Local resistance of T-piece for ventilation. Determination of local resistance coefficients of tees in ventilation systems. Correction values ​​β w

You can also use the 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 pressure loss due to friction for the entire section is obtained by multiplying the specific losses R by the length of the section 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 air duct material K e (Table 3) and the value v f .

					table 2
		Correction values ​​βsh
v f , m/s			βsh at values ​​of K e, mm

Table 3 Absolute equivalent roughness of air duct material

						Plasterer-
						on the grid
K e, mm

For steel air ducts βsh = 1. More detailed values ​​of βsh can be found in table. 22.12. Taking into account this amendment, the updated friction pressure loss Rl βsh, Pa, is obtained by multiplying Rl by the value βsh. Then the dynamic pressure on the participants is determined

under standard conditions ρw = 1.2 kg/m3.

Next, local resistances are identified in the area, local resistance coefficients (LRC) ξ are determined, and the sum of the IMR in this area (Σξ) is calculated. All local resistances are recorded in the following form.

SHEET KMS VENTILATION SYSTEMS

Etc.

IN the “local resistance” column records the names of the resistances (bend, tee, cross, elbow, grille, air distributor, umbrella, etc.) available in this area. In addition, their quantity and characteristics are noted, by which the CMR values ​​are determined for these elements. For example, for a round outlet this is the angle of rotation and the ratio of the radius of rotation to the diameter of the duct r /d, for a rectangular outlet - the angle of rotation and dimensions of the sides of the air duct a and b. For side openings in an air duct or channel (for example, at the location where an air intake grille is installed) - the ratio of the area of ​​the opening to the cross-section of the air duct

f otv / f o . For tees and crosses on the passage, the ratio of the cross-sectional area of ​​the passage and the trunk f p /f s and the flow rate in the branch and in the trunk L o /L s is taken into account, for tees and crosses on the branch - the ratio of the cross-sectional area of ​​the branch and the trunk f p /f s and again the value of L o / L c . It should be borne in mind that each tee or cross connects two adjacent sections, but they relate to the one of these sections with less air flow L. The difference between tees and crosses on a pass and on a branch has to do with how the design direction runs. This is shown in Fig. 11. Here the calculated direction is depicted by a thick line, and the directions of air flows are depicted by thin arrows. In addition, it is signed where exactly in each option the barrel, passage and opening are located.

tee branching for the right choice relations fп/fс, fo/fс and Lо/Lс. Note that in supply ventilation systems the calculation is usually carried out against the air movement, and in exhaust ventilation systems - along this movement. The areas to which the tees in question belong are indicated with check marks. The same applies to crosses. As a rule, although not always, tees and crosses on the passage appear when calculating the main direction, and on the branch they appear when aerodynamically linking secondary sections (see below). In this case, the same tee in the main direction can be taken into account as a tee for passage, and in the secondary direction

– as a branch with a different coefficient. KMS for crosses

accepted in the same size as for the corresponding tees.

Rice. 11. Tee calculation diagram

Approximate values ​​of ξ for commonly encountered resistances are given in Table. 4.

			Table 4
Values ​​ξ of some local resistances
Name		Name
resistance		resistance
Round bend 90o,		The grille is not adjustable
r/d = 1		May RS-G (exhaust or
Rectangular bend 90°		air intake)
Tee on the passage (on-		Sudden expansion
oppression)
Tee on branch		Sudden contraction
Tee on the passage (all-		The first side hole
		sity (entrance into air intake
Tee on branch	–0.5* …	boron mine)
Lamp lamp (anemostat) ST-KR,		Rectangular elbow
		90o
Adjustable grille RS-		Umbrella over the exhaust
VG (supply)

*) negative CMR can occur at low Lo/Lс due to the ejection (suction) of air from the branch by the main flow.

More detailed data for KMS are shown in table. 22.16 – 22.43. For the most common local resistances -

tees in 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)
– for tees during discharge (supply);
at L"	0.4 you can use a simplified formula
			prox pr 0. 425 0. 25 f p ";
		0.2 1.7 f"		0.35 0.25f"		2.4L"		0. 2 2

– for suction (exhaust) tees.

Here L"						f o	and f"		f p
						f with

After determining the value of Σξ, calculate the pressure loss at local resistances Z P d , Pa, and the total pressure loss

leniya in the area Rl βш + Z, Pa.

The calculation results are entered into a table in the following form.

AERODYNAMIC CALCULATION OF THE VENTILATION SYSTEM

Calculated

Duct dimensions

pressure

for friction

Rlβ w

Rd,

βsh

d or

f op,

ff,

Vf,

d eq

l, m

a×b,

When the calculation of all sections of the main direction is completed, the values ​​of Rl βш + Z for them are summed up and the total resistance is determined.

ventilation network P network = Σ(Rl βш + Z ).

After calculating the main direction, one or two branches are linked. If the system serves several floors, you can select floor branches on intermediate floors for linking. If the system serves one floor, branches from the main line that are not included in the main direction are linked (see example in paragraph 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 completed if the amount

pressure loss Σ(Rl βш + Z) along the linked sections deviates from the sum Σ(Rl βш + Z) along the parallel connected sections of the main direction by no more than 10%. Parallel connected sections are considered to be sections along the main and linked directions from the point of their branching to the end air distributors. If the circuit looks like shown in Fig. 12 (the main direction is highlighted with a thick line), then linking direction 2 requires that the value of Rl βш + Z for section 2 be equal to Rl βш + Z for section 1, obtained from the calculation of the main direction, with an accuracy of 10%. Linking is achieved by selecting the diameters of round or section sizes of rectangular air ducts in the linked areas, and if this is not possible, by installing throttle valves or diaphragms on the branches.

Fan selection should be made according to the manufacturer’s catalogs or data. The fan pressure is equal to the sum of pressure losses in the ventilation network in the main direction, determined during the aerodynamic calculation of the ventilation system, and the sum of pressure losses in the elements of the ventilation unit ( air valve, filter, air heater, silencer, etc.).

Rice. 12. Fragment of the ventilation system diagram with the choice of branch for linking

It is possible to finally select a fan only after an acoustic calculation, when the issue of installing a noise suppressor has been decided. An acoustic calculation can only be performed after preliminary selection of a fan, since the initial data for it are the levels of sound power emitted by the fan into the air ducts. Acoustic calculations are performed following the instructions in Chapter 12. If necessary, calculate and determine the standard size of the silencer, then finally select the fan.

4.3. An example of calculating a supply ventilation system

Under consideration supply system ventilation for the dining room. The drawing of air ducts and air distributors on the plan is given in paragraph 3.1 in the first version ( typical diagram for halls).

System diagram

1000x400 5 8310 m3/h

	2772 m3/h2

More details about the calculation methodology and the necessary initial data can be found at. The corresponding terminology is given in.

SHEET KMS SYSTEM P1

		Local resistance
		924 m3/h
		1. Round bend 90o r /d =1
		2. Tee on the passage (discharge)
		fп/fc		Lo/Lc
		fп/fc		Lo/Lc
		1. Tee on the passage (discharge)
		fп/fc		Lo/Lc
		1. Tee on the passage (discharge)
		fп/fc		Lo/Lc
		1. Rectangular bend 1000×400 90o 4 pcs.
		1. Air intake shaft with umbrella
		(first side hole)
		1. Louvered air intake grille
	SHEET OF KMS SYSTEM P1 (BRANCH No. 1)
		Local resistance
		1. Air distributor PRM3 at flow rate
		924 m3/h
		1. Round bend 90o r /d =1
		2. Branch tee (discharge)
		fo/fc		Lo/Lc

APPENDIX Characteristics ventilation grilles and lampshades

I. Clear cross-sections, m2, of supply and exhaust louver grilles RS-VG and RS-G

Length, mm			Height, mm

Speed ​​coefficient m = 6.3, temperature coefficient n = 5.1.

II. Characteristics of lampshades ST-KR and ST-KV

Name		Dimensions, mm		f fact, m 2
		Dimensional	Interior
Lamp ST-KR
(round)
Lamp ST-KV
(square)

Speed ​​coefficient m = 2.5, temperature coefficient n = 3.

BIBLIOGRAPHICAL LIST

1. Samarin O.D. Selection of air supply equipment ventilation units(air conditioners) type KTsKP. Guidelines for completing coursework and diploma projects for students of specialty 270109 “Heat and gas supply and ventilation.” – M.: MGSU, 2009. – 32 p.

2. Belova E.M. Central systems air conditioning in buildings. – M.: Euroclimate, 2006. – 640 p.

3. SNiP 41-01-2003 “Heating, ventilation and air conditioning”. – M.: State Unitary Enterprise TsPP, 2004.

4. Catalog of Arktos equipment.

5. sanitary facilities. Part 3. Ventilation and air conditioning. Book 2. / Ed. N.N. Pavlov and Yu.I. Schiller. – M.: Stroyizdat, 1992. – 416 p.

6. GOST 21.602-2003. System of design documents for construction. Execution Rules working documentation heating, ventilation and air conditioning. – M.: State Unitary Enterprise 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's Handbook. Domestic sanitary facilities. Part 3. Ventilation and air conditioning. Book 1. / Ed. N.N. Pavlov and Yu.I. Schiller. – M.: Stroyizdat, 1992. – 320 p.

9. Kamenev P.N., Tertichnik E.I. Ventilation. – M.: ASV, 2006. – 616 p.

10. Krupnov B.A. Terminology on building thermal physics, heating, ventilation and air conditioning: guidelines for students of the specialty "Heat and Gas Supply and Ventilation".

The programs can be useful to designers, managers, and engineers. Basically, Microsoft Excel is enough to use the programs. Many program authors are unknown. I would like to acknowledge the work of these people, who were able to prepare such useful calculation programs using Excel. Calculation programs for ventilation and air conditioning are free to download. But, don't forget! You cannot absolutely trust the program; check its data.

Sincerely, site administration

Especially useful for engineers and designers in the field of design engineering structures and sanitary systems. Developer Vlad Volkov

An updated calculator was sent by user ok, for which Ventportal thanks him!

Program for calculating thermodynamic parameters humid air or a mixture of two streams. Convenient and intuitive interface; the program does not require installation.

The program converts values ​​from one measurement scale to another. The "Transformer" knows the most commonly used, less common and outdated measures. In total, the program database contains information about 800 measures, many of which have brief information. There are possibilities to search the database, sort and filter records.

The Vent-Calc program was created for the calculation and design of ventilation systems. The program is based on the method of hydraulic calculation of air ducts using the Altschul formulas given in

A program for converting various units of measurement. Program language - Russian/English.

The program algorithm is based on the use of an approximate analytical method for calculating changes in air condition. The calculation error is no more than 3%

Creating comfortable living conditions in premises is impossible without aerodynamic calculation of air ducts. Based on the data obtained, the cross-sectional diameter of the pipes, the power of the fans, the number and features of the branches are determined. Additionally, the power of heaters and the parameters of inlet and outlet openings can be calculated. Depending on the specific purpose of the rooms, the maximum permissible noise level, air exchange rate, direction and speed of flows in the room are taken into account.

Modern requirements are specified in the Code of Rules SP 60.13330.2012. Normalized parameters of microclimate indicators in premises for various purposes are given in GOST 30494, SanPiN 2.1.3.2630, SanPiN 2.4.1.1249 and SanPiN 2.1.2.2645. During calculation of indicators ventilation systems all provisions must be taken into account.

Aerodynamic calculation of air ducts - algorithm of actions

The work includes several successive stages, each of which solves local problems. The obtained data is formatted in the form of tables, and based on them, schematic diagrams and graphs are drawn up. The work is divided into the following stages:

1. Development of an axonometric diagram of air distribution throughout the system. Based on the diagram, a specific calculation methodology is determined, taking into account the features and tasks of the ventilation system.
2. An aerodynamic calculation of air ducts is performed both along the main routes and all branches.
3. Based on the data obtained, the geometric shape and cross-sectional area of ​​the air ducts are selected, and the technical parameters of fans and air heaters are determined. Additionally, the possibility of installing fire extinguishing sensors, preventing the spread of smoke, and the possibility of automatically adjusting the ventilation power taking into account the program compiled by the users are taken into account.

Development of a ventilation system diagram

Depending on the linear parameters of the diagram, the scale is selected; the diagram indicates the spatial position of the air ducts, points of connection of additional technical devices, existing branches, places of air supply and intake.

The diagram indicates the main line, its location and parameters, connection points and technical characteristics of the branches. The location of air ducts takes into account the architectural characteristics of the premises and the building as a whole. During compilation supply circuit The calculation procedure begins from the point furthest from the fan or from the room for which the maximum air exchange rate is required. During compilation exhaust ventilation the main criterion is taken maximum values by air flow. During calculations, the general line is divided into separate sections, and each section must have the same cross-sections of air ducts, stable air consumption, the same manufacturing materials and pipe geometry.

The segments are numbered in sequence from the section with the lowest flow rate and in increasing order to the highest. Next, the actual length of each individual section is determined, the individual sections are summed up, and the total length of the ventilation system is determined.

When planning a ventilation scheme, they can be taken as common for the following premises:

• residential or public in any combination;
• industrial, if they belong to group A or B according to the fire safety category and are located on no more than three floors;
• one of the categories of industrial buildings categories B1 - B4;
• category industrial buildings B1 m B2 are allowed to be connected to one ventilation system in any combination.

If the ventilation systems completely lack the possibility of natural ventilation, then the diagram must provide for the mandatory connection of emergency equipment. The power and installation location of additional fans are calculated according to general rules. For rooms that have openings that are constantly open or open when necessary, the diagram can be drawn up without the possibility of a backup emergency connection.

Systems for suctioning contaminated air directly from technological or work areas must have one backup fan; turning the device into operation can be automatic or manual. The requirements apply to work areas of hazard classes 1 and 2. It is allowed not to include a backup fan in the installation diagram only in the following cases:

1. Synchronous stop of harmful production processes in case of disruption of the functionality of the ventilation system.
2. IN production premises Separate emergency ventilation with its own air ducts is provided. Such ventilation parameters must remove at least 10% of the volume of air provided by stationary systems.

The ventilation scheme must provide a separate possibility of showering on workplace with increased levels of air pollution. All sections and connection points are indicated on the diagram and included in the general calculation algorithm.

It is prohibited to place air receiving devices closer than eight meters horizontally from garbage dumps, car parking areas, roads with heavy traffic, exhaust pipes and chimneys. Air receiving devices must be protected with special devices on the windward side. Resistance indicators protective devices are taken into account during aerodynamic calculations of the overall ventilation system.
Calculation of air flow pressure loss Aerodynamic calculation of air ducts based on air losses is done in order to correctly select sections to ensure technical requirements system and selection of fan power. Losses are determined by the formula:

R yd is the value of specific pressure losses in all sections of the air duct;

P gr – gravitational air pressure in vertical channels;

Σ l – the sum of individual sections of the ventilation system.

Pressure losses are obtained in Pa, the length of sections is determined in meters. If the movement of air flows in ventilation systems occurs due to a natural pressure difference, then the calculated pressure reduction is Σ = (Rln + Z) for each individual section. To calculate the gravitational pressure you need to use the formula:

P gr – gravitational pressure, Pa;

h – height of the air column, m;

ρ n – air density outside the room, kg/m3;

ρ in – indoor air density, kg/m3.

Further calculations for natural ventilation systems are performed using the formulas:

Definition cross section air ducts

Determination of the speed of movement of air masses in gas ducts

Calculation of losses based on local resistances of the ventilation system

Determination of friction loss

Determination of air flow speed in channels
The calculation begins with the longest and most remote section of the ventilation system. As a result of aerodynamic calculations of air ducts, the required ventilation mode in the room must be ensured.

The cross-sectional area is determined by the formula:

F P = L P /V T .

F P – cross-sectional area of ​​the air channel;

L P – actual air flow in the calculated section of the ventilation system;

V T – speed of air flow to ensure the required frequency of air exchange in the required volume.

Taking into account the results obtained, the pressure loss during the forced movement of air masses through the air ducts is determined.

For each air duct material, correction factors are applied, depending on the surface roughness indicators and the speed of movement of air flows. To facilitate aerodynamic calculations of air ducts, you can use tables.

Table No. 1. Calculation of metal air ducts of round profile.

Table No. 2. Values ​​of correction factors taking into account the material of air ducts and air flow speed.

The roughness coefficients used for calculations for each material depend not only on its physical characteristics, but also on the speed of air flow. The faster the air moves, the more resistance it experiences. This feature must be taken into account when selecting a specific coefficient.

Aerodynamic calculations for air flow in square and round air ducts show different flow rates for the same cross-sectional area conditional passage. This is explained by differences in the nature of vortices, their meaning and ability to resist movement.

The main condition for calculations is that the speed of air movement constantly increases as the area approaches the fan. Taking this into account, requirements are imposed on the diameters of the channels. In this case, the parameters of air exchange in the premises must be taken into account. The locations of the inflow and outlet flows are selected in such a way that people staying in the room do not feel drafts. If it is not possible to achieve the regulated result using a straight section, then diaphragms with through holes are inserted into the air ducts. By changing the diameter of the holes, optimal regulation of air flow is achieved. The diaphragm resistance is calculated using the formula:

The general calculation of ventilation systems should take into account:

1. Dynamic air pressure during movement. The data is consistent with terms of reference and serve as the main criterion when choosing a specific fan, its location and operating principle. If it is impossible to ensure the planned operating modes of the ventilation system with one unit, installation of several is provided. Specific place their installation depends on the features schematic diagram air ducts and permissible parameters.
2. The volume (flow rate) of transported air masses in the context of each branch and room per unit of time. Initial data - requirements of sanitary authorities for cleanliness of the premises and features technological process industrial enterprises.
3. Unavoidable pressure losses resulting from vortex phenomena during the movement of air flows at various speeds. In addition to this parameter, the actual cross-section of the air duct and its geometric shape are taken into account.
4. Optimal air movement speed in the main channel and separately for each branch. The indicator influences the choice of fan power and their installation locations.

To facilitate calculations, it is allowed to use a simplified scheme; it is used for all premises with non-critical requirements. To guarantee the required parameters, the selection of fans in terms of power and quantity is done with a margin of up to 15%. Simplified aerodynamic calculations of ventilation systems are performed using the following algorithm:

1. Determination of the cross-sectional area of ​​the channel depending on the optimal speed of air flow.
2. Selecting a standard channel cross-section close to the design one. Specific indicators should always be selected upward. Air channels may be enlarged technical indicators, it is prohibited to reduce their capabilities. If it is impossible to select standard channels in technical conditions It is envisaged that they will be manufactured according to individual sketches.
3. Checking air speed indicators taking into account the actual values ​​of the conventional cross-section of the main channel and all branches.

The task of aerodynamic calculation of air ducts is to ensure the planned ventilation rates of premises with minimal losses of financial resources. At the same time, it is necessary to strive to reduce the labor intensity and metal consumption of construction and installation work, to ensure the reliable operation of the installed equipment in various modes.

Special equipment must be installed in accessible places, with unhindered access to it for routine technical inspections and other work to maintain the system in working order.

According to the provisions of GOST R EN 13779-2007 for calculating ventilation efficiency ε v you need to apply the formula:

with ENA– indicators of the concentration of harmful compounds and suspended substances in the removed air;

With IDA– concentration of harmful chemical compounds and suspended substances in the room or work area;

c sup– indicators of contaminants entering with the supply air.

The efficiency of ventilation systems depends not only on the power of the connected exhaust or blower devices, but also on the location of the sources of air pollution. During aerodynamic calculations, the minimum performance indicators of the system must be taken into account.

Specific power (P Sfp > W∙s / m 3) of fans is calculated using the formula:

de P – power of the electric motor installed on the fan, W;

q v – air flow rate supplied by the fans during optimal operation, m 3 /s;

∆ p – indicator of the pressure drop at the air inlet and outlet of the fan;

η tot is the total efficiency for the electric motor, air fan and air ducts.

During calculations, the following types of air flows are taken into account according to the numbering in the diagram:

Diagram 1. Types of air flows in the ventilation system.

1. External, enters the air conditioning system from the external environment.
2. Supply. Air flows supplied to the air duct system after preliminary preparation (heating or cleaning).
3. The air in the room.
4. Flowing air currents. Air moving from one room to another.
5. Exhaust. Air exhausted from the room to the outside or into the system.
6. Recirculating. The portion of the flow returned to the system to maintain the internal temperature within the specified values.
7. Removable. Air that is removed from the premises irrevocably.
8. Secondary air. Returned back to the room after cleaning, heating, cooling, etc.
9. Air loss. Possible leaks due to leaky air duct connections.
10. Infiltration. The process of air entering indoors naturally.
11. Exfiltration. Natural air leakage from the room.
12. Air mixture. Simultaneous suppression of multiple threads.

Each type of air has its own state standards. All calculations of ventilation systems must take them into account.

2017-08-15

UDC 697.9 Determination of local resistance coefficients of tees in ventilation systems O. D. Samarin, Ph.D., Associate Professor (National Research University MGSU) The current situation with determining the values ​​of local resistance coefficients (KMR) of ventilation network elements during 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 regarding the ease of using its data for carrying out engineering calculations using MS Excel spreadsheets are identified. The main results of approximation of the available tables for the KMS of unified tees on the branch during discharge and suction in ventilation and air conditioning systems are presented in the form of corresponding engineering formulas. An assessment of the accuracy of the obtained dependencies and the permissible range of their applicability is given, and recommendations for their use in the practice of mass design are presented. The presentation is illustrated with numerical and graphic examples. Keywords:local resistance coefficient, tee, branch, discharge, suction.

UDC 697.9 Determination of local resistance coefficients of teeth 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 definition of values ​​of coefficients of local resistance (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 identified 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 teas 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 air flow moves in air ducts and channels of ventilation and air conditioning systems (V and AC), in addition to pressure losses due to friction, a significant role is played by losses on local resistances - shaped parts of air ducts, air distributors and network equipment.

Such losses are proportional to the dynamic pressure R d = 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 cross section of the channel behind the resistance.

Proportionality coefficients ξ, called local resistance coefficients (KMC), for various elements of B and HF systems are usually determined from tables available, in particular, in a number of other sources. The greatest difficulty in this case is most often 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 (pass or branch) and the mode of air movement (discharge or suction), as well as the ratio of air flow in the branch to the flow in the trunk L´ o = L o /L c and the cross-sectional area of ​​the passage to the cross-sectional area of ​​the trunk F´ p = F p /F s.

For tees during suction, it is also necessary to take into account the ratio of the cross-sectional area of ​​the branch to the cross-sectional area of ​​the trunk F´ o = F o /F s. In the manual, the relevant data is given in table. 22.36-22.40. However, when carrying out calculations using Excel spreadsheets, which is currently quite common due to the widespread use of various standard software and ease of presentation of calculation results, it is desirable to have analytical formulas for CMS, at least in the most common ranges of changes in the characteristics of tees.

In addition, this would be advisable in the educational process to reduce technical work students and transferring the main load to development constructive solutions systems

Similar formulas are available in such a fairly 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 in some cases require reference to certain tables. On the other hand, programs that have appeared recently for automated aerodynamic calculations of B and HF systems use some algorithms to determine the CMC, but, as a rule, they are unknown to the user and may therefore raise doubts about their validity and correctness.

Also, at present, some works are appearing, 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 very large, and are based primarily on numerical modeling of turbulent flows using a computer or on direct experimental studies. 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 engineering form.

In this regard, it seems appropriate to analyze the data contained in the tables and obtain on their basis approximation dependencies that would have the simplest and most convenient form for engineering practice and at the same time would adequately reflect the nature of the existing dependencies for CMS tees. For their most common varieties - tees on the passage (unified branch nodes), this problem was solved by the author in the work. At the same time, it is more difficult to find analytical relationships for tees on a branch, since the dependencies themselves look more complex here. General form approximation formulas, as always in such cases, are obtained based on the location of the calculated points on the correlation field, and the corresponding coefficients are selected by the method least squares in order to minimize the deviation of the constructed 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 the expressions:

at L´ about= 0.20-0.75 and F´ about= 0.40-0.65 - for tees during discharge (supply);

at L´ about = 0,2-0,7, F´ about= 0.3-0.5 and F´ p= 0.6-0.8 - for suction (exhaust) tees.

The accuracy of dependencies (1) and (2) is demonstrated in Fig. 1 and 2, which show the results of processing the table. 22.36 and 22.37 for KMS unified tees (branch assemblies) on a round branch during suction. When rectangular section the results will differ insignificantly.

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 Simultaneously simplifying calculations when using Excel. At the same time, the obtained relationships do not require any other initial data other than those already available in the aerodynamic calculation table. In fact, it should explicitly indicate both air flow rates and cross sections at the current and at neighboring plot, included in the listed formulas. First of all, this simplifies calculations when using Excel spreadsheets. At the same time, Fig. 1 and 2 make it possible to verify that the found analytical dependencies quite adequately reflect the nature of the influence of all the main factors on the CMC of tees and the physical essence of the processes occurring in them during the movement of air flow.

In this case, 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 to directly calculate the local resistance coefficients of tees on a branch in a very wide range of cross-sectional ratios and air flow rates in the trunk and branches.

This is quite sufficient for the design of ventilation and air conditioning systems in most residential and public buildings.

1. Designer's Handbook. Internal sanitary installations. Part 3. Ventilation and air conditioning. Book 2 / Ed. N.N. Pavlova and Yu.I. Schiller. - M.: Stroyizdat, 1992. 416 p.
2. Idelchik I.E. Handbook of hydraulic resistance / Ed. M.O. Steinberg. - Ed. 3rd. - M.: Mechanical Engineering, 1992. 672 p.
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