which is marked pipe rolling);
• For polymer, metal-polymer, etc. the inner diameter is equal to the difference between the outer one, with which the pipes are marked, and twice the wall thickness (it is also usually present in the marking). The radius, respectively, is half the inner diameter.

1. The inner diameter is 50-3 * 2 = 44 mm, or 0.044 meters;
2. The radius will be 0.044/2=0.022 meters;
3. The area of ​​​​the internal section will be equal to 3.1415 * 0.022 ^ 2 \u003d 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.

head loss

How to calculate how much pressure is lost on a water supply system 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 cherished pressure drop in meters;
• i - hydraulic slope of the water pipe meter;
• L is the length of the water supply in meters;
• K- coefficient, which makes it possible to simplify the calculation of the pressure drop on the stop 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 roulette yet.

The 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 1000i values ​​(hydraulic slope per 1000 meters of water supply) can be found in Shevelev's tables, which, in fact, are used for hydraulic calculation. The tables are too large for an article as they give 1000i values ​​for all possible diameters, flow rates and life corrected materials.

Here is a small fragment of the Shevelev table for a 25 mm plastic pipe.

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

Let's use this table to calculate the pressure drop across 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. With a flow velocity as close as possible to 1.5 m/s (1.38 m/s), the value of 1000i will be equal to 142.8 meters;
2. The hydraulic slope of one meter of pipe will be equal to 142.8 / 1000 \u003d 0.1428 meters;
3. The correction factor for domestic water pipes 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 at 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 the 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 through a water supply system with known characteristics, one can select in the “flow rate” column of the complete Shevelev table such a value at which the pressure at the end of the pipe does not fall below 0.5 atmospheres.

Conclusion

Dear reader, if the above instructions, despite the extreme simplification, still seemed tedious to you, just use one of the many online calculators. As always, more information can be found in the video in this article. I will be grateful for your additions, corrections and comments. Good luck, comrades!

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

Why do we need such calculations

When drawing up a plan for the construction of a large cottage with several bathrooms, a private hotel, the organization of a fire system, it is very important to have more or less accurate information about the transport capabilities of the existing pipe, taking into account its diameter and pressure in the system. It's all about pressure fluctuations during the peak of water consumption: such phenomena seriously affect the quality of the services provided.

In addition, if the water supply system is not equipped with water meters, then when paying for utility services, the so-called. "Permeability of the pipe". In this case, the question of the tariffs applied in this case quite logically emerges.

At the same time, it is important to understand that the second option does not apply to private premises (apartments and cottages), where, in the absence of meters, sanitary standards are taken into account when calculating payment: usually this is up to 360 l / day per person.

What determines the permeability of the pipe

What determines the flow of water in a round pipe? One gets the impression that the search for an answer should not cause difficulties: the larger the cross section of the pipe, the greater the volume of water it can pass in a certain time. At the same time, pressure is also remembered, because the higher the water column, the faster the water will be forced through the communication. However, practice shows that these are far from all the factors affecting water consumption.

In addition to them, the following points also have to be taken into account:

1. Pipe length. With an increase in its length, the water rubs against its walls more strongly, which leads to a slowdown in the flow. Indeed, at the very beginning of the system, water is only affected by pressure, but it is also important how quickly the next portions will have the opportunity to enter the communication. Braking inside the pipe often reaches large values.
2. Water consumption depends on the diameter to a much more complex extent than it seems at first glance. When the size of the pipe diameter is small, the walls resist the water flow by an order of magnitude more than in thicker systems. As a result, as the diameter of the pipe decreases, its benefit in terms of the ratio of the water flow rate to the indicator of the internal area in a section of a fixed length decreases. To put it simply, a thick plumbing system transports water much faster than a thin one.
3. Production material. Another important point, which directly affects the speed of movement of water through the pipe. For example, smooth propylene promotes water sliding to a much greater extent than rough steel walls.
4. Service life. Over time, rust appears on steel water pipes. In addition, for steel, as well as for cast iron, it is typical to gradually accumulate lime deposits. The resistance to water flow of a pipe with deposits is much higher than that of new steel products: this difference sometimes reaches 200 times. In addition, the overgrowth of the pipe leads to a decrease in its diameter: even if we do not take into account the increased friction, its permeability clearly decreases. It is also important to note that products made of plastic and metal-plastic do not have such problems: even after decades of intensive use, the level of their resistance to water flows remains at the original level.
5. The presence of turns, fittings, adapters, valves contributes to additional braking of water flows.

All of the above factors must be taken into account we are talking not about some small errors, but about a serious difference several times over. As a conclusion, it can be said that a simple determination of the pipe diameter from the water flow is hardly possible.

New possibility of water consumption calculations

If the use of water is carried out by means of a tap, this greatly simplifies the task. The main thing in this case is that the dimensions of the hole for the outpouring of water are much smaller than the diameter of the water pipe. In this case, the formula for calculating water over the cross section of the Torricelli pipe v ^ 2 \u003d 2gh is applicable, where v is the speed of flow through small hole, g is the free fall acceleration, and h is the height of the water column above the faucet (a hole with a cross section s passes water volume s * v per unit time). It is important to remember that the term "section" is used not to denote the diameter, but its area. To calculate it, use the formula pi * r ^ 2.

If the column of water has a height of 10 meters and the hole has a diameter of 0.01 m, the water flow through the pipe at a pressure of one atmosphere is calculated as follows: v^2=2*9.78*10=195.6. After taking the square root, v=13.98570698963767. After rounding to get a simpler speed figure, the result is 14m/s. The cross section of the hole, having a diameter of 0.01 m, is calculated as follows: 3.14159265*0.01^2=0.000314159265 m2. As a result, it turns out that the maximum water flow through the pipe corresponds to 0.000314159265 * 14 = 0.00439822971 m3 / s (slightly less than 4.5 liters of water / second). As you can see, in this case, the calculation of water over the cross section of the pipe is quite simple. also in free access there are special tables showing the water consumption for the most popular plumbing products, with a minimum value for the diameter of the water pipe.

As you can already understand, there is no universal simple way to calculate the diameter of the pipeline depending on the water flow. However, you can still deduce certain indicators for yourself. This is especially true in cases where the system is equipped with plastic or metal-plastic pipes, and water is consumed by taps with a small outlet cross section. In some cases, this method of calculation is applicable to steel systems, but we are talking primarily about new water pipes that did not have time to become covered with internal deposits on the walls.

Water flow rate by pipe diameter: determination of the pipeline diameter depending on the flow rate, calculation by section, formula for the maximum flow rate at pressure in a round pipe

Water flow through a pipe: is a simple calculation possible?

Is it possible to calculate the flow of water by the diameter of the pipe in any simple way? Or the only way- contact specialists, having previously depicted detailed map all the water pipes in the area?

After all, hydrodynamic calculations are extremely complex ...

Our task is to find out how much water this pipe can pass.

What is it for?

1. When self-calculation of plumbing systems.

If you plan to build big house with several guest baths, a mini-hotel, think over a fire extinguishing system - it is desirable to know how much water a pipe of a given diameter can supply at a certain pressure.

After all, a significant drop in pressure at the peaks of water consumption is unlikely to please residents. And a weak trickle of water from a fire hose is likely to be useless.

1. In the absence of water meters, utilities usually bill "pipe pass" organizations.

Please note: the second scenario does not affect apartments and private houses. If there are no water meters, utilities charge for water according to sanitary norms. For modern comfortable houses, this is no more than 360 liters per person per day.

It must be admitted: the water meter greatly simplifies relations with utilities

Factors affecting the patency of the pipe

What affects the maximum water flow in a round pipe?

The obvious answer

Common sense dictates that the answer should be very simple. There is a water pipe. There is a hole in it. The larger it is, the more water passes through it per unit of time. Ah, sorry, more pressure.

Obviously, a column of water 10 centimeters will force less water through a centimeter hole than a water column with a height of a ten-story building.

So, from the internal section of the pipe and from the pressure in the water supply, right?

Is there really something else needed?

Correct answer

No. These factors affect consumption, but they are just the beginning of a long list. Calculating the flow of water by the diameter of the pipe and the pressure in it is the same as calculating the trajectory of a rocket flying to the Moon, based on the apparent position of our satellite.

If you do not take into account the rotation of the Earth, the movement of the Moon in its own orbit, atmospheric drag and gravity celestial bodies- hardly our spaceship hit at least approximately desired point space.

How much water will pour out of a pipe with a diameter x at a pressure in the track y is influenced not only by these two factors, but also by:

• Pipe length. The longer it is, the stronger the friction of water against the walls slows down the flow of water in it. Yes, only the pressure in it affects the water at the very end of the pipe, but the following volumes of water should take its place. And the water pipe slows them down, and how.

It is because of the loss of pressure in a long pipe that oil pipelines have pumping stations.

• The diameter of the pipe affects the flow of water is much more complicated than "common sense" suggests. For small diameter pipes, the wall resistance to flow is much greater than for thick pipes.

The reason is that the smaller the pipe, the less favorable the ratio of internal volume and surface area in it from the point of view of the water flow rate at a fixed length.

Simply put, it is easier for water to move through a thick pipe than through a thin one.

• Wall material - one more the most important factor, on which the speed of water movement depends. While water glides over smooth polypropylene like the sirloin of a clumsy lady on a pavement in ice, rough steel creates much more resistance to flow.
• The age of the pipe also greatly affects the permeability of the pipe.. Steel water pipes rust, in addition, steel and cast iron are overgrown with lime deposits over the years of operation.

An overgrown pipe has much more resistance to flow (resistance of a polished new steel pipe and rusty differ by 200 times!). Moreover, the sections inside the pipe, due to overgrowth, reduce their clearance; even in ideal conditions much less water will pass through an overgrown pipe.

Do you think it makes sense to calculate the permeability by the diameter of the pipe at the flange?

Please note: the surface condition of plastic and metal-polymer pipes does not deteriorate over time. After 20 years, the pipe will have the same resistance to water flow as it did at the time of installation.

• Finally, any turn, diameter transition, varied shut-off valves and fittings - all this also slows down the flow of water.

Ah, if the above factors could be neglected! However, we are not talking about deviations within the error, but about a difference at times.

All this leads us to a sad conclusion: a simple calculation of the flow of water through a pipe is impossible.

Beam of light in the dark realm

In the case of water flow through a faucet, however, the task can be greatly simplified. Basic condition simple calculation: the hole through which the water flows must be negligible compared to the diameter of the water supply pipe.

Then Torricelli's law applies: v^2=2gh, where v is the velocity of the outflow from the small hole, g is the free fall acceleration, and h is the height of the water column above the hole. In this case, a volume of liquid s * v will pass through a hole with a cross section s per unit time.

The master left you a gift

Don't forget: the cross section of the hole is not the diameter, it's the area equal to pi*r^2.

For a water column of 10 meters (which corresponds to an overpressure of one atmosphere) and a hole with a diameter of 0.01 meter, the calculation will be as follows:

We extract Square root and we get v=13.98570698963767. For ease of calculation, we will round the value of the flow velocity to 14 m/s.

The cross section of a hole with a diameter of 0.01 m is 3.14159265*0.01^2=0.000314159265 m2.

Thus, the flow of water through our hole will be 0.000314159265 * 14 = 0.00439822971 m3 / s, or a little less than four and a half liters per second.

As you can see, in this variant the calculation is not very complicated.

In addition, in the appendix to the article you will find a table of water consumption by the most common plumbing fixtures, indicating the minimum diameter of the liner.

Conclusion

That's all in a nutshell. As you can see, universal simple solution We have not found; however, we hope the article will be useful to you. Good luck!

How to calculate pipe throughput

Throughput calculation is one of the most challenging tasks when laying a pipeline. In this article, we will try to figure out exactly how this is done for different types pipelines and pipe materials.

High capacity pipes

Throughput is an important parameter for any pipes, canals and other heirs of the Roman aqueduct. However, the throughput is not always indicated on the pipe packaging (or on the product itself). In addition, it also depends on the pipeline scheme how much liquid the pipe passes through the section. How to correctly calculate the throughput of pipelines?

Methods for calculating the throughput of pipelines

There are several methods for calculating this parameter, each of which is suitable for a particular case. Some notations that are important in determining the throughput of a pipe:

Outer diameter - the physical size of the pipe section from one edge of the outer wall to the other. In calculations, it is designated as Dn or Dn. This parameter is indicated in the marking.

Nominal diameter is the approximate value of the diameter of the internal section of the pipe, rounded up to a whole number. In calculations, it is designated as Du or Du.

Physical methods for calculating the throughput of pipes

Pipe throughput values ​​are determined by special formulas. For each type of product - for gas, water supply, sewerage - the methods of calculation are different.

Tabular calculation methods

There is a table of approximate values ​​\u200b\u200bcreated to facilitate the determination of the throughput of pipes for intra-apartment wiring. In most cases, high precision is not required, so the values ​​can be applied without complex calculations. But this table does not take into account the decrease in throughput due to the appearance of sedimentary growths inside the pipe, which is typical for old highways.

There is an exact capacity calculation table, called the Shevelev table, which takes into account the pipe material and many other factors. These tables are rarely used when laying water pipes around the apartment, but in a private house with several non-standard risers they can come in handy.

Calculation using programs

At the disposal of modern plumbing companies there are special computer programs for calculating the throughput of pipes, as well as many other similar parameters. In addition, online calculators have been developed that, although less accurate, are free and do not require installation on a PC. One of the stationary programs "TAScope" is a creation of Western engineers, which is shareware. AT large companies use "Hydrosystem" - this is a domestic program that calculates pipes according to criteria that affect their operation in the regions of the Russian Federation. In addition to hydraulic calculation, it allows you to calculate other parameters of pipelines. average price 150,000 rubles.

How to calculate the throughput of a gas pipe

Gas is one of the most complex materials for transportation, in particular because it tends to shrink and therefore is able to flow through the smallest gaps in pipes. To the calculation of throughput gas pipes(similar to design gas system in general) have special requirements.

The formula for calculating the throughput of a gas pipe

The maximum capacity of gas pipelines is determined by the formula:

Qmax = 0.67 DN2 * p

where p is equal to the working pressure in the gas pipeline system + 0.10 MPa or the absolute pressure of the gas;

Do - conditional pass pipes.

There is a complex formula for calculating the throughput of a gas pipe. When carrying out preliminary calculations, as well as when calculating a domestic gas pipeline, it is usually not used.

Qmax = 196.386 Du2 * p/z*T

where z is the compressibility factor;

T is the temperature of the transported gas, K;

According to this formula, the direct dependence of the temperature of the transported medium on pressure is determined. The higher the T value, the more the gas expands and presses against the walls. Therefore, when calculating large highways, engineers take into account possible weather conditions in the area where the pipeline passes. If the nominal value of the pipe DN is less than the pressure of the gas formed during high temperatures in summer (for example, at +38 ... +45 degrees Celsius), then damage to the line is likely. This entails the leakage of valuable raw materials, and creates the possibility of an explosion of the pipe section.

Table of capacities of gas pipes depending on pressure

There is a table for calculating the throughput of a gas pipeline for commonly used diameters and nominal working pressure of pipes. To determine the characteristics of the gas pipeline custom sizes and pressure will require engineering calculations. Also, the pressure, speed of movement and volume of gas is affected by the temperature of the outside air.

The maximum velocity (W) of the gas in the table is 25 m/s and z (compressibility factor) is 1. The temperature (T) is 20 degrees Celsius or 293 Kelvin.

Capacity of the sewer pipe

Bandwidth sewer pipe- an important parameter that depends on the type of pipeline (pressure or non-pressure). The calculation formula is based on the laws of hydraulics. In addition to the laborious calculation, tables are used to determine the capacity of the sewer.

Hydraulic Calculation Formula

For the hydraulic calculation of sewerage, it is required to determine the unknowns:

1. pipeline diameter Du;
2. average flow velocity v;
3. hydraulic slope l;
4. degree of filling h / Du (in calculations, they are repelled from the hydraulic radius, which is associated with this value).

In practice, they are limited to calculating the value of l or h / d, since the remaining parameters are easy to calculate. hydraulic slope in preliminary calculations considered to be equal to the slope of the earth's surface, at which the movement Wastewater will not be lower than the self-cleaning speed. The speed values ​​as well as the maximum h/Dn values ​​for domestic networks can be found in Table 3.

In addition, there is a normalized value minimum slope for pipes with small diameter: 150 mm

(i=0.008) and 200 (i=0.007) mm.

The formula for the volumetric flow rate of a liquid looks like this:

where a is the free area of ​​the flow,

v is the flow velocity, m/s.

The speed is calculated by the formula:

where R is the hydraulic radius;

C is the wetting coefficient;

From this we can derive the formula for the hydraulic slope:

According to it, this parameter is determined if calculation is necessary.

where n is the roughness factor, ranging from 0.012 to 0.015 depending on the pipe material.

The hydraulic radius is considered equal to the usual radius, but only when the pipe is completely filled. In other cases, use the formula:

where A is the area of ​​the transverse fluid flow,

P - wetted perimeter, or transverse length inner surface pipe that touches the liquid.

Bandwidth tables without pressure pipes sewers

The table takes into account all the parameters used to perform the hydraulic calculation. The data is selected according to the value of the pipe diameter and substituted into the formula. Here, the volumetric flow rate q of the liquid passing through the pipe section has already been calculated, which can be taken as the throughput of the pipeline.

In addition, there are more detailed Lukin tables containing ready-made pipe throughput values different diameter from 50 to 2000 mm.

Capacity tables for pressurized sewer systems

In the capacity tables for sewer pressure pipes, the values ​​depend on the maximum degree of filling and the estimated average flow rate of the waste water.

Capacity of the water pipe

Water pipes in the house are used most often. And since they are under a heavy load, then the calculation of the throughput of the water main becomes important condition reliable operation.

Passability of the pipe depending on the diameter

Diameter is not the most important parameter when calculating pipe patency, but it also affects its value. The larger the inner diameter of the pipe, the higher the permeability, as well as the lower the chance of blockages and plugs. However, in addition to the diameter, it is necessary to take into account the coefficient of friction of water on the pipe walls (table value for each material), the length of the line and the difference in fluid pressure at the inlet and outlet. In addition, the number of bends and fittings in the pipeline will greatly affect the patency.

Table of pipe capacity by coolant temperature

The higher the temperature in the pipe, the lower its capacity, as the water expands and thus creates additional friction. For plumbing, this is not important, but in heating systems is the key parameter.

There is a table for calculations of heat and coolant.

Pipe capacity table depending on the coolant pressure

There is a table describing the throughput of pipes depending on the pressure.

Pipe capacity table depending on diameter (according to Shevelev)

The tables of F.A. and A.F. Shevelev are one of the most accurate tabular methods for calculating the throughput of a water supply system. In addition, they contain all the necessary calculation formulas for each specific material. This is a voluminous informative material used by hydraulic engineers most often.

The tables take into account:

1. pipe diameters - internal and external;
2. wall thickness;
3. service life of the pipeline;
4. line length;
5. pipe assignment.

Pipe capacity depending on diameter, pressure: tables, calculation formulas, online calculator