Pipeline throughput. How to calculate the flow rate of water through a pipe by pressure and diameter How much water does the pipe pass per hour
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Pipeline capacity: simple about the complex
How does the throughput of a pipe change depending on the diameter? What factors, besides the cross-section, affect this parameter? Finally, how to calculate, even approximately, the permeability of a water supply system for a known diameter? In this article I will try to give the simplest and most accessible answers to these questions.
Our task is to learn how to calculate the optimal cross-section of water pipes.
Why is it needed
Hydraulic calculation allows you to get the optimal minimal the value of the diameter of the water supply.
On the one hand, money for construction and repair is always sorely lacking, and the price of a running meter of pipes grows non-linearly with increasing diameter. On the other hand, an underestimated cross-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, a drop in pressure at the end device will lead to the fact that the water temperature with open cold water and hot water supply taps will change dramatically. As a result, you will either be doused ice water, or scald with boiling water.
Restrictions
I deliberately limit the scope of the tasks under consideration to the plumbing of a small private house. There are two reasons:
- Gases and liquids of different viscosities behave completely differently during pipeline transportation. Consideration of the behavior of natural and liquefied gas, oil and other environments would increase the volume of this material several times and would take us far from my specialty - plumbing;
- 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 likelihood of the simultaneous use of several draw-off points. V small house the calculation is performed for the peak consumption of all available devices, which greatly simplifies the task.
Factors
Hydraulic calculation of a water supply system is a search for one of two values:
- Calculation of the throughput of a pipe at a known cross-section;
- Calculation of the optimal diameter for a known planned flow rate.
In real conditions (when designing a water supply system), it is much more often necessary 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 decelerated by friction against the walls. Moreover, the material and condition of the walls predictably affect the degree of inhibition.
Here full list factors affecting the performance of the water pipe:
- Pressure at the beginning of the water supply system (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 a much lower roughness than steel and cast iron;
- Age pipes. Over time, the 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 still in a new state after 50 years of operation. An exception is the silting up of the water supply system when a large number suspensions and the absence of filters at the inlet.
- Quantity and angle turns;
- Diameter changes water supply;
- Presence or absence welds, burrs from soldering and connecting fittings;
- Shut-off valves... Even full bore Ball Valves provide a certain resistance to flow movement.
Any calculation of the throughput of the pipeline will be very approximate. Willy-nilly, we will have to use averaged 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 an opening of known dimensions.
For the Torricelli formula to work, you must:
- So that we know the water pressure (the height of the water column above the hole);
One atmosphere with earth's gravity is capable of raising a water column by 10 meters. Therefore, pressure in atmospheres is converted to head by simply multiplying by 10.
- To make the hole significantly less than the diameter of the vessel, thus eliminating the loss of pressure due to friction against the walls.
In practice, the Torrricelli formula calculates the flow rate of water through a pipe with an internal section of known dimensions for 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 across 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 rate at the outlet from the hole in meters per second;
- g - acceleration of the 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 in our task? And the fact that fluid flow through a hole(the same bandwidth) is S * v where S is the orifice area and v is the flow rate from the above formula.
Captain Evidence suggests: knowing the cross-sectional area, it is not difficult 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 roughly taken equal to 3.14159265.
In this case, the Torricelli formula will have the form 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 into SI units (meters), we get 3.14159265 * 0.01 ^ 2 = 0.0003141593. And now we calculate the water consumption: 20 * 0.0003141593 = 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. Obviously, for a more accurate hydraulic calculation, some additional data is needed.
Usually, the design problem is solved from the opposite: with known water flow through plumbing fixtures, the length of the water supply system and its material, a diameter is selected that ensures a drop in pressure to acceptable values. The limiting factor is the flow rate.
Reference data
The normal flow rate for internal water pipelines is 0.7 - 1.5 m / s. Exceeding the latter value leads to the appearance of hydraulic noise (primarily on bends and fittings).
Water consumption rates for plumbing fixtures are easy to find in the regulatory documentation. In particular, they are brought by the appendix to SNiP 2.04.01-85. To save the reader from lengthy searches, I will present 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 cabin with the flow through the mixer when the bath is set.
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 this instruction is not followed, surprises will await you, such as a sharp drop in the temperature in the shower when you turn on the tap. hot water on the .
If there is a fire water supply in the building, 2.5 l / s for each hydrant is added to the planned flow. For a fire water supply system, the flow rate is limited to a value of 3 m / s: in case of fire, hydraulic noise is the last thing that will irritate residents.
When calculating the pressure, it is usually assumed that on the device extreme from the inlet, it must be at least 5 meters, which corresponds to a pressure of 0.5 kgf / cm2. Some plumbing fixtures (instantaneous water heaters, filling valves of automatic washing machines etc.) simply do not work if the pressure in the water supply is below 0.3 atmospheres. In addition, the hydraulic losses on the device itself have to be taken into account.
On the picture - instantaneous water heater Atmor Basic. It includes heating only at a pressure of 0.3 kgf / cm2 and higher.
Consumption, diameter, speed
Let me remind you that they are linked by two formulas:
- Q = SV... The flow rate of water in cubic meters per second is equal to the cross-sectional area in square meters multiplied by the flow rate in meters per second;
- 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 values of the radius of the inner section?
- Have steel pipes with a minimum error it is equal to half of the remote control(conditional passage, which marks the rolled pipe);
- For polymer, metal-polymer, etc. the inner diameter is equal to the difference between the outer, which the pipes are marked with, and twice the wall thickness (it is also usually present in the marking). The radius is correspondingly half the inner diameter.
- The inner diameter is 50-3 * 2 = 44 mm, or 0.044 meters;
- The radius will be 0.044 / 2 = 0.022 meters;
- The internal section area will be 3.1415 * 0.022 ^ 2 = 0.001520486 m2;
- 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 head
How to calculate how much pressure is lost on a water supply system with known parameters?
The simplest formula for calculating the head drop is H = iL (1 + K). What do the variables in it mean?
- H is the coveted head drop in meters;
- i - hydraulic slope of the water supply meter;
- L is the length of the water supply system in meters;
- K - coefficient, which makes it possible to simplify the calculation of the pressure drop on the 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, nobody has canceled the tape measure yet.
The coefficient K is taken equal to:
With a hydraulic bias, the picture is much more complicated. The pipe resistance to flow depends on:
- Internal section;
- Roughness of the walls;
- Flow rates.
A list of 1000i values (hydraulic slope per 1000 meters of water supply) can be found in Shevelev tables, which, in fact, are used for hydraulic calculations. The tables are too large for this article as they provide 1000i values for all possible diameters, flow rates and materials, adjusted for life.
Here is a small fragment of Shevelev's 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, corrected for wall thickness. However, the tables were published in 1973, when the corresponding market segment was 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 head drop by 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.
- With a flow velocity as close as possible to 1.5 m / s (1.38 m / s), the 1000i value will be 142.8 meters;
- The hydraulic slope of one meter of the pipe will be equal to 142.8 / 1000 = 0.1428 meters;
- The correction factor for domestic water supply is 0.3;
- 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 (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 flow rate 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 rate through a water supply system with known characteristics, you 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 atmosphere.
Conclusion
Dear reader, if the instructions given, despite the extreme simplicity, still seemed tiresome to you, just use one of the many online calculators... As always, more information can be found in the video in this article. I would be grateful for your additions, corrections and comments. Good luck, comrades!
July 31, 2016If you want to express gratitude, add clarification or objection, ask the author something - add a comment or say thank you!
When laying water mains, the most difficult thing is to calculate the throughput of pipe sections. Correct calculations will ensure that the water flow rate is not too large and its pressure does not decrease.
The importance of correct calculations
Calculation of water consumption allows you to choose the right material and pipe diameter
When designing a cottage with two or more bathrooms or a small hotel, it is necessary to take into account how much water the pipes of the selected section can supply. After all, if the pressure in the pipeline drops with a large consumption, this will lead to the fact that it will be impossible to take a shower or a bath normally. If a problem arises in a fire, you may even lose your home. Therefore, the calculation of the cross-country ability of highways is carried out even before the start of construction.
For small business owners, it is also important to know the throughput rates. Indeed, in the absence of metering devices, utilities, as a rule, present an invoice for water consumption to organizations according to the volume passed by the pipe. Knowing the data on your water supply will allow you to control water consumption and not pay extra.
What determines the permeability of the pipe
Water consumption will depend on the configuration of the water supply system, as well as the type of pipes from which the network is mounted
The permeability of pipe sections is a metric value that characterizes the volume of liquid passed through the pipeline for a certain time interval. This figure depends on the material used in the manufacture of pipes.
Plastic pipelines maintain almost the same permeability throughout the entire operating period. Plastic, in comparison with metal, does not rust, thanks to this, the lines do not become clogged for a long time.
For metal models, the throughput decreases year after year. Due to the fact that the pipes rust, the inner surface gradually flakes off and becomes rough. Because of this, much more plaque forms on the walls. In particular, hot water pipes clog up quickly.
In addition to the material of manufacture, the permeability also depends on other characteristics:
- The length of the water supply. The greater the length, the lower the flow rate due to the effect of the friction force, and the pressure also decreases accordingly.
- Pipe diameter. The walls of narrow lines create more resistance. The smaller the cross-section, the worse the ratio of the flow rate to the value of the internal area in a section of a fixed length will be. In wider pipelines, water moves faster.
- The presence of bends, fittings, adapters, taps. Any fittings slow down the movement of water flows.
When determining the indicator of throughput, it is necessary to take into account all these factors in combination. In order not to get confused by the numbers, it is worth using proven formulas and tables.
Calculation methods
The coefficient of friction is influenced by the presence of locking elements and their number
To determine the permeability of the water supply system, you can use three calculation methods:
The last method, although the most accurate, is not suitable for calculating ordinary household communications. It is quite complex, and for its application you will need to know a variety of indicators. To calculate a simple network for a private house, you should resort to using an online calculator. Although not as accurate, it is free and does not need to be installed on a computer. You can get more accurate information by comparing the data calculated by the program with the table.
How to calculate bandwidth
The tabular method is the simplest. Several tables of counting have been developed: you can choose the one that is suitable depending on the known parameters.
Calculation based on pipe section
In SNiP 2.04.01-85, it is proposed to find out the amount of water consumption by the pipe circumference.
In accordance with the SNiP standards, the daily water consumption by one person is no more than 60 liters. This data is for a house without running water. If a water supply network is installed, the volume increases to 200 liters.
Calculation based on the temperature of the coolant
As the temperature rises, the permeability of the pipe decreases - the water expands and thereby creates additional friction.
You can calculate the required data using a special table:
| Pipe section (mm) | Bandwidth | |||
| By heat (hl / h) | By heat carrier (t / h) | |||
| Water | Steam | Water | Steam | |
| 15 | 0,011 | 0,005 | 0,182 | 0,009 |
| 25 | 0,039 | 0,018 | 0,650 | 0,033 |
| 38 | 0,11 | 0,05 | 1,82 | 0,091 |
| 50 | 0,24 | 0,11 | 4,00 | 0,20 |
| 75 | 0,72 | 0,33 | 12,0 | 0,60 |
| 100 | 1,51 | 0,69 | 25,0 | 1,25 |
| 125 | 2,70 | 1,24 | 45,0 | 2,25 |
| 150 | 4,36 | 2,00 | 72,8 | 3,64 |
| 200 | 9,23 | 4,24 | 154 | 7,70 |
| 250 | 16,6 | 7,60 | 276 | 13,8 |
| 300 | 26,6 | 12,2 | 444 | 22,2 |
| 350 | 40,3 | 18,5 | 672 | 33,6 |
| 400 | 56,5 | 26,0 | 940 | 47,0 |
| 450 | 68,3 | 36,0 | 1310 | 65,5 |
| 500 | 103 | 47,4 | 1730 | 86,5 |
| 600 | 167 | 76,5 | 2780 | 139 |
| 700 | 250 | 115 | 4160 | 208 |
| 800 | 354 | 162 | 5900 | 295 |
| 900 | 633 | 291 | 10500 | 525 |
| 1000 | 1020 | 470 | 17100 | 855 |
To summarize plumbing system this information is not extremely important, but for heating circuits it is considered the main indicator.
Searching data depending on pressure
The water flow pressure of the common line is taken into account when selecting pipes
When selecting pipes for the installation of any communication network, it is necessary to take into account the flow pressure in the common line. If there is a head under high pressure, it is necessary to install pipes with a larger cross-section than when moving by gravity. If, when selecting pipe sections, these parameters are not taken into account, and a large water flow is passed through small networks, they will make noise, vibrate and quickly become unusable.
To find the largest calculated water flow, a table is used for the throughput of pipes depending on the diameter and different indicators of water pressure:
| Consumption | Bandwidth | |||||||||
| Pipe section | 15 mm | 20 mm | 25 mm | 32 mm | 40 mm | 50 mm | 65 mm | 80 mm | 100 mm | |
| Pa / m | Mbar / m | Less than 0.15 m / s | 0.15 m / s | 0.3 m / s | ||||||
| 90,0 | 0,900 | 173 | 403 | 745 | 1627 | 2488 | 4716 | 9612 | 14940 | 30240 |
| 92,5 | 0,925 | 176 | 407 | 756 | 1652 | 2524 | 4788 | 9756 | 15156 | 30672 |
| 95,0 | 0,950 | 176 | 414 | 767 | 1678 | 2560 | 4860 | 9900 | 15372 | 31104 |
| 97,5 | 0,975 | 180 | 421 | 778 | 1699 | 2596 | 4932 | 10044 | 15552 | 31500 |
| 100,0 | 1000,0 | 184 | 425 | 788 | 1724 | 2632 | 5004 | 10152 | 15768 | 31932 |
| 120,0 | 1200,0 | 202 | 472 | 871 | 1897 | 2898 | 5508 | 11196 | 17352 | 35100 |
| 140,0 | 1400,0 | 220 | 511 | 943 | 2059 | 3143 | 5976 | 12132 | 18792 | 38160 |
| 160,0 | 1600,0 | 234 | 547 | 1015 | 2210 | 3373 | 6408 | 12996 | 20160 | 40680 |
| 180,0 | 1800,0 | 252 | 583 | 1080 | 2354 | 3589 | 6804 | 13824 | 21420 | 43200 |
| 200,0 | 2000,0 | 266 | 619 | 1151 | 2488 | 3780 | 7200 | 14580 | 22644 | 45720 |
| 220,0 | 2200,0 | 281 | 652 | 1202 | 2617 | 3996 | 7560 | 15336 | 23760 | 47880 |
| 240,0 | 2400,0 | 288 | 680 | 1256 | 2740 | 4176 | 7920 | 16056 | 24876 | 50400 |
| 260,0 | 2600,0 | 306 | 713 | 1310 | 2855 | 4356 | 8244 | 16740 | 25920 | 52200 |
| 280,0 | 2800,0 | 317 | 742 | 1364 | 2970 | 4356 | 8568 | 17338 | 26928 | 54360 |
| 300,0 | 3000, | 331 | 767 | 1415 | 3078 | 4680 | 8892 | 18000 | 27900 | 56160 |
The average pressure in most of the risers varies from 1.5 to 2.5 atmospheres. The dependence on the number of floors is regulated by dividing the water supply network into several branches. Water injection by means of pumps also affects the change in flow rate.
Also, when calculating the water flow through the pipe according to the table of pipe diameter and pressure values, not only the number of taps is taken into account, but also the number of water heaters, bathtubs and other consumers.
Hydraulic calculation according to Shevelev
For the most accurate identification of the indicators of the entire water supply network, special reference materials are used. They define the running characteristics for pipes made of different materials.
Sometimes it is very important to accurately calculate the volume of water passing through the pipe. For example, when you need to design a new heating system. Hence the question arises: how to calculate the volume of the pipe? This indicator helps to choose the right equipment for example, the size of the expansion tank. In addition, this indicator is very important when antifreeze is used. It is usually sold in several forms:
- Diluted;
- Undiluted.
The first type can withstand temperatures - 65 degrees. The second will freeze already at -30 degrees. To buy the right amount of antifreeze, you need to know the volume of the coolant. In other words, if the volume of liquid is 70 liters, then 35 liters of undiluted liquid can be purchased. It is enough to dilute them, observing the proportion of 50-50, and you will get the same 70 liters.
To get accurate data, you need to prepare:
- Calculator;
- Calipers;
- A ruler.
First, the radius is measured, indicated by the letter R. It can be:
- Internal;
- Outside.
The outer radius is needed to determine the size of the space that it will take.
For the calculation, you need to know the data of the pipe diameter. It is designated by the letter D and is calculated by the formula R x 2. The circumference is also determined. It is designated by the letter L.
To calculate the volume of a pipe, measured in cubic meters (m3), you must first calculate its area.
To obtain an accurate value, you must first calculate the cross-sectional area.
To do this, apply the formula:
- S = R x Pi.
- The required area - S;
- Pipe radius - R;
- Pi number - 3.14159265.
The resulting value must be multiplied by the length of the pipeline.
How to find the volume of a pipe using the formula? You need to know only 2 values. The calculation formula itself is as follows:
- V = S x L
- Pipe volume - V;
- Sectional area - S;
- Length - L
For example, we have a metal pipe with a diameter of 0.5 meters and a length of two meters. To carry out the calculation, the size of the outer cross member of stainless metal is inserted into the formula for calculating the area of a circle. The pipe area will be equal to;
S = (D / 2) = 3.14 x (0.5 / 2) = 0.0625 sq. meters.
The final calculation formula will take the following form:
V = HS = 2 x 0.0625 = 0.125 cc meters.
This formula calculates the volume of absolutely any pipe. Moreover, it is absolutely not important what material it is from. If the pipeline has many components, using this formula, you can calculate separately the volume of each section.
When performing a calculation, it is very important that the dimensions are expressed in the same units of measurement. The easiest way to calculate is if all values are converted to square centimeters.
If you use different units of measurement, you can get very questionable results... They will be very far from their real values. When performing constant daily calculations, you can use the calculator's memory by setting a constant value. For example, pi times two. This will help to calculate the volume of pipes of different diameters much faster.
Today, for the calculation, you can use ready-made computer programs, in which standard parameters are indicated in advance. To perform the calculation, you only need to enter additional variable values.
Download the program https://yadi.sk/d/_1ZA9Mmf3AJKXy
How to calculate cross-sectional area
If the pipe is round, the cross-sectional area must be calculated using the formula for the area of a circle: S = π * R2. Where R is the radius (inner), π - 3.14. In total, you need to square the radius and multiply it by 3.14.
For example, the cross-sectional area of a pipe with a diameter of 90 mm. Find the radius - 90 mm / 2 = 45 mm. In centimeters, this is 4.5 cm. We square it: 4.5 * 4.5 = 2.025 cm2, we substitute in the formula S = 2 * 20.25 cm2 = 40.5 cm2.
The cross-sectional area of the profiled product is calculated using the formula for the area of a rectangle: S = a * b, where a and b are the lengths of the sides of the rectangle. If we consider the section of the profile 40 x 50 mm, we get S = 40 mm * 50 mm = 2000 mm2 or 20 cm2 or 0.002 m2.
Calculation of the volume of water in the entire system
To determine such a parameter, it is necessary to substitute the value of the inner radius into the formula. However, the problem immediately appears. And how to calculate the total volume of water in the entire pipe heating system, which includes:
- Radiators;
- Expansion tank;
- Heating boiler.
First, the volume of the radiator is calculated. To do this, his technical passport is opened and the volume values of one section are written out. This parameter is multiplied by the number of sections in a particular battery. For example, one is equal to 1.5 liters.
When installed bimetal radiator, this value is much less. The amount of water in the boiler can be found in the passport of the device.
To determine the volume of the expansion tank, it is filled with a predetermined amount of liquid.
It is very easy to determine the volume of pipes. The available data for one meter, a certain diameter, just need to be multiplied by the length of the entire pipeline.
Note that in the global network and reference books, you can see special tables. They show approximate product data. The error of the given data is quite small, therefore, the values given in the table can be safely used to calculate the volume of water.
I must say that when calculating the values, you need to take into account some characteristic differences. Metal pipes having large diameter, pass the amount of water, significantly less than the same polypropylene pipes.
The reason lies in the smoothness of the pipe surface. In steel products, it is made with a large roughness. PPR pipes have no roughness on the inner walls. However, in this case, steel products have a larger volume of water than in other pipes of the same cross section. Therefore, in order to make sure that the calculation of the volume of water in the pipes is correct, you need to double-check all the data and support the result with an online calculator.
Internal volume of a running meter of a pipe in liters - table
The table shows the internal volume of a running meter of the pipe in liters. That is, how much water, antifreeze or other liquid (coolant) is required to fill the pipeline. The inner diameter of pipes is taken from 4 to 1000 mm.
| Inner diameter, mm | Internal volume of 1 m running pipe, liters | Internal volume of 10 m running pipes, liters |
|---|---|---|
| 4 | 0.0126 | 0.1257 |
| 5 | 0.0196 | 0.1963 |
| 6 | 0.0283 | 0.2827 |
| 7 | 0.0385 | 0.3848 |
| 8 | 0.0503 | 0.5027 |
| 9 | 0.0636 | 0.6362 |
| 10 | 0.0785 | 0.7854 |
| 11 | 0.095 | 0.9503 |
| 12 | 0.1131 | 1.131 |
| 13 | 0.1327 | 1.3273 |
| 14 | 0.1539 | 1.5394 |
| 15 | 0.1767 | 1.7671 |
| 16 | 0.2011 | 2.0106 |
| 17 | 0.227 | 2.2698 |
| 18 | 0.2545 | 2.5447 |
| 19 | 0.2835 | 2.8353 |
| 20 | 0.3142 | 3.1416 |
| 21 | 0.3464 | 3.4636 |
| 22 | 0.3801 | 3.8013 |
| 23 | 0.4155 | 4.1548 |
| 24 | 0.4524 | 4.5239 |
| 26 | 0.5309 | 5.3093 |
| 28 | 0.6158 | 6.1575 |
| 30 | 0.7069 | 7.0686 |
| 32 | 0.8042 | 8.0425 |
| 34 | 0.9079 | 9.0792 |
| 36 | 1.0179 | 10.1788 |
| 38 | 1.1341 | 11.3411 |
| 40 | 1.2566 | 12.5664 |
| 42 | 1.3854 | 13.8544 |
| 44 | 1.5205 | 15.2053 |
| 46 | 1.6619 | 16.619 |
| 48 | 1.8096 | 18.0956 |
| 50 | 1.9635 | 19.635 |
| 52 | 2.1237 | 21.2372 |
| 54 | 2.2902 | 22.9022 |
| 56 | 2.463 | 24.6301 |
| 58 | 2.6421 | 26.4208 |
| 60 | 2.8274 | 28.2743 |
| 62 | 3.0191 | 30.1907 |
| 64 | 3.217 | 32.1699 |
| 66 | 3.4212 | 34.2119 |
| 68 | 3.6317 | 36.3168 |
| 70 | 3.8485 | 38.4845 |
| 72 | 4.0715 | 40.715 |
| 74 | 4.3008 | 43.0084 |
| 76 | 4.5365 | 45.3646 |
| 78 | 4.7784 | 47.7836 |
| 80 | 5.0265 | 50.2655 |
| 82 | 5.281 | 52.8102 |
| 84 | 5.5418 | 55.4177 |
| 86 | 5.8088 | 58.088 |
| 88 | 6.0821 | 60.8212 |
| 90 | 6.3617 | 63.6173 |
| 92 | 6.6476 | 66.4761 |
| 94 | 6.9398 | 69.3978 |
| 96 | 7.2382 | 72.3823 |
| 98 | 7.543 | 75.4296 |
| 100 | 7.854 | 78.5398 |
| 105 | 8.659 | 86.5901 |
| 110 | 9.5033 | 95.0332 |
| 115 | 10.3869 | 103.8689 |
| 120 | 11.3097 | 113.0973 |
| 125 | 12.2718 | 122.7185 |
| 130 | 13.2732 | 132.7323 |
| 135 | 14.3139 | 143.1388 |
| 140 | 15.3938 | 153.938 |
| 145 | 16.513 | 165.13 |
| 150 | 17.6715 | 176.7146 |
| 160 | 20.1062 | 201.0619 |
| 170 | 22.698 | 226.9801 |
| 180 | 25.4469 | 254.469 |
| 190 | 28.3529 | 283.5287 |
| 200 | 31.4159 | 314.1593 |
| 210 | 34.6361 | 346.3606 |
| 220 | 38.0133 | 380.1327 |
| 230 | 41.5476 | 415.4756 |
| 240 | 45.2389 | 452.3893 |
| 250 | 49.0874 | 490.8739 |
| 260 | 53.0929 | 530.9292 |
| 270 | 57.2555 | 572.5553 |
| 280 | 61.5752 | 615.7522 |
| 290 | 66.052 | 660.5199 |
| 300 | 70.6858 | 706.8583 |
| 320 | 80.4248 | 804.2477 |
| 340 | 90.792 | 907.9203 |
| 360 | 101.7876 | 1017.876 |
| 380 | 113.4115 | 1134.1149 |
| 400 | 125.6637 | 1256.6371 |
| 420 | 138.5442 | 1385.4424 |
| 440 | 152.0531 | 1520.5308 |
| 460 | 166.1903 | 1661.9025 |
| 480 | 180.9557 | 1809.5574 |
| 500 | 196.3495 | 1963.4954 |
| 520 | 212.3717 | 2123.7166 |
| 540 | 229.0221 | 2290.221 |
| 560 | 246.3009 | 2463.0086 |
| 580 | 264.2079 | 2642.0794 |
| 600 | 282.7433 | 2827.4334 |
| 620 | 301.9071 | 3019.0705 |
| 640 | 321.6991 | 3216.9909 |
| 660 | 342.1194 | 3421.1944 |
| 680 | 363.1681 | 3631.6811 |
| 700 | 384.8451 | 3848.451 |
| 720 | 407.1504 | 4071.5041 |
| 740 | 430.084 | 4300.8403 |
| 760 | 453.646 | 4536.4598 |
| 780 | 477.8362 | 4778.3624 |
| 800 | 502.6548 | 5026.5482 |
| 820 | 528.1017 | 5281.0173 |
| 840 | 554.1769 | 5541.7694 |
| 860 | 580.8805 | 5808.8048 |
| 880 | 608.2123 | 6082.1234 |
| 900 | 636.1725 | 6361.7251 |
| 920 | 664.761 | 6647.6101 |
| 940 | 693.9778 | 6939.7782 |
| 960 | 723.8229 | 7238.2295 |
| 980 | 754.2964 | 7542.964 |
| 1000 | 785.3982 | 7853.9816 |
If you have a specific design or pipe, then the formula above shows how to calculate the exact data for the correct flow of water or other coolant.
Online settlement
http://mozgan.ru/Geometry/VolumeCylinder
Conclusion
To find the exact figure for the consumption of the coolant of your system, you will have to sit a little. Either search the internet or use the calculator we recommend. Perhaps he can save you time.
If you have a water-type system, then you should not bother and carry out an accurate selection of volume. It is enough to estimate approximately. An accurate calculation is needed more in order not to buy too much and to minimize costs. Since many stop at the choice of an expensive coolant.
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 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 such a task when calculating required diameter pipes, enjoy reference materials. 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, 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. Design basis process pipeline the permissible speed is taken.
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. This is why high velocity fluids require right choice configurations, competent selection of the dimensions of the pipeline.
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.