This section presents the simplest calculation programs for ventilation, air conditioning. How to find the resistance coefficient of a ventilation grill
Ph.D. SB Gorunovich, engineer of PTO, "Ust-Ilimskaya CHPP" branch of OJSC "Irkutskenergo", Ust-Ilimsk, Irkutsk region.
Statement of a question
It is known that at many enterprises that in the recent past had reserves of thermal and electric energy, insufficient attention was paid to its losses during transportation. For example, various pumps were put into the project, as a rule, with a large power reserve; pressure losses in the pipelines were compensated by an increase in flow. The main steam lines were designed with bulkheads and long lines, allowing, if necessary, to transfer excess steam to neighboring turbine units. During the reconstruction and repair of transportation networks, preference was given to the versatility of the schemes, which led to additional tie-ins (fittings) and jumpers, the installation of additional tees and, as a result, to additional local total pressure losses. At the same time, it is known that in long pipelines at significant speeds of the medium, local losses of total pressure (local resistances) can entail significant losses of costs for consumers.
Currently, the requirements for efficiency, energy saving, total optimization of production force us to take a fresh look at many issues and aspects of the design, reconstruction and operation of pipelines and steam pipelines, therefore, taking into account local resistances in tees, forks and unions in hydraulic calculations of pipelines becomes an urgent task.
The purpose of this work is to describe the tees and fittings most often used at energy enterprises, exchange of experience in the field of ways to reduce local resistance coefficients, methods of comparative assessment of the effectiveness of such measures.
To assess local resistances in modern hydraulic calculations, they operate with a dimensionless coefficient of hydraulic resistance, which is very convenient because in dynamically similar flows, in which the geometric similarity of the sections and the equality of Reynolds numbers are observed, it has the same value, regardless of the type of liquid (gas) , as well as on the flow rate and transverse dimensions of the calculated sections.
The coefficient of hydraulic resistance is the ratio of the total energy (power) lost in a given section to the kinetic energy (power) in the accepted section or the ratio of the total pressure lost in the same section to the dynamic pressure in the adopted section:
where p total is the total pressure lost (in this area); p is the density of the liquid (gas); w, is the speed in the i-th section.
The value of the drag coefficient depends on what design speed and, therefore, to what section it is reduced.
Exhaust and supply tees
It is known that a significant part of local losses in branched pipelines are local resistances in tees. As an object representing local resistance, the tee is characterized by the branch angle a and the ratios of the cross-sectional areas of the branches (lateral and straight) F b / F q, Fh / Fq and F B / Fn. In the tee, the flow rate ratio Q b / Q q, Q n / Q c and, accordingly, the speed ratio w B / w Q, w n / w Q can change. Tees can be installed both in the suction sections (exhaust tee) and in the discharge sections (inlet tees) when separating the flow (Fig. 1).
The resistance coefficients of the exhaust tees depend on the parameters listed above, and for the supply tees of the usual form, practically only on the branch angle and the ratio of the speeds w n / w Q and w n / w Q, respectively.
Resistance coefficients for exhaust tees of normal shape (without rounding and expansion or narrowing of a side branch, or straight passage) can be calculated using the following formulas.
Resistance in the lateral branch (in section B):
where Q B \u003d F B w B, Q q \u003d F q w q - volumetric flow rates in section B and C, respectively.
For tees of type F n \u003d F c and for all a the values \u200b\u200bof A are given in table. 1.
When the ratio Q b / Q q changes from 0 to 1, the resistance coefficient changes from -0.9 to 1.1 (F q \u003d F b, a \u003d 90 O). Negative values \u200b\u200bare explained by the suction effect in the line at low Q B.
From the structure of formula (1) it follows that the resistance coefficient will rapidly increase with a decrease in the cross-sectional area of \u200b\u200bthe choke (with an increase in F c / F b). For example, when Q b / Q c \u003d 1, F q / F b \u003d 2, and \u003d 90 O, the coefficient is 2.75.
It is obvious that a decrease in resistance can be achieved by decreasing the angle of the side branch (choke). For example, when F c \u003d F b, α \u003d 45 O, when the ratio Q b / Q c changes from 0 to 1, the coefficient changes in the range from -0.9 to 0.322, i.e. its positive values \u200b\u200bdecrease by almost 3 times.
The resistance in the direct passage should be determined by the formula:
For tees of type Fn \u003d F c, the values \u200b\u200bof K P are given in table. 2.
It is easy to verify that the range of variation of the drag coefficient in the direct passage
de when changing the ratio Q b / Q c from 0 to 1 is in the range from 0 to 0.6 (F c \u003d F b, α \u003d 90 O).
Reducing the angle of the side branch (choke) also leads to a significant reduction in resistance. For example, when F c \u003d F b, α \u003d 45 O, when the ratio Q b / Q c changes from 0 to 1, the coefficient changes from 0 to -0.414, i.e. with an increase in Q B, a "suction" appears in the direct passage, further reducing the resistance. It should be noted that dependence (2) has a pronounced maximum, i.e. the maximum value of the resistance coefficient falls on the value of Q b / Q c \u003d 0.41 and is equal to 0.244 (with F c \u003d F b, α \u003d 45 O).
The drag coefficients of the supply tees of normal shape in turbulent flow can be calculated using the formulas.
Side branch resistance:
where K B is the flow compression ratio.
For tees of type Fn \u003d F c, the values \u200b\u200bof A1 are given in table. 3, K B \u003d 0.
If we take F c \u003d F b, a \u003d 90 O, then when the ratio Q b / Q c changes from 0 to 1, we get the coefficient values \u200b\u200bin the range from 1 to 1.2.
It should be noted that the source provides other data for the coefficient A 1. According to the data, you should take A 1 \u003d 1 with w B / w c<0,8 и А 1 =0,9 при w B /w c >0.8. If we use the data from, then when the ratio Q B / Q C changes from 0 to 1, we get the coefficient values \u200b\u200bin the range from 1 to 1.8 (F c \u003d F b). In general, we will receive slightly higher values \u200b\u200bfor the resistance coefficients in all ranges.
A decisive influence on the growth of the resistance coefficient, as in formula (1), is exerted by the sectional area B (choke) - with an increase in F g / F b, the resistance coefficient increases rapidly.
Resistance in the straight passage for supply tees type Fn \u003d Fc within
The values \u200b\u200bof t P are shown in table. 4.
When the ratio Q B / Qc changes (3 from 0 to 1 (Fc \u003d F B, α \u003d 90 O), we obtain the coefficient values \u200b\u200bin the range from 0 to 0.3.
The resistance of conventional tees can also be significantly reduced by rounding off the junction of the side branch with the collection sleeve. In this case, for exhaust tees, the flow angle should be rounded off (R 1 in Fig. 16). For supply tees, rounding should also be performed on the dividing edge (R 2 in Fig. 16); it makes the flow more stable and reduces the possibility of its separation from this edge.
In practice, rounding of the edges of the mating of the generatrices of the lateral branch and the main pipeline is sufficient at R / D (3 \u003d 0.2-0.3.
The above formulas for calculating the resistance coefficients of tees and the corresponding tabular data refer to carefully manufactured (turned) tees. Manufacturing defects in tees made during their manufacture ("dips" of the side branch and "overlap" of its section by an incorrect wall cut in the straight section - the main pipeline), become a source of a sharp increase in hydraulic resistance. In practice, this happens when there is a poor-quality tie-in into the main pipeline of the choke, which occurs quite often, because Factory tees are relatively expensive.
The gradual expansion (diffuser) of the side branch effectively reduces the resistance of both the exhaust and supply tees. The combination of rounding, bevelling and side branch widening further reduces the resistance of the tee. Resistance coefficients of improved form tees can be determined by the formulas and diagrams given in the source. Tees with side branches in the form of smooth branches also have the lowest resistance, and where practical, tees with small branch angles (up to 60 O) should be used.
In turbulent flow (Re\u003e 4.10 3), the drag coefficients of the tees depend little on the Reynolds numbers. In the transition from turbulent to laminar, there is an abrupt increase in the resistance coefficient of the side branch both in the exhaust and supply tees (by about 2-3 times).
In the calculations, it is important to take into account in which section it is reduced to the average speed. There is a link in the source about this before each formula. The sources give a general formula, which indicates the rate of reduction with the corresponding index.
Symmetrical tee for merging and splitting
The resistance coefficient of each branch of a symmetrical tee at a merger (Fig.2a) can be calculated by the formula:
When the ratio Q b / Q c changes from 0 to 0.5, the coefficient changes in the range from 2 to 1.25, and then with an increase in Q b / Q c from 0.5 to 1, the coefficient acquires values \u200b\u200bfrom 1.25 to 2 (for the case F c \u003d F b). Obviously, dependence (5) has the form of an inverted parabola with a minimum at the point Q b / Q c \u003d 0.5.
The drag coefficient of a symmetrical tee (Fig.2a) located in the injection (separation) section can also be calculated using the formula:
where K 1 \u003d 0.3 - for welded tees.
When the ratio w B / w c changes from 0 to 1, the coefficient changes in the range from 1 to 1.3 (F c \u003d F b).
Analyzing the structure of formulas (5, 6) (as well as (1) and (3)), one can make sure that a decrease in the section (diameter) of the side branches (sections B) negatively affects the resistance of the tee.
The flow resistance can be reduced by 2-3 times when using forked tees (Fig. 26, 2c).
The resistance coefficient of the split tee during flow separation (Fig.2b) can be calculated using the formulas:
When the ratio Q 2 / Q 1 changes from 0 to 1, the coefficient changes in the range from 0.32 to 0.6.
The resistance coefficient of the tee-fork at merging (Fig.2b) can be calculated by the formulas:
When the ratio Q 2 / Q 1 changes from 0 to 1, the coefficient changes in the range from 0.33 to -0.4.
A symmetrical tee can be made with smooth branches (Fig. 2c), then its resistance can be further reduced.
Manufacturing. Standards
Industry energy standards prescribe for pipelines of thermal power plants of low pressure (at operating pressure P work.<22 кгс/см 2 и температуре среды t<425 О С) использовать тройники сварные по ОСТ34-42-762
OST34-42-765-85. For higher parameters of the environment (R ra b.<40 кгс/см 2) изготавливают тройники из углеродистых и кремнемарганцовистых сталей: штампованные по ОСТ108.720.01, ОСТ108.720.02-82; сварные по ОСТ108.104.01 - ОСТ108.104.03-82; с обжатием (с вытянутой горловиной) по ОСТ108.104.04, ОСТ108.104.05-82. Из хромомолибденованадиевых сталей изготавливают тройники: штампованные по ОСТ108.720.05, ОСТ108.720.06-82; сварные по ОСТ108.104.10 - ОСТ108.104.12-82; с обжатием (с вытянутой горловиной) по ОСТ108.104.13 - ОСТ108.104.15-82 для паропроводов высокого давления (с параметрами Р раб. до 255 кгс/см 2 и температурой t до 560 О С). Существуют соответствующие нормативы и для штуцеров.
The design of tees made according to the existing (above) standards is far from always optimal in terms of hydraulic losses. The reduction of the coefficient of local resistance is facilitated only by the shape of stamped tees with an elongated neck, where a radius of rounding is provided in the lateral branch of the type shown in Fig. 1b and Fig. 3c, as well as with compression of the ends, when the diameter of the main pipeline is slightly less than the diameter of the tee (of the type shown in Fig. 3b). Fork tees are obviously custom made to "factory" standards. In RD 10-249-98 there is a paragraph devoted to the strength calculation of tees-forks and unions.
When designing and reconstructing networks, it is important to take into account the direction of movement of the media and the possible ranges of changes in flow rates in tees. If the direction of the transported medium is unambiguously determined, it is advisable to use inclined unions (side branches) and tees-forks. Nevertheless, the problem of significant hydraulic losses remains in the case of a universal tee, which combines the properties of supply and exhaust, in which both merging and separation of the flow is possible in operating modes associated with significant changes in flow rates. The aforementioned qualities are typical, for example, for switching nodes of feed water pipelines or main steam pipelines at TPPs with "jumpers".
It should be borne in mind that for steam and hot water pipelines, the design and geometric dimensions of welded tees from pipes, as well as fittings (pipes, nozzles) welded on straight sections of pipelines, must meet the requirements of industry standards, norms and technical conditions. In other words, for critical pipelines, it is necessary to order tees made in accordance with technical conditions from certified manufacturers. In practice, due to the relative high cost of "factory" tees, tapping is often performed by local contractors using industry or factory standards.
In general, it is advisable to make the final decision on the insertion method after a comparative technical and economic analysis. If a decision is made to carry out the tie-in "on its own", the engineering and technical staff must prepare a template for the nozzle, make a strength calculation (if necessary), control the quality of the tie-in (do not allow the nozzle to “fail” and “overlap” its section by an incorrect wall cut in the straight section) ... It is advisable to make the internal joint between the metal of the fitting and the main pipeline with a rounding (Fig. 3c).
There are a number of design solutions to reduce hydraulic resistance in standard tees and line switching assemblies. One of the simplest is to increase the size of the tees themselves to reduce the relative velocities of the medium in them (Fig. 3a, 3b). In this case, tees must be completed with transitions, the angles of expansion (contraction) of which are also advisable to choose from a number of hydraulically optimal ones. A split tee with a jumper can also be used as a universal tee with reduced hydraulic losses (Fig. 3d). The use of tees-forks for the switching nodes of the main lines will also slightly complicate the design of the unit, but will have a positive effect on hydraulic losses (Fig. 3d, 3f).
It is important to note that with a relatively close location of local (L \u003d (10-20) d) resistances of various types, the phenomenon of interference of local resistances takes place. According to some researchers, with the maximum convergence of local resistances, it is possible to achieve a decrease in their sum, while at some distance (L \u003d (5-7) d), the total resistance has a maximum (higher by 3-7% than a simple amount) ... The reduction effect could be of interest to large manufacturers willing to manufacture and supply switching assemblies with reduced local resistances, but applied laboratory research is required to achieve a good result.
Feasibility study
When making a constructive decision, it is important to pay attention to the economic side of the problem. As mentioned above, "factory" tees of a conventional design, and even more so custom-made (hydraulically optimal), will cost significantly more than tapping in a union. At the same time, it is important to roughly evaluate the benefits in the case of reducing hydraulic losses in the new tee and its payback period.
It is known that the pressure loss in station pipelines with ordinary velocities of media movement (for Re\u003e 2.10 5) can be estimated by the following formula:
where p is the pressure loss, kgf / cm 2; w is the speed of the medium, m / s; L is the expanded length of the pipeline, m; g - acceleration of gravity, m / s 2; d is the estimated diameter of the pipeline, m; k - coefficient of friction resistance; ∑ἐ m - the sum of the coefficients of local resistance; v - specific volume of the medium, m 3 / kg
Dependence (7) is usually called the hydraulic characteristic of the pipeline.
If we take into account the dependence: w \u003d 10Gv / 9nd 2, where G is the flow rate, t / h.
Then (7) can be represented as:
If it is possible to reduce the local resistance (tee, union, switching unit), then, obviously, formula (9) can be represented as:
Here ∑ἐ m is the difference between the coefficients of local resistance of the old and new nodes.
Let us assume that the hydraulic system "pump-pipeline" operates in the nominal mode (or in the mode close to the nominal). Then:
where Р n - nominal pressure (according to the flow characteristic of the pump / boiler), kgf / cm 2; G h - nominal flow rate (according to the flow characteristic of the pump / boiler), t / h.
If we assume that after replacing the old resistances, the "pump - pipeline" system will remain operational (P "R n), then from (10), using (12), we can determine a new flow rate (after reducing the resistance):
The operation of the "pump-pipeline" system, the change in its characteristics can be graphically represented in Fig. 4.
Obviously, G 1\u003e G M. If we are talking about the main steam pipeline transporting steam from the boiler to the turbine, then the difference in flow rates LG \u003d G 1 -G n can be used to determine the gain in the amount of heat (from the selection of the turbine) and / or in the amount of generated electrical energy according to the operating characteristics of this turbine.
Comparing the cost of a new unit and the amount of heat (electricity), one can roughly estimate the profitability of its installation.
Calculation example
For example, it is necessary to assess the profitability of replacing an equal tee of the main steam line at the confluence of flows (Fig.2a) with a forked tee with a jumper of the type shown in Fig. 3d. Steam consumer - heating turbine PO TMZ type Т-100 / 120-130. Steam enters through one thread of the steam line (through a tee, sections B, C).
We have the following initial data:
■ design diameter of the steam line d \u003d 0.287 m;
■ rated steam consumption G h \u003d Q (3 \u003d Q ^ 420 t / h;
■ nominal boiler pressure P n \u003d 140 kgf / cm 2;
■ specific volume of steam (at P ra b \u003d 140 kgf / cm 2, t \u003d 560 О С) n \u003d 0.026 m 3 / kg.
Let's calculate the resistance coefficient of a standard tee at the confluence of flows (Fig.2a) according to the formula (5) - ^ СБ1 \u003d 2.
To calculate the resistance coefficient of a split tee with a jumper, assume:
■ division of flows in the branches occurs in the proportion Q b / Q c “0.5;
■ the total resistance coefficient is equal to the sum of the resistances of the supply tee (with a 45 O outlet, see Fig. 1a) and the split tee at merging (Fig. 2b), i.e. we neglect the interference.
We use formulas (11, 13) and obtain the expected increase in flow rate by G \u003d G 1 -G n \u003d 0.789 t / h.
According to the regime diagram of the T-100 / 120-130 turbine, the flow rate of 420 t / h can correspond to an electrical load of 100 MW and a heat load of 400 GJ / h. The relationship between consumption and electrical load is close to direct proportional.
The gain in electrical load can be: P e \u003d 100AG / Q n \u003d 0.188 MW.
The gain in thermal load can be: T e \u003d 400AG / 4.19Q n \u003d 0.179 Gcal / h.
Prices for products made of chromium-molybdenum-vanadium steels (for tees-fork 377x50) can vary widely from 200 to 600 thousand rubles, therefore, the payback period can be judged only after careful market research at the time of making a decision.
1. This article describes various types of tees and fittings, gives a brief description of tees used in the pipelines of power plants. Formulas for determining the coefficients of hydraulic resistance are given, ways and methods of their reduction are shown.
2. Prospective designs of tees-forks, a node for switching main pipelines with reduced coefficients of local resistance are proposed.
3. Formulas, an example are given, and the feasibility of a technical and economic analysis is shown when choosing or replacing tees, when reconstructing switching nodes.
Literature
1. Idelchik I.E. Reference book on hydraulic resistance. Moscow: Mechanical Engineering, 1992.
2. Nikitina I.K. Reference book on pipelines of thermal power plants. M .: Energoatomizdat, 1983.
3. Reference book on calculations of hydraulic and ventilation systems / Ed. A.S. Yuriev. S.-Pb .: ANO NPO "Peace and Family", 2001.
4. Rabinovich E.Z. Hydraulics. Moscow: Nedra, 1978.
5. Benenson E.I., Ioffe L.S. Heating steam turbines / Ed. D.P. Elder. M: Energoizdat, 1986.
You can also use an approximate formula:
0, 195 v 1, 8
R f. (10) d 100 1, 2
Its error does not exceed 3 - 5%, which is sufficient for engineering calculations.
The total friction pressure losses for the entire section are obtained by multiplying the specific losses R by the section length l, Rl, Pa. If air ducts or channels made of other materials are used, it is necessary to introduce a correction for roughness βsh according to table. 2. It depends on the absolute equivalent roughness of the material of the air duct K e (Table 3) and the value of v f.
table 2 |
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Correction values \u200b\u200bβsh |
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v f, m / s |
βsh at the values \u200b\u200bof Ke, mm |
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Table 3 Absolute equivalent roughness of the duct material
Plasterer- |
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ka on the grid |
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K e, mm |
For steel air ducts βsh \u003d 1. More detailed values \u200b\u200bof βsh can be found in table. 22.12. Taking into account this correction, the refined friction pressure loss Rl βsh, Pa, is obtained by multiplying Rl by the value of βsh. Then determine the dynamic pressure on the site
standard conditions ρw \u003d 1.2 kg / m3.
Further, local resistances are identified on the site, the coefficients of local resistance (LRR) ξ are determined, and the sum of LRR in this area (Σξ) is calculated. All local resistances are recorded in the list in the following form.
STATEMENT OF KMS VENTILATION SYSTEM
Etc.
IN the column "local resistances" write down the names of the resistances (branch, tee, cross, elbow, grille, air distributor, umbrella, etc.) available in this area. In addition, their number and characteristics are noted, according to which the values \u200b\u200bof the CMR are determined for these elements. For example, for a round bend, this is the angle of rotation and the ratio of the radius of rotation to the diameter of the ductr / d, for a rectangular outlet - the angle of rotation and dimensions of the sides of the duct a and b. For lateral openings in an air duct or duct (for example, at the place where the air intake grille is installed) - the ratio of the opening area to the air duct cross-section
f hole / f o. For tees and crosses on the passage, the ratio of the cross-sectional area of \u200b\u200bthe passage and the trunk f p / f s and the flow rate in the branch and in the trunk L о / L s, for tees and crosses on the branch - the ratio of the cross-sectional area of \u200b\u200bthe branch and the trunk f p / f s and again, the value of L about / L s. It should be borne in mind that each tee or cross connects two adjacent sections, but they refer to the one of these sections, for which the air flow L is less. The difference between tees and crosses on the passage and on the branch is related to how the calculated direction runs. This is shown in Fig. 11. Here, the calculated direction is shown with a bold line, and the directions of air flows are shown with thin arrows. In addition, it is signed where exactly in each option is the trunk, passage and from-
branching of the tee for the correct choice of ratios fп / fс, fо / fс and L о / L с. Note that in supply ventilation systems, the calculation is usually carried out against the movement of air, and in exhaust ventilation systems - along this movement. The sections to which the considered tees belong are indicated by checkmarks. The same applies to the crosspieces. As a rule, although not always, tees and crosses on a passage appear when calculating the main direction, and on a branch they appear when aerodynamic linkage of secondary sections (see below). In this case, the same tee in the main direction can be taken into account as a tee per passage, and in the secondary direction
– as a branch with a different ratio. CCM for crosspieces
take the same size as for the corresponding tees.
Figure: 11. Scheme for calculating tees
Approximate values \u200b\u200bof ξ for common resistances are given in table. 4.
Table 4 |
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Ξ values \u200b\u200bof some local resistances |
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Name |
Name |
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resistance |
resistance |
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Round bend 90o, |
The grille is not adjustable |
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r / d \u003d 1 |
may RS-G (exhaust or |
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Rectangular elbow 90 ° |
air intake) |
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A tee in the passage (on- |
Sudden expansion |
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oppression) |
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Branch tee |
Sudden constriction |
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A tee on the passage (su- |
First side hole |
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stie (entrance to the air |
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Branch tee |
–0.5* … |
boron mine) |
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Plafond (anemostat) ST-KR, |
Elbow rectangular |
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90o |
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Adjustable grille RS- |
Umbrella above the exhaust |
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VG (supply) |
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*) negative CMR can occur at low Lo / Lc due to the ejection (suction) of air from the branch by the main flow.
More detailed data for the CCM are shown in table. 22.16 - 22.43. For the most common local resistances -
tees on the passage - KMS can also be approximately calculated using the following formulas:
0.41 f "25 L" 0.2 4 |
0.25 at |
0.7 and |
f "0.5 (11) |
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- for tees at discharge (supply); |
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at L " |
0.4 you can use a simplified formula |
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prox pr 0.425 0.25 f p "; |
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0. 2 1. 7 f " |
0.35 0.25 f " |
2.4 L " |
0. 2 2 |
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- for tees for suction (exhaust).
Here L " |
f about |
and f " |
f p |
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f with |
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After determining the value of Σξ, the pressure loss at the local resistances Z P d, Pa, and the total pressure loss are calculated
in the section Rl βsh + Z, Pa.
The calculation results are entered in the table in the following form.
AERODYNAMIC CALCULATION OF THE VENTILATION SYSTEM
Estimated |
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Duct dimensions |
pressure |
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on friction |
Rlβ w |
RD, |
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βsh |
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d or |
f op, |
ff, |
Vph, |
d eq |
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l, m |
a × b, |
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When the calculation of all sections of the main direction is completed, the values \u200b\u200bof Rl βsh + Z for them are summed up and the total resistance
ventilation network pressure P network \u003d Σ (Rl βsh + Z).
After calculating the main direction, one or two branches are linked. If the system serves multiple floors, you can select the floor branches on the intermediate floors for linking. If the system serves one floor, the branches from the main line that are not included in the main direction are tied (see example in section 4.3). The calculation of the linked sections is carried out in the same sequence as for the main direction, and is recorded in the table in the same form. The linking is considered complete if the amount
pressure loss Σ (Rl βsh + Z) along the connected sections deviates from the sum Σ (Rl βsh + Z) along the parallel connected sections of the main direction by no more than 10%. Parallel connected are the sections along the main and linked directions from the point of their branching to the terminal air distributors. If the circuit looks like the one shown in fig. 12 (the main direction is highlighted by a bold line), then linking direction 2 requires that the value of Rl βsh + Z for section 2 be equal to Rl βsh + Z for section 1, obtained from the calculation of the main direction, with an accuracy of 10%. The tie is achieved by selecting the diameters of the round or the dimensions of the sections of rectangular ducts in the areas to be tied, and if this is not possible, by installing choke valves or diaphragms on the branches.
Fan selection should be carried out according to the manufacturer's catalogs or according to the data. The fan pressure is equal to the sum of the pressure losses in the ventilation network in the main direction, determined during the aerodynamic calculation of the ventilation system, and the sum of the pressure losses in the elements of the ventilation unit (air valve, filter, air heater, noise damper, etc.).
Figure: 12. Fragment of the ventilation system diagram with the choice of a branch for linking
Finally, it is possible to select a fan only after an acoustic calculation, when the issue of installing a silencer is resolved. The acoustic calculation can be performed only after preliminary selection of the fan, since the initial data for it are the sound power levels emitted by the fan into the air ducts. The acoustic calculation is performed in accordance with the instructions in chapter 12. If necessary, calculate and determine the standard size of the silencer, and then finally select the fan.
4.3. An example of calculating a supply ventilation system
A supply ventilation system for the dining room is considered. Nanoska of air ducts and air distributors on the plan is shown in clause 3.1 in the first version (typical layout for halls).
System diagram
1000х400 5 8310 m3 / h
2772 m3 / h2 |
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More information on the calculation methodology and the necessary initial data can be found at,. The corresponding terminology is given in.
STATEMENT OF KMS SYSTEM P1
Local resistance |
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924 m3 / h |
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1. Round bend 90о r / d \u003d 1 |
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2. T-piece in the passage (discharge) |
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fп / fc |
Lo / Lc |
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fп / fc |
Lo / Lc |
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1. T-piece in the passage (delivery) |
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fп / fc |
Lo / Lc |
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1. T-piece in the passage (delivery) |
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fп / fc |
Lo / Lc |
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1. Bend rectangular 1000 × 400 90о 4 pcs |
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1.Air intake with umbrella |
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(first side hole) |
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1. Air intake louver |
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STATEMENT OF KMS SYSTEM P1 (BRANCH No.1) |
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Local resistance |
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1. Air distributor PRM3 at flow rate |
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924 m3 / h |
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1. Round bend 90о r / d \u003d 1 |
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2. Branch tee (discharge) |
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fo / fc |
Lo / Lc |
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APPENDIX Characteristics of ventilation grilles and shades
I. Free cross-sections, m2, for supply and exhaust louvres RS-VG and RS-G
Length mm |
Height, mm |
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Speed \u200b\u200bcoefficient m \u003d 6.3, temperature coefficient n \u003d 5.1.
II. Characteristics of plafonds ST-KR and ST-KV
Name |
Dimensions, mm |
f fact, m 2 |
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Overall |
Interior |
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Plafond ST-KR |
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(round) |
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Plafond ST-KV |
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(square) |
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Speed \u200b\u200bfactor m \u003d 2.5, temperature factor n \u003d 3.
BIBLIOGRAPHIC LIST
1. Samarin O.D. Selection of equipment for supply ventilation units (air conditioners) of the KCKP type. Methodical instructions for the implementation of course and diploma projects for students of the specialty 270109 "Heat and gas supply and ventilation". - M .: MGSU, 2009 .-- 32 p.
2. Belova E.M. Central air conditioning systems in buildings. - M .: Evroklimat, 2006 .-- 640 p.
3. SNiP 41-01-2003 "Heating, ventilation and air conditioning". - M .: GUP TsPP, 2004.
4. Arktos equipment catalog.
5. sanitary devices. Part 3. Ventilation and air conditioning. Book 2. / Ed. N.N. Pavlov and Yu.I. Shiller. - M .: Stroyizdat, 1992 .-- 416 p.
6.GOST 21.602-2003. System of design documents for construction. Rules for the implementation of working documentation for heating, ventilation and air conditioning. - M .: GUP TsPP, 2004.
7. Samarin O.D. About the mode of air movement in steel air ducts.
// SOK, 2006, No. 7, p. 90 - 91.
8. Designer handbook. Internalsanitary devices. Part 3. Ventilation and air conditioning. Book 1. / Ed. N.N. Pavlov and Yu.I. Shiller. - M .: Stroyizdat, 1992 .-- 320 p.
9. Kamenev P.N., Tertichnik E.I. Ventilation. - M .: ASV, 2006 .-- 616 p.
10. B.A. Krupnov Terminology for building thermal physics, heating, ventilation and air conditioning: guidelines for students of the specialty "Heat and gas supply and ventilation".
|
Appointment |
Basic requirement | ||||
| Noiselessness | Min. head loss | ||||
| Trunk channels | Main channels | Branches | |||
| Inflow | Hood | Inflow | Hood | ||
| Living spaces | 3 | 5 | 4 | 3 | 3 |
| Hotels | 5 | 7.5 | 6.5 | 6 | 5 |
| Institutions | 6 | 8 | 6.5 | 6 | 5 |
| Restaurants | 7 | 9 | 7 | 7 | 6 |
| The shops | 8 | 9 | 7 | 7 | 6 |
Based on these values, the linear parameters of the ducts should be calculated.
Algorithm for calculating the loss of air pressure
The calculation must begin with drawing up a diagram of the ventilation system with the obligatory indication of the spatial arrangement of air ducts, the length of each section, ventilation grilles, additional equipment for air purification, technical fittings and fans. Losses are determined first for each separate line, and then summed up. For a separate technological section, the losses are determined using the formula P \u003d L × R + Z, where P is the air pressure loss in the calculated section, R is the losses per linear meter of the section, L is the total length of the air ducts in the section, Z is the losses in the additional system fittings ventilation.
To calculate the pressure loss in a circular duct, the formula Ptr is used. \u003d (L / d × X) × (Y × V) / 2g. X is the tabular coefficient of air friction, depends on the material of the air duct, L is the length of the calculated section, d is the diameter of the air duct, V is the required air flow rate, Y is the air density taking into account the temperature, g is the acceleration of falling (free). If the ventilation system has square ducts, then table No. 2 should be used to convert round values \u200b\u200bto square ones.
Tab. No. 2. Equivalent diameters of round ducts for square
| 150 | 200 | 250 | 300 | 350 | 400 | 450 | 500 | |
| 250 | 210 | 245 | 275 | |||||
| 300 | 230 | 265 | 300 | 330 | ||||
| 350 | 245 | 285 | 325 | 355 | 380 | |||
| 400 | 260 | 305 | 345 | 370 | 410 | 440 | ||
| 450 | 275 | 320 | 365 | 400 | 435 | 465 | 490 | |
| 500 | 290 | 340 | 380 | 425 | 455 | 490 | 520 | 545 |
| 550 | 300 | 350 | 400 | 440 | 475 | 515 | 545 | 575 |
| 600 | 310 | 365 | 415 | 460 | 495 | 535 | 565 | 600 |
| 650 | 320 | 380 | 430 | 475 | 515 | 555 | 590 | 625 |
| 700 | 390 | 445 | 490 | 535 | 575 | 610 | 645 | |
| 750 | 400 | 455 | 505 | 550 | 590 | 630 | 665 | |
| 800 | 415 | 470 | 520 | 565 | 610 | 650 | 685 | |
| 850 | 480 | 535 | 580 | 625 | 670 | 710 | ||
| 900 | 495 | 550 | 600 | 645 | 685 | 725 | ||
| 950 | 505 | 560 | 615 | 660 | 705 | 745 | ||
| 1000 | 520 | 575 | 625 | 675 | 720 | 760 | ||
| 1200 | 620 | 680 | 730 | 780 | 830 | |||
| 1400 | 725 | 780 | 835 | 880 | ||||
| 1600 | 830 | 885 | 940 | |||||
| 1800 | 870 | 935 | 990 |
The horizontal is the height of the square duct, and the vertical is the width. The equivalent value of the circular section is at the intersection of the lines.
The air pressure losses in the bends are taken from Table 3.
Tab. No. 3. Pressure loss at bends
To determine the pressure loss in the diffusers, the data from Table 4 are used.
Tab. No. 4. Pressure loss in diffusers
Table 5 gives a general diagram of losses in a straight section.
Tab. No. 5. Diagram of air pressure losses in straight air ducts
All individual losses in this section of the duct are summed up and corrected with table No. 6. Tab. No. 6. Calculation of the decrease in flow pressure in ventilation systems
During design and calculations, existing regulations recommend that the difference in the magnitude of pressure losses between individual sections does not exceed 10%. The fan should be installed in the area of \u200b\u200bthe ventilation system with the highest resistance, the most distant air ducts should have the lowest resistance. If these conditions are not met, then it is necessary to change the layout of the air ducts and additional equipment, taking into account the requirements of the provisions.
Aerodynamic calculation of air ducts begins with drawing an axonometric scheme M 1: 100, setting the numbers of sections, their loads L m / h, and lengths 1, m. The direction of the aerodynamic calculation is determined - from the most remote and loaded section to the fan. If in doubt, all possible options are calculated when determining the direction.
The calculation starts from a remote area, its diameter is calculated D, m, or
Square cross-section of a rectangular duct P, m:
System start at fan
Administrative buildings 4-5 m / s 8-12 m / s
Industrial buildings 5-6 m / s 10-16 m / s,
Increasing as you approach the fan.
Using Appendix 21, we take the nearest standard values \u200b\u200bof Dst or (a x b) st
Then we calculate the actual speed:
Or ———————— ———— -, m / s.
FACT 3660 * (a * 6) st
For further calculations, we determine the hydraulic radius of rectangular ducts:
£\u003e 1 \u003d -, m. a + b
To avoid using tables and interpolating the values \u200b\u200bof specific friction losses, we apply a direct solution to the problem:
We define the Reynolds criterion:
Re \u003d 64 100 * Ost * Ufact (for rectangular Ost \u003d Ob) (14.6)
And the coefficient of hydraulic friction:
0.3164 * Re 0 25 at Re< 60 ООО (14.7)
0.1266 * Ne 0167 for Re\u003e 60,000. (14.8)
The pressure loss in the calculated area will be:
Where KMS is the sum of the coefficients of local resistances at the duct section.
Local resistances lying on the border of two sections (tees, crosses) should be attributed to a section with a lower flow rate.
Local resistance coefficients are given in the appendices.
Initial data:
Duct material - galvanized sheet steel, thickness and dimensions in accordance with App. 21.
The material of the air intake shaft is brick. As air diffusers, PP type adjustable grilles with possible cross-sections are used:
100 x 200; 200 x 200; 400 x 200 and 600 x 200 mm, shading coefficient 0.8 and maximum outlet air speed up to 3 m / s.
The resistance of the intake insulated valve with fully open blades is 10 Pa. The hydraulic resistance of the air heater is 132 Pa (according to a separate calculation). Filter resistance 0-4 250 Pa. The hydraulic resistance of the muffler is 36 Pa (according to the acoustic calculation). Based on architectural requirements, air ducts are designed with rectangular cross-section.
|
Delivery L, m3 / h |
Length 1, m |
Section a * b, m |
Losses in the section p, Pa |
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|
PP grille at the outlet |
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|
250 × 250 b \u003d 1030 |
|
|
|
|
UDC 697.9 Determination of local resistance coefficients of tees in ventilation systems O.D.Samarin, Ph.D., Associate Professor (NRU MGSU) The current situation with the determination of the values \u200b\u200bof the coefficients of local resistance (LRR) of the elements of ventilation networks in their aerodynamic calculation is considered. An analysis of some modern theoretical and experimental works in the area under consideration is given and the shortcomings of the existing reference literature concerning the convenience of using its data for the implementation of engineering calculations using MS Excel spreadsheets are revealed. The main results of the approximation of the available tables for the CMS of unified tees on the branch during injection and suction in ventilation and air conditioning systems are presented in the form of the corresponding engineering formulas. An assessment of the accuracy of the obtained dependencies and the permissible range of their applicability is given, as well as recommendations for their use in the practice of mass design are presented. The presentation is illustrated with numerical and graphic examples. Keywords:coefficient of local resistance, tee, branch, discharge, suction. |
UDC 697.9 Determination of local resistance coeffi cients of tees in ventilating systems O. D. Samarin, PhD, Assistant Professor, National Research Moscow State University of Civil Engineering (NR MSUCE) The current situation is reviewed with the defi nition of values \u200b\u200bof coeffi cients of local resistances (CLR) of elements of the ventilation systems at their aerodynamic calculation. The analysis of some contemporary theoretical and experimental works in this fi eld is given and defi ciencies are identifi ed in the existing reference literature for the usability of its data to perform engineering calculations using MS Excel spreadsheets. The main results of approximation of the existing tables to the CLR for the uniform tees on the branch of the injection and the suction in the ventilating and air-conditioning systems are presented in the appropriate engineering formulas. The estimation of accuracy of the obtained dependencies and valid range of their applicability are given, as well as recommendations for their use in practice mass design. The presentation is illustrated by numerical and graphical examples. Keywords:coefficient of local resistance, tee, branch, injection, suction. |
When the air flow moves in air ducts and channels of ventilation and air conditioning systems (V and KV), in addition to friction pressure losses, losses on local resistances - shaped parts of air ducts, air distributors and network equipment play a significant role.
Such losses are proportional to the dynamic pressure r q \u003d ρ v² / 2, where ρ is the air density, approximately equal to 1.2 kg / m³ at a temperature of about +20 ° C; v - its speed [m / s], determined, as a rule, in the channel section behind the resistance.
The proportionality coefficients ξ, called the coefficients of local resistance (LRR), for various elements of systems B and KV are usually determined from the tables available, in particular, in and in a number of other sources. The greatest difficulty in this case is most often caused by the search for CMS for tees or branch nodes. The fact is that in this case it is necessary to take into account the type of tee (per passage or branch) and the mode of air movement (injection or suction), as well as the ratio of the air flow rate in the branch to the flow rate in the barrel L´ o \u003d L o / L c and cross-sectional area of \u200b\u200bthe passage to the cross-sectional area of \u200b\u200bthe trunk F´ p \u003d F p / F s.
For tees during suction, it is also necessary to take into account the ratio of the branch cross-sectional area to the trunk cross-sectional area. F´ o \u003d F o / F s... In the manual, the corresponding data are given in table. 22.36-22.40. However, when carrying out calculations using Excel spreadsheets, which is currently quite common due to the wide use of various standard software and the convenience of formatting the calculation results, it is desirable to have analytical formulas for the CMR, at least in the most common ranges of change in the characteristics of tees ...
In addition, it would be advisable in the educational process to reduce the technical work of students and transfer the main load to the development of design solutions for systems.
Similar formulas are available in such a rather fundamental source as, but there they are presented in a very generalized form, without taking into account the design features of specific elements of existing ventilation systems, and also use a significant number of additional parameters and require, in some cases, referring to certain tables. On the other hand, the programs for automated aerodynamic calculation of B and KV systems that have appeared recently use some algorithms to determine the CMR, but, as a rule, they are unknown to the user and may therefore raise doubts about their validity and correctness.
Also, at the present time, there are some works, the authors of which continue research to refine the calculation of the CMR or expand the range of parameters of the corresponding element of the system for which the results obtained will be valid. These publications appear both in our country and abroad, although in general their number is not too large, and are based mainly on the numerical simulation of turbulent flows using a computer or on direct experimental research. However, the data obtained by the authors is, as a rule, difficult to use in the practice of mass design, since they are not yet presented in an engineering form.
In this regard, it seems expedient to analyze the data contained in the tables and obtain, on their basis, approximation dependences that would have the simplest and most convenient form for engineering practice and at the same time adequately reflect the nature of the existing dependences for the CMR of tees. For the most common types of them - tees on the passage (unified branch nodes), this problem was solved by the author in the work. At the same time, analytical relationships are more difficult to find for tees on a branch, since the dependencies themselves look more complicated here. The general view of the approximation formulas, as always in such cases, is obtained based on the location of the calculated points in the correlation field, and the corresponding coefficients are selected by the least squares method in order to minimize the deviation of the plotted graph using Excel. Then, for some of the most common ranges F p / F s, F o / F s and L o / L s you can get expressions:
at L´ o \u003d 0.20-0.75 and F´ o\u003d 0.40-0.65 - for tees during injection (supply);
at L´ o = 0,2-0,7, F´ o \u003d 0.3-0.5 and F´ n \u003d 0.6-0.8 - for tees for suction (exhaust).
The accuracy of dependences (1) and (2) is shown in Fig. 1 and 2, which shows the results of processing table. 22.36 and 22.37 for KMS of unified tees (branch units) on a branch with a circular cross-section during suction. In the case of a rectangular section, the results will not differ significantly.
It can be noted that the discrepancy here is greater than for tees per passage, and averages 10-15%, sometimes even up to 20%, but for engineering calculations this may be acceptable, especially taking into account the obvious initial error contained in the tables, and Simultaneous simplification of calculations when using Excel. At the same time, the obtained ratios do not require any other initial data, except for those already available in the aerodynamic calculation table. In fact, it must explicitly indicate both the air flow rates and the cross-sections in the current and in the adjacent section, included in the listed formulas. This primarily simplifies calculations when using Excel spreadsheets. At the same time fig. 1 and 2 make it possible to make sure that the found analytical dependences quite adequately reflect the nature of the influence of all the main factors on the CMR of tees and the physical essence of the processes occurring in them when the air flow moves.
At the same time, the formulas given in this work are very simple, visual and easily accessible for engineering calculations, especially in Excel, as well as in the educational process. Their use makes it possible to abandon the interpolation of tables while maintaining the accuracy required for engineering calculations, and directly calculate the coefficients of local resistance of tees on the branch in a very wide range of ratios of cross-sections and air flow rates in the trunk and branches.
This is sufficient for designing ventilation and air conditioning systems in most residential and public buildings.
- Designer handbook. Internal sanitary facilities. Part 3. Ventilation and air conditioning. Book. 2 / Ed. N.N. Pavlova and Yu.I. Schiller. - M .: Stroyizdat, 1992.416 p.
- Idelchik I.E. Handbook on hydraulic resistance / Ed. M.O. Steinberg. - Ed. 3rd. - M .: Mashinostroenie, 1992.672 p.
- Posokhin V.N., Ziganshin A.M., Batalova A.V. To the determination of the coefficients of local resistances of disturbing elements of pipeline systems // Izvestiya vuzov: Construction, 2012. No. 9. S. 108-112.
- Posokhin V.N., Ziganshin A.M., Varsegova E.V. To the calculation of pressure losses in local resistances: Commun. 1 // Izvestiya vuzov: Construction, 2016. No. 4. S. 66–73.
- Averkova O.A. Experimental study of separated flows at the inlet to the suction openings. Vestnik BGTU im. V.G. Shukhov, 2012. No. 1. S. 158-160.
- Kamel A.H., Shaqlaih A.S. Frictional pressure losses of fluids flowing in circular conduits: A review. SPE Drilling and Completion. 2015. Vol. 30. No. 2. Pp. 129-140.
- Gabrielaitiene I. Numerical simulation of a district heating system with emphases on transient temperature behavior. Proc. of the 8th International Conference “Environmental Engineering”. Vilnius. VGTU Publishers. 2011. Vol. 2. Pp. 747-754.
- Horikiri K., Yao Y., Yao J. Modeling conjugate flow and heat transfer in a ventilated room for indoor thermal comfort assessment. Building and Environment. 2014. No. 77. Pp. 135-147.
- Samarin O.D. Calculation of local resistances in ventilation systems of buildings // Journal of SOK, 2012. №2. S. 68–70.
