Such losses are proportional to the dynamic pressure of PD \u003d ρv2 / 2, where ρ is the density of the air, equal to about 1.2 kg / m3 at a temperature of about +20 ° C, and V is its speed [m / s], as a rule, due to resistance. The proportionality coefficients ζ, called local resistance coefficients (CCM), for various elements of systems in and kV are usually determined by tables available, in particular, in and in a number of other sources.

The greatest complexity at the same time it is most often called KSM for tees or branch sites, since in this case it is necessary to take into account the type of tee (on the passage or on the branch) and the mode of air movement (discharge or suction), as well as the ratio of air flow in the branch to Consumption in the barrel LO '\u003d LO / LC and the cross-sectional area of \u200b\u200bthe cross section of the Fn' \u003d Fn / Fc.

For tees, during suction, it is necessary to take into account the ratio of the area of \u200b\u200bthe branch cross section to the cross-sectional area FO '\u003d FO / FC. In the manual, the relevant data is shown in Table. 22.36-22.40. However, at large relative expenses in the branch of the CCM, they change very sharply, therefore, in this area, the tables in question are manually interpolated with difficulty and with a significant error.

In addition, in the case of using MS Excel spreadsheets, it is advisable to have formulas to directly calculate the CMC through the ratio of expenses and sections. At the same time, such formulas should be, on the one hand, rather simple and convenient for mass design and use in the educational process, but at the same time should not give an error exceeding the usual accuracy of engineering calculation.

Earlier, such a task was solved by the author in relation to the resistance found in the water heating systems. Consider now this issue for mechanical systems in and square. Below are the results of approximation of data for unified tees (branch sites) on the passage. General form The dependencies were chosen on the basis of physical considerations, taking into account the convenience of using the obtained expressions while ensuring a permissible deviation from tabular data:

It is easy to notice that the relative facility of the Fn 'passage under the injection or respectively, the foal branch effect affects the CCM in the same way, namely, with increasing Fn' or FO ', the resistance will decrease, and the numerical coefficient at the same parameters in all the above formulas one and that same, namely (-0.25). In addition, and for airflow, and for exhaust tees when the air flow rate changes in the branch, the relative minimum of the CCM takes place at the same level LO '\u003d 0.2.

These circumstances suggest that the expressions obtained, despite their simplicity, sufficiently reflect general physical patterns underlying the influence of the parameters under study on the pressure loss in the tees of any type. In particular, the more Fn 'or Fo', i.e. The closer they are to one, the less the flow structure when the resistance is changed, which means that less than the CCM.

For the magnitude of the LO 'dependence is more complex, but here it will be the total two modes of air movement. The idea of \u200b\u200bthe degree of conformity of the considered relations and the initial CMS values \u200b\u200bgives rice. 1, where the results of processing table 22.37 for CMC unified tees (branch assemblies) on the passage of circular and rectangular cross section in injection. Approximately the same picture is also obtained for approximation Table. 22.38 with formula (3).

Note that, although in the latter case we are talking about a circular section, it is not difficult to make sure that the expression (3) successfully describes the data of the table. 22.39, related to rectangular nodes. The error of the formula for CCC is mainly 5-10% (as much as possible up to 15%). Some higher deviations can give expression (3) for tees during suction, but here this can be considered satisfactory, taking into account the complexity of resistance changes in such elements.

In any case, the nature of the dependence of the CMS from the factors affecting it here is reflected very well. In this case, the obtained ratios do not require any other source data, except for the aerodynamic calculation available in the table. In fact, it should be indicated in it explicitly and the costs of air, and section on the current and in the neighboring plot included in the listed formulas should be indicated. This particularly simplifies calculations when using MS Excel spreadsheets.

At the same time, the formulas given in the present work is very simple, visual and easily accessible to engineering calculations, especially in MS Excel, as well as in the educational process. Their use allows you to abandon the interpolation of tables while maintaining the accuracy required for engineering calculations, and directly calculate the CMS tees on the passage with a wide variety of sections and air costs in the trunk and branches.

This is quite enough to design systems in and square in most residential and public buildings.

Programs may be useful to designers, managers, engineers. Basically, to use the programs enough Microsoft Excel.. Many program authors are not known. I would like to note the work of these people who, on the basis of Excel, was able to prepare such useful settlement programs. Estimated ventilation and air conditioning programs are free for download. But, do not forget! It is impossible to believe the program, check its data.

Sincerely, site administration

By this material, the editors of the Climate World magazine continues the publication of chapters from the book "Ventilation and Air Conditioning. Design Recommendations for
Water and public buildings. " Author Krasnov Yu.S.

The aerodynamic calculation of the air ducts begin with the drawing of the axonometric scheme (M 1: 100), the stations of the areas of the sections, their loads L (m 3 / h) and lengths I (m). Determine the direction of the aerodynamic calculation - from the most remote and loaded portion to the fan. If doubt, when determining the direction, all possible options are calculated.

Calculation starts from a remote section: Determine the diameter D (m) of the round or area F (M 2) of the cross section of the rectangular duct:

Speed \u200b\u200bgrows as the fan approaches.

By Appendix N from the nearest standard values: D CT or (A X B) ST (M).

Hydraulic radius of rectangular ducts (M):

where is the sum of the coefficients of local resistances on the area of \u200b\u200bthe air ducts.

Local resistance on the border of two sites (tees, crossmen) refer to a plot with less consumption.

The coefficients of local resistances are given in applications.

Scheme of the supply system of ventilation serving 3-storey administrative building

Example of calculation

Initial data:

Air ducts are made of galvanized thin polystylene steel, the thickness and size of which corresponds to the ad. H out Material air intake mine - brick. As an air distributors, an adjustable type of PR type with possible sections are applied: 100 x 200; 200 x 200; 400 x 200 and 600 x 200 mm, the shading coefficient of 0.8 and the maximum air velocity at an output to 3 m / s.

Resistance of the receiving warmed valve with fully open blades of 10 Pa. Hydraulic resistance of the caloric installation of 100 Pa (according to a separate calculation). Filter resistance G-4 250 Pa. Hydraulic resistance of the muffler 36 Pa (acoustic calculation). Based on architectural requirements, rectangular ducts design.

The sections of brick channels are taken in Table. 22.7.

The coefficients of local resistances

Plot 1. Grating PP at the exit of a cross section of 200 × 400 mm (calculated separately):

Plots number	View of local resistance	Sketch	Angle α, hail.	Attitude			Justification	KSM
				F 0 / F 1	L 0 / L ST	F Prok / F
1	Diffuser		20	0,62	—	—	Table. 25.1	0,09
	Out		90	—	—	—	Table. 25.11	0,19
	Tee-pass		—	—	0,3	0,8	Arr. 25.8.	0,2
							∑ =	0,48
2	Tee-pass		—	—	0,48	0,63	Arr. 25.8.	0,4
3	Tee-branched		—	0,63	0,61	—	Arr. 25.9	0,48
4	2 Top	250 × 400.	90	—	—	—	Arr. 25.11
	Out	400 × 250.	90	—	—	—	Arr. 25.11	0,22
	Tee-pass		—	—	0,49	0,64	Table. 25.8.	0,4
							∑ =	1,44
5	Tee-pass		—	—	0,34	0,83	Arr. 25.8.	0,2
6	Diffuser after fan		H \u003d 0.6	1,53	—	—	Arr. 25.13	0,14
	Out	600 × 500.	90	—	—	—	Arr. 25.11	0,5
							∑=	0,64
6A.	Confuus in front of the fan			D g \u003d 0.42 m			Table. 25.12.	0
7	Knee		90	—	—	—	Table. 25.1	1,2
	Ladge jelly						Table. 25.1	1,3
							∑ =	1,44
Table 2. Definition of local resistances

Krasnov Yu.S.,

"Ventilation and air conditioning systems. Recommendations for the design for production and public buildings ", Chapter 15." Thermocul "

• Refrigerators and refrigeration units. Design Example Refrigeration Centers
• "Calculation of thermal balance, moisture receipts, air exchange, construction of J- D diagrams. Multi zone air conditioning. Examples of solutions "
• Designer. Materials of the magazine "World of Climate"
  • Basic air parameters, Filter classes, Calculating Calf Power, Standards and Regulatory Documents, Table of Physical Values
  • Separate technical solutions, equipment
  What is an elliptical plug and why it is needed
The impact of existing temperature standards for power consumption data centers New methods for improving the energy efficiency of the air conditioning systems of data processing centers Improving the efficiency of solid fuel fireplace Heat utilization systems in refrigeration Vinural microclimate and equipment for its creation Selection of equipment for specialized outdoor air supply systems (DOAS) Tunnel ventilation system. TLT-TURBO GMBH Application of Wesper equipment in the complex for the deep processing of oil of the enterprise "Kirishinefteorgsintez" Air exchange control in laboratory premises Complex use of air distribution systems in underground channels (UFAD) in combination with cooling beams Tunnel ventilation system. Selection of ventilation scheme Calculation of air-thermal curtains based on a new type of presentation of experimental data on thermal and mass losses Experience in creating a decentralized ventilation system during the reconstruction of the building Cold beams for laboratories. Using double energy recovery Ensuring reliability at the design stage Disposal heat released during the operation of the refrigeration plant of an industrial enterprise
• Methods of aerodynamic calculation of air ducts
Methods of selection of split-system from Daichi Vibration characteristics of fans New standard design of thermal insulation Applied Questions Classification of Rooms for Climate Parameters Optimization of control and structure of ventilation systems Variators and drainage pumps from EDC New Reference Edition from Avok New approach to the construction and operation of cooling systems of air conditioning buildings

After selecting the diameter or dimensions of the section, the air velocity is specified:, m / s, where F f is the actual sectional area, m 2. For round air ducts for square for rectangular m 2. In addition, the equivalent diameter, mm, is calculated for rectangular air ducts. Square equivalent diameter is equal to the side of the square.

You can also use the approximate formula . Its error does not exceed 3 - 5%, which is enough for engineering calculations. Full loss of friction pressure for the entire section RL, Pa, obtained by multiplying the specific loss R to the length of the L. If ducts or channels from other materials are used, it is necessary to introduce an amendment to the roughness β w. It depends on the absolute equivalent roughness of the material of the duct to E and the value of V f.

Absolute equivalent duct material roughness:

The values \u200b\u200bof the amendment β sh:

For steel and viniplast air ducts β sh \u003d 1. More detailed values β w can be found in Table 22.12. Taking into account this amendment, refined loss of pressure on the friction RLβ W, Pa, obtained by multiplying RL by β sh.

Then the dynamic pressure on the plot, Pa. Here ρ B is the density of the transported air, kg / m 3. Typically take ρ B \u003d 1.2 kg / m 3.

The "Local Resistance" column records the names of the resistance (tap, tee, cross, knee, grille, ceiling, umbrella, etc.) available in this area. In addition, their number and characteristics on which the CMC values \u200b\u200bare defined for these elements. For example, for a round removal, this is the angle of rotation and the ratio of the rotation radius to the diameter of the radius R / D, for a rectangular removal, an angle of rotation and sizes of the sides of the air duct A and b. For side holes in the air duct or channel (for example, in the place of installation of the air intake lattice) - the ratio of the area of \u200b\u200bthe hole to the cross section of the air duct F dv / f about. For tees and crossbars on the aisle, the attitude of the cross-section of the passage of the passage and the trunk F p / f C and the flow rate in the branch and in the trunk l О / l C, for tees and crossbars on the branch - the ratio of the area of \u200b\u200bthe cross section of the branch and the barrel F C / F C and Again the magnitude l about / l with. It should be borne in mind that each tee or crosses connect two adjacent areas, but they relate to that of these areas, which has less air flow. The difference between tees and crossbars on the passage and on the branch is due to how the calculated direction passes. This is shown in the following figure.

Here, the estimated direction is depicted in a fatty line, and the directions of air flows are thin arrows. In addition, it signed, where exactly in each version is the trunk, passage and branch of the tee for right choice Relations F P / F C, F O / F C and L O / L C. Note that in the supply systems, the calculation is usually carried out against the movement of air, and in the exhaust - along this movement. Plots to which the tees under consideration are indicated by checkmarks. The same applies to crosses. As a rule, although not always, tees and crossmen on the passage appear when calculating the main direction, and on the branch appear in the aerodynamic linking of minor sites (see below). In this case, the same tee in the main direction can be taken into account as a tee on the passage, and on the secondary - as a branch with another coefficient.

Exemplary values \u200b\u200bξ for frequent resistance are shown below. Lattices and ceiling are taken into account only on end areas. Camsal coefficients are accepted in the same size as for the corresponding tees.

The values \u200b\u200bξ of some local resistance.

*) Negative CMC may occur at small L О / l with an ejection (suction) of air from the branch of the main flow.

More detailed data for CCM are listed in Tables 22.16 - 22.43. After determining the value of σξ, the pressure losses on local resistances, Pa, and the total pressure loss on the RLβ segment sh + z, Pa was calculated. When the calculation of all parts of the main direction is completed, the values \u200b\u200bof RLβ sh + z are summed up for them and the overall resistance of the ventilation network ΔP \u003d σ (RLβ S + Z) is determined. The value of the ΔP network serves as one of the source data for selecting the fan. After selecting the fan in supply system The acoustic calculation of the ventilation network is made (see chapter 12) and if necessary, the silencer is selected.

The results of the calculations are recorded in the table according to the following form.

After calculating the main direction, a linkage of one - two branches is made. If the system serves several floors, it is possible to choose floor branches on intermediate floors. If the system serves one floor, branches are listed from the highway that are not included in the main direction (see example in clause 2.3). The calculation of the linked areas is made in the same sequence as for the main direction, and is recorded in the table in the same form. The link is considered to be made if the sum of the pressure loss σ (rlβ sh + z) along the linked areas deviates from the sum σ (Rlβ sh + Z) along the parallel plots of the main direction by no more than ± 10%. Parallel attached areas along the main and linked direction from the point of branching to the terminal air distributors. If the scheme looks like shown in the following figure (the main direction is highlighted with a fat line), then the direction of direction 2 requires that the value of RLβ sh + z for section 2 is equal to RLβ W + Z for section 1 obtained from the calculation of the main direction, with accuracy ± 10%.

When the air flow moves in air ducts and channels of ventilation and air conditioning systems (B and KV), except for the loss of friction pressure, losses on local resistances - shaped parts of air ducts, air distributors and network equipment play a significant role.

Such losses are proportional to dynamic pressure. r d \u003d ρ. v.² / 2, where ρ is the density of air, 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 cross section of the channel for resistance.

The ratios of the proportionality ξ, called the coefficients of local resistance (CCM), for various elements of systems in and kV are usually determined by tables available, in particular, in and in a number of other sources. The greatest complexity at the same time is most often called KMS for tees or branch sites. The fact is that in this case it is necessary to take into account the type of tee (on the passage or on the branch) and the mode of air movement (discharge or suction), as well as the ratio of air flow rate in the branch to the flow rate in the trunk L'O \u003d L O / L C and cross-sectional area of \u200b\u200bthe trunk cross section F'n \u003d F p / f with.

For tees during suction, it is necessary to take into account the ratio of the area of \u200b\u200bthe branch cross section to the area of \u200b\u200bthe trunk cross section F'O \u003d F o / f with. In the manual, the relevant data is shown in Table. 22.36-22.40. However, when calculating using EXCEL's spreadsheets, which is currently quite common due to the wide use of various standard software and the ease of registration of the results of calculations, it is desirable to have analytical formulas for CCC, at least in the most common ranges of changes in the characteristics of tees.

In addition, it would be advisable in the educational process to reduce technical work Studying and transferring the main load on the development of constructive solutions of systems.

Such formulas are available in such a fairly fundamental source, as, but they are presented in a very generalized form, without taking into account the design features of the specific elements of existing ventilation systemsAnd also use a significant number of additional parameters and require in some cases access to specific tables. On the other hand, the programs that have recently appeared for the automated aerodynamic calculation of systems in and kV are used by some algorithms to determine the CMC, but, as a rule, they are unknown for the user and may therefore cause doubts about their validity and correctness.

Also, some work are currently emerging, the authors of which continue to research on clarifying the CMS calculation or expansion of the parameter range of the corresponding element of the system, for which the results obtained will be fair. These publications arise both in our country and abroad, although in general their number is not too large, and are based primarily on the numerical modeling of turbulent flows using a computer or direct experimental studies. However, the data obtained by the authors, as a rule, is difficult to use in the practice of mass design, since they are not yet represented in engineering.

In this regard, it is advisable to analyze the data contained in the tables and obtaining approximation dependencies on them, which would have the easiest and most convenient appearance for engineering practices and at the same time quite adequately reflect the nature of the dependences for CMC tees. For the most common varieties - tees on the passage (unified branches), this task was solved by the author in the work. At the same time, for tees on the branch, analytical ratios are harder to find, since the dependencies themselves look more difficult. The general appearance of the approximation formulas, as always in such cases, it turns out on the basis of location settlement points On the correlation field, and the corresponding coefficients are selected by the least squares method in order to minimize the deviation of the designed schedule using Excel. Then for some of the most common ranges F P / F C, F O / F C and L O / L with You can get expressions:

for L'O. \u003d 0.20-0.75 I. F'O.\u003d 0.40-0.65 - for tees in disposal (supply);

for L'O. = 0,2-0,7, F'O. \u003d 0.3-0.5 I. F. P. \u003d 0.6-0.8 - for tees during suction (exhaust).

The accuracy of dependencies (1) and (2) demonstrate Fig. 1 and 2, where the results of processing Table are shown. 22.36 and 22.37 for CMC unified tees (branching sites) on the branch of the circular section during suction. In the case of rectangular section, the results will differ insignificant.

It can be noted that the discrepancy here is greater than for tees on the passage, and averages 10-15%, sometimes even up to 20%, but for engineering calculations it may be permissible, especially with the obvious source 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 source data except the aerodynamic calculation in the table. In fact, it should be indicated in it explicitly and the costs of air, and section on the current and in the neighboring plot included in the listed formulas should be indicated. First of all, it simplifies calculations when applying Excel spreadsheets. At the same time rice. 1 and 2 make sure that the analytic dependences found quite adequately reflect the nature of the influence of all the main factors on the KSC tees and the physical essence of the processes occurring in them when the air flow moves.

At the same time, the formulas given in the present work are very simple, visual and easily accessible to engineering calculations, especially in Excel, as well as in the educational process. Their use allows you to abandon the interpolation of tables while maintaining the accuracy required for engineering calculations, and directly calculate the coefficients of the local resistance of tees on the branch in a very wide range of relationships and air costs in the trunk and branches.

This is quite enough to design ventilation and air conditioning systems in most residential and public buildings.

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