Dependence of the pipe diameter on the water flow rate. How to calculate water flow by pipe diameter - theory and practice. Methods for calculating the throughput of the pipeline

The calculation of water consumption is carried out before the construction of pipelines and is an integral part of the hydrodynamic calculations. During the construction of main and industrial pipelines, these calculations are performed using special programs. When building a domestic pipeline with your own hands, you can do the calculation yourself, but it should be borne in mind that the result obtained will not be as accurate as possible. How to calculate the water consumption parameter, read on.

Factors affecting throughput

The main factor by which the calculation of the pipeline system is made is the throughput. This indicator is influenced by many different parameters, the most significant of which are:

pressure in the existing pipeline (in the main network, if the pipeline under construction will be connected to an external source). The calculation method taking into account pressure is more complex, but also more accurate, since it is the pressure that depends on such an indicator as the throughput, that is, the ability to pass a certain amount of water in a certain unit of time;
total pipeline length. The larger this parameter, the more losses are manifested during its use and, accordingly, to avoid a pressure drop, it is required to use pipes of a larger diameter. Therefore, this factor is also taken into account by specialists;
the material from which the pipes are made. If metal pipes are used for a structure or another pipeline, then the uneven inner surface and the possibility of gradual clogging by sediments contained in the water will lead to a decrease in throughput and, accordingly, a small increase in diameter. When using plastic pipes (PVC), polypropylene pipes, and so, the possibility of clogging with deposits is practically excluded. Moreover, the inner surface of the plastic pipes is smoother;

section of pipes. According to the inner section of the pipe, you can independently make a preliminary calculation.

There are other factors that are taken into account by specialists. But for this article, they are not essential.

Method for calculating the diameter depending on the cross-section of the pipes

If, when calculating the pipeline, it is necessary to take into account all of the above factors, it is recommended to make calculations using special programs. If preliminary calculations are sufficient for the construction of the system, then they are carried out in the following sequence:

preliminary determination of the amount of water consumption by all family members;
calculation of the optimal size of the diameter.

How to calculate water consumption in a house

You can independently determine the amount of cold or hot water consumed in the house by several methods:

according to the meter readings. If meters are installed when the pipeline is introduced into the house, then it is not a problem to determine the water consumption per day per person. Moreover, when observing for several days, you can get fairly accurate parameters;

according to established standards determined by specialists. The rate of water consumption per person is set for certain types of premises with the presence / absence of certain conditions;

according to the formula.

To determine the total amount of pumped water in the room, it is necessary to calculate for each plumbing unit (bath, shower, mixer, and so on) separately. Calculation formula:

Qs = 5 x q0 x Р, where

Qs is an indicator that determines the flow rate;

q0 is the established rate;

P is a coefficient that takes into account the possibility of using several types of plumbing fixtures at the same time.

The q0 index is determined depending on the type of plumbing equipment according to the following table:

The probability P is determined by the following formula:

P = L x N1 / q0 x 3600 x N2, where

L - peak water consumption for 1 hour;

N1 is the number of people using plumbing fixtures;

q0 - established standards for a separate sanitary unit;

N2 is the number of installed plumbing fixtures.

It is unacceptable to determine the water consumption without taking into account the probability, since the simultaneous use of plumbing fixtures leads to an increase in the flow rate.

Let's calculate water using a specific example. It is necessary to determine the water consumption according to the following parameters:

the house is home to 5 people;
6 units of plumbing equipment were installed: a bath, a toilet, a sink in the kitchen, a washing machine and a dishwasher installed in the kitchen, a shower cabin;
peak water consumption for 1 hour in accordance with SNiP is set equal to 5.6 l / s.

Determine the size of the probability:

P = 5.6 x 4 / 0.25 x 3600 x 6 = 0.00415

We determine the consumption of oxen for the bath, kitchen and toilet room:

Qs (baths) = 4 x 0.25 x 0.00518 = 0.00415 (l / s)

Qs (kitchens) = 4 x 0.12 x 0.00518 = 0.002 (l / s)

Qs (toilet) = 4 x 0.4 x 0.00518 = 0.00664 (l / s)

Optimal cross-section calculation

To determine the cross section, the following formula is used:

Q = (πd² / 4) xW, where

Q is the calculated amount of consumed water;

d is the required diameter;

W is the speed of water movement in the system.

By the simplest mathematical operations, one can deduce that

d = √ (4Q / πW)

The W indicator can be obtained from the table:

The figures presented in the table are used for approximate calculations. To obtain more accurate parameters, a complex mathematical formula is used.

Let's determine the diameter of pipes for a bath, kitchen and toilet according to the parameters presented in this example:

d (bathroom) = √ (4 x 0.00415 / (3.14 x 3)) = 0.042 (m)

d (for kitchen) = √ (4 x 0.002 / (3.14 x 3)) = 0.03 (m)

d (for toilet) = √ (4 x 0.00664 / (3.14 x 3)) = 0.053 (m)

To determine the cross-section of the pipes, the largest calculated indicator is taken. Taking into account the small margin in this example, it is possible to carry out the wiring of the water supply with pipes with a cross section of 55 mm.

How to calculate using a special semi-professional program, see the video.

Large amounts of water are consumed in enterprises, as well as in apartments and houses. The numbers are huge, but can they say anything more than the fact of a certain expense? Yes they can. Namely, the water flow rate can help to calculate the pipe diameter. These are seemingly unrelated parameters, but in fact the relationship is obvious.

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

Factors affecting the permeability of water through the pipe

The flow rate of water through a circular pipe with 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, don't forget about pressure. An example can be given. A meter pillar will push water through a centimeter hole much less per unit of time than a pillar with a height of several tens of meters. It is obvious. Therefore, the water consumption will reach its maximum at the maximum internal section of the product, as well as at the maximum pressure.

Diameter calculation

If you need to get a certain flow rate of 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, has an impact on the throughput indicator.

Of course, there are special tables that are on the Web and in specialized literature that allow you to bypass the calculations, focusing on certain parameters. However, one 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 calculate it yourself.

To do this, you need the following data:

Consumption of water consumption.
Head loss from the starting point to the point of consumption.

It is not necessary to calculate the consumption of water consumption - there is a digital standard. You can take the data on the mixer, which says 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 head loss at the site. As you know, the head pressure in standard water supply risers is in the range from 1 to 0.6 atmospheres. The average indicator 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 stories high), floor dividing is sometimes used to normalize the pressure.

With regard to the head loss, this figure can be calculated using pressure gauges at the starting point and before the consumption point.

If, nevertheless, knowledge and patience for self-calculation is not enough, then you can use tabular data. And although they have certain errors, the data will be accurate enough for certain conditions. And then, according to the water flow rate, it will be very simple and quick to obtain the diameter of the pipe. This means that the water supply system will be calculated correctly, which will allow you to get such an amount of liquid that will satisfy your needs.

Why do we need such calculations

When drawing up a plan for the construction of a large cottage with several bathrooms, a private hotel, organization of a fire system, it is very important to have more or less accurate information about the transporting 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 quite 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. "Passability of the pipe". In this case, the question of the tariffs applied in this case is quite logical.

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

What determines the permeability of the pipe

What determines the flow rate of water in a circular 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 will be able to pass in a certain time. And a simple formula for the volume of a pipe will allow you to find out this value. At the same time, the 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 must also be taken into account:

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, the water is affected exclusively 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 high values.
Water consumption depends on the diameter to a much more complex degree than it seems at first glance. When the pipe diameter is small, the walls resist water flow by an order of magnitude more than in thicker systems. As a result, as the diameter of the pipe decreases, its advantage in terms of the ratio of the flow rate to the internal area index in the fixed length section decreases. To put it simply, a thick water pipe transports water much faster than a thin one.
Manufacturing material... Another important point that directly affects the speed of water movement through the pipe. For example, smooth propylene is much more conducive to water sliding than rough steel walls.
Duration of service... Over time, rust appears on steel pipes. In addition, it is typical for steel, as well as for cast iron, to gradually accumulate lime deposits. The resistance to water flow of pipes with deposits is much higher than that of new steel products: this difference sometimes reaches 200 times. In addition, overgrowing 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 plastic and metal-plastic products do not have such problems: even after decades of intensive use, the level of their resistance to water flows remains at the original level.
The presence of turns, fittings, adapters, valves contributes to additional inhibition of water flows.

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

New ability to calculate water consumption

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 outflow hole are much smaller than the diameter of the water supply. In this case, the formula for calculating water over the cross section of the Torricelli pipe v ^ 2 = 2gh is applicable, where v is the speed of flow through a small hole, g is the acceleration of gravity, and h is the height of the water column above the tap (a hole with a cross section s, per unit time passes the water volume s * v). 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 water column is 10 meters high and the hole is 0.01 m in diameter, 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 extracting the square root, v = 13.98570698963767 comes out. After rounding off to get a simpler speed reading, the result is 14m / s. The cross-section of a 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 to carry out. Also in the public domain there are special tables indicating water consumption for the most popular sanitary ware, with a minimum value of 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 rate. However, you can still derive certain indicators for yourself. This is especially true if the system is equipped with plastic or metal-plastic pipes, and water is consumed by taps with a small outlet section. In some cases, this method of calculation is applicable to steel systems, but we are talking primarily about new water pipelines, which did not have time to be covered with internal deposits on the walls.

In some cases, you have to deal with the need to calculate the water flow through the pipe. This indicator indicates how much water the pipe can pass, measured in m³ / s.

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

It is important to make sure that each branch of the water supply system will be able to receive its share of the main pipe even during peak flow times. The water supply system is designed for comfort, convenience, and ease of labor for a person.

If every evening the residents of the upper floors will practically not reach the water, what kind of comfort can we talk about? How can you drink tea, wash dishes, swim? And everyone drinks tea and bathes, so the amount of water that the pipe could provide was distributed over the lower floors. This problem can play a very bad role in firefighting. If the 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 system by would-be masters, replacing part of the pipes, the pressure has dropped significantly.

Hydrodynamic calculations are not easy and are usually performed by qualified professionals. But let's say you are engaged in private construction, designing your cozy spacious house.

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

Pipe section... An obvious factor. The starting point for fluid dynamics calculations.
Pipe pressure... With increasing pressure, more water passes through a pipe with the same cross section.
Bends, turns, diameters, bifurcations inhibit the movement of water through the pipe. Different options to varying degrees.
Pipe length... Longer pipes will carry less water per unit of time than shorter ones. The secret is friction. Just as it delays the movement of objects familiar to us (cars, bicycles, sledges, etc.), the frictional force impedes the flow of water.
A pipe with a smaller diameter turns out to have more area of contact of water with the surface of the pipe in relation to the volume of water flow. And from each point of contact, a friction force appears. As in longer pipes, in narrower pipes the speed of water movement becomes slower.
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.
Duration of pipe operation... Lime deposits, rust greatly impair the flow capacity of the water supply system. This is the most tricky factor, because the degree of pipe clogging, its new internal relief and the coefficient of friction are very difficult to calculate with mathematical precision. Fortunately, water flow calculations are most often required for new construction and fresh, unused materials. On the other hand, this system will be connected to the existing communications that have been existing for many years. And how will she behave herself in 10, 20, 50 years? The latest technology has greatly improved this situation. Plastic pipes do not rust, their surface practically does not deteriorate over time.

Calculation of water flow through the tap

The volume of the outflowing liquid is found by multiplying the section of the pipe opening S by the outflow velocity V. The section is the area of a certain part of the volumetric figure, in this case, the area of a circle. Found by the formula S = πR2... R will be the radius of the pipe hole, not to be confused with the radius of the pipe. π is a constant, the ratio of the circumference of a circle to its diameter, approximately 3.14.

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

Example

Let's calculate the water flow through a faucet with an opening with a diameter of 0.01 m and a column height of 10 m.

Hole section = πR2 = 3.14 x 0.012 = 3.14 x 0.0001 = 0.000314 m2.

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

Water flow = SV = 0.000314 x 14 = 0.004396 m³ / s.

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

In order to properly mount the water supply structure, starting the development and planning of the system, it is necessary to calculate the water flow through the pipe.

The main parameters of the domestic water supply depend on the data obtained.

In this article, readers will be able to get acquainted with the basic techniques that will help them independently calculate their plumbing system.

The purpose of calculating the diameter of the pipeline by the flow rate: Determination of the diameter and cross-section of the pipeline based on the data on the flow rate and the rate of longitudinal movement of water.

It is quite difficult to perform such a calculation. There are a lot of technical and economic data points to consider. These parameters are interrelated. The diameter of the pipeline depends on the type of liquid that will be pumped through it.

If you increase the flow rate, you can reduce the pipe diameter. Material consumption will automatically decrease. It will be much easier to mount such a system, and the cost of work will drop.

However, an increase in flow will cause head losses that require additional energy to be pumped. If you reduce it very much, undesirable consequences may appear.

When designing a pipeline, in most cases, the amount of water flow is immediately set. Two quantities remain unknown:

Pipe diameter;
Flow rate.

It is very difficult to make a completely technical and economic calculation. This requires appropriate engineering knowledge and a lot of time. To facilitate this task, when calculating the required pipe diameter, reference materials are used. They give the values of the best flow rate obtained empirically.

The final design formula for the optimal pipeline diameter is as follows:

d = √ (4Q / Πw)
Q - flow rate of the pumped-over liquid, m3 / s
d - pipeline diameter, m
w - flow speed, m / s

Suitable fluid velocity, depending on the type of pipeline

First of all, the minimum costs are taken into account, without which it is impossible to pump liquid. In addition, the cost of the pipeline must be considered.

When calculating, one should always remember about the speed limits of the moving medium. In some cases, the size of the main pipeline must meet the requirements laid down in the technological process.

Possible pressure surges also affect the dimensions of the pipeline.

When preliminary calculations are made, the change in pressure is not taken into account. The design of the process pipeline is based on the permissible speed.

When there are changes in the direction of movement in the designed pipeline, the surface of the pipe begins to experience a lot of pressure directed perpendicular to the flow.

This increase is associated with several indicators:

Fluid speed;
Density;
Initial pressure (head).

Moreover, the speed is always in inverse proportion to the pipe diameter. That is why high-speed fluids require the correct choice of configuration, competent selection of pipeline dimensions.

For example, if sulfuric acid is being pumped, the speed is limited to a value that will not cause erosion on the walls of the pipe bends. As a result, the structure of the pipe will never be disturbed.

Water velocity in the pipeline formula

The volumetric flow rate V (60m³ / h or 60 / 3600m³ / s) is calculated as the product of the flow velocity w and the cross section of the pipe S (and the cross section, in turn, is considered as S = 3.14 d² / 4): V = 3.14 w d² / 4. From this we obtain w = 4V / (3.14 d²). Do not forget to convert the diameter from millimeters to meters, that is, the diameter will be 0.159 m.

Water consumption formula

In general, the methodology for measuring water flow in rivers and pipelines is based on a simplified form of the equation of continuity for incompressible fluids:

Water flow through the pipe table

Flow versus pressure

There is no such dependence of the liquid flow rate on pressure, but there is - on the pressure drop. The formula is easy to deduce. There is a generally accepted equation for the pressure drop during fluid flow in a pipe Δp = (λL / d) ρw² / 2, λ is the friction coefficient (it is searched depending on the speed and diameter of the pipe according to graphs or corresponding formulas), L is the length of the pipe, d is its diameter , ρ is the density of the liquid, w is the velocity. On the other hand, there is a definition of the flow rate G = ρwπd² / 4. We express the speed from this formula, substitute it into the first equation and find the flow rate dependence G = π SQRT (Δp d ^ 5 / λ / L) / 4, SQRT is the square root.

The coefficient of friction is sought by selection. First, set a certain value of the fluid velocity from the flashlight and determine the Reynolds number Re = ρwd / μ, where μ is the dynamic viscosity of the fluid (do not confuse it with kinematic viscosity, these are different things). According to Reynolds, you are looking for the values of the friction coefficient λ = 64 / Re for the laminar regime and λ = 1 / (1.82 lgRe - 1.64) ² for the turbulent one (here lg is the decimal logarithm). And take the value that is higher. After finding the fluid flow rate and speed, it will be necessary to repeat the entire calculation again with a new coefficient of friction. And this recalculation is repeated until the value of the speed specified for determining the coefficient of friction coincides, to some extent, with the value that you will find from the calculation.