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» Coefficient of local resistance of the duct transition. Aerodynamic calculation of air ducts

Coefficient of local resistance of the duct transition. Aerodynamic calculation of air ducts

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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 heat and electrical 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 medium velocities, 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 nozzles 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 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, at 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 dynamic pressure in the accepted 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 which design speed and, therefore, to which section it is reduced.


Exhaust and supply tees

It is known that a significant part 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 rate 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 shape, 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 the side branch, or straight passage) can be calculated using the following formulas.

Resistance in the lateral branch (in section B):

where Q B = F B w B, Q q = F q w q - volumetric flow rates in section B and C, respectively.

For tees of type F n = F c and for all a, the values ​​of A are given in table. one.



When the ratio Q b / Q q changes from 0 to 1, the resistance coefficient changes in the range from -0.9 to 1.1 (F q = F b, a = 90 O). Negative values ​​are 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 ​​the choke (with an increase in F c / F b). For example, when Q b / Q c = 1, F q / F b = 2, and = 90 O, the coefficient is 2.75.

Obviously, a decrease in resistance can be achieved by decreasing the angle of the lateral branch (choke). For example, when F c = F b, α = 45 O, when the ratio Q b / Q c changes from 0 to 1, the coefficient changes from -0.9 to 0.322, i.e. its positive values ​​are reduced by almost 3 times.

The resistance in the straight passage should be determined by the formula:

For tees of type Fn = F c, the values ​​of 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 = F b, α = 90 O).

Reducing the angle of the side branch (choke) also leads to a significant decrease in resistance. For example, when F c = F b, α = 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, "suction" appears in the direct passage, which further reduces 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 = 0.41 and is equal to 0.244 (with F c = F b, α = 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 = F c, the values ​​of A 1 are given in table. 3, K B = 0.



If we take F c = F b, a = 90 O, then when the ratio Q b / Q c changes from 0 to 1, we get the coefficient values ​​in 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 = 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 ​​in the range from 1 to 1.8 (F c = F b). In general, we will receive slightly higher values ​​for the resistance coefficients in all ranges.

The decisive influence on the growth of the drag coefficient, as in formula (1), is exerted by the cross-sectional area B (choke) - with an increase in F g / F b, the drag coefficient increases rapidly.

Resistance in the straight passage for supply tees type Fn = Fc within

The values ​​of t P are shown in table. 4.



When the ratio Q B / Qc changes (3 from 0 to 1 (Fc = F B, α = 90 O), we obtain the coefficient values ​​in the range from 0 to 0.3.

The resistance of conventional tees can also be significantly reduced by rounding off the junction of the lateral branch with the collecting sleeve. In this case, for exhaust tees, the angle of rotation of the flow 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 = 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 exhaust and supply tees. The combination of rounding, bevelling and side branch widening further reduces the resistance of the tee. Resistance coefficients of improved tees can be determined from 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 a turbulent flow (Re> 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 every formula. The sources provide 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 merging (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 ​​from 1.25 to 2 (for the case F c = F b). Obviously, dependence (5) has the form of an inverted parabola with a minimum at the point Q b / Q c = 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 = 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 = 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 using 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

Energy industry standards prescribe for pipelines in thermal power plants low pressure(at working 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. Reducing 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). The split 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 uniquely determined, it is advisable to use inclined unions (side branches) and tees-bifurcations. Nevertheless, there remains the problem of significant hydraulic losses in the case of a universal tee that 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 pipelines of steam and hot water, the design and geometrical 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 plant codes.

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 insertion “on their own”, the engineering and technical staff must prepare a template for the nozzle, make a strength calculation (if necessary), control the quality of the insertion (avoid “failures” of the nozzle and “overlap” of its section by an incorrect cut of the wall in a 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 for reducing 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 arrangement of local (L = (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 a certain distance (L = (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 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 estimate the benefits in case of reducing hydraulic losses in the new tee and its payback period.

It is known that the pressure loss in station pipelines with normal velocities of media movement (for Re> 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 resistances; 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 = 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 "pump-pipeline" hydraulic system operates in the nominal mode (or in the mode close to the nominal). Then:

where R n is the nominal pressure (according to the flow characteristic of the pump / boiler), kgf / cm 2; G h - nominal flow rate (according to the flow rate characteristics of the pump / boiler), t / h.

If we assume that after replacing the old resistances, the "pump - pipeline" system will remain operational (Р "Р 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> 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 = 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), you can roughly estimate the profitability of its installation.


Calculation example

For example, it is necessary to evaluate 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 the tee, sections B, C).

We have the following initial data:

■ design diameter of the steam line d = 0.287 m;

■ nominal steam consumption G h = Q (3 = Q ^ 420 t / h;

■ nominal boiler pressure P n = 140 kgf / cm 2;

■ specific volume of steam (at P ra b = 140 kgf / cm 2, t = 560 О С) n = 0.026 m 3 / kg.

Let us calculate the resistance coefficient of a standard tee at the confluence of flows (Fig.2a) according to the formula (5) - ^ СБ1 = 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 we obtain the expected increase in consumption by  G = G 1 -G n = 0.789 t / h.

According to the regime diagram of the T-100 / 120-130 turbine, a 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 = 100AG / Q n = 0.188 MW.

The gain in thermal load can be: T e = 400AG / 4.19Q n = 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 the various types of tees and fittings, gives a brief description of the 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 switching unit of main pipelines with reduced local resistance coefficients 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. Handbook of 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.

Calculation of supply and exhaust air duct systems is reduced to determining the dimensions of the cross-section of the channels, their resistance to air movement and balancing the pressure in parallel connections. Calculation of head losses should be carried out by the method of specific friction head losses.

Calculation method:

      An axonometric diagram of the ventilation system is built, the system is divided into sections, on which the length and flow rate are applied. The design scheme is shown in Figure 1.

      The main (main) direction is selected, which is the most extended chain of successively located sections.

3. The sections of the highway are numbered, starting with the section with the lowest flow rate.

4. The dimensions of the cross-section of the air ducts on the calculated sections of the line are determined. Determine the cross-sectional area, m 2:

F p = L p / 3600V p ,

where L p is the estimated air consumption at the site, m 3 / h;

According to the found values ​​of F p], the dimensions of the air ducts are taken, i.e. is F f.

5. The actual speed V f, m / s is determined:

V f = L p / F f,

where L p is the estimated air consumption at the site, m 3 / h;

F f - the actual cross-sectional area of ​​the duct, m 2.

Determine the equivalent diameter by the formula:

d eq = 2 α b / (α + b),

where α and b are the transverse dimensions of the duct, m.

6. The values ​​of specific pressure losses for friction R are determined from the values ​​of d eq and V f.

The pressure loss due to friction in the calculated area will be

P t = R · l · β w,

where R is the specific pressure loss due to friction, Pa / m;

l is the length of the duct section, m;

β w - roughness coefficient.

7. The coefficients of local resistances are determined and the pressure losses in local resistances on the site are calculated:

z = ∑ζ P d,

where P d - dynamic pressure:

Pd = ρV f 2/2,

where ρ is the air density, kg / m 3;

V f - the actual air speed in the area, m / s;

∑ζ - the amount of CCM on the site,

8. The total losses are calculated for the sections:

ΔР = R · l · β w + z,

l is the length of the section, m;

z - pressure loss in local resistances in the section, Pa.

9. Determine the pressure loss in the system:

ΔР п = ∑ (R · l · β w + z),

where R is the specific pressure loss due to friction, Pa / m;

l is the length of the section, m;

β w - roughness coefficient;

z - pressure loss in local resistances on the site, Pa.

10. The linking of the branches is being carried out. Tying is done starting with the longest branches. It is similar to calculating the main direction. Resistances in all parallel sections must be equal: residual no more than 10%:

where Δр 1 and Δр 2 are losses in branches with large and smaller pressure losses, Pa. If the discrepancy exceeds the set value, then a throttle valve is installed.

Figure 1 - Design diagram of the supply system P1.

The sequence of calculating the supply system P1

Plot 1-2, 12-13, 14-15, 2-2 ', 3-3', 4-4 ', 5-5', 6-6 ', 13-13', 15-15 ', 16- sixteen':

Plot 2 -3, 7-13, 15-16:

Section 3-4, 8-16:

Section 4-5:

Section 5-6:

Section 6-7:

Section 7-8:

Section 8-9:

Local resistance

Section 1-2:

a) at the exit: ξ = 1.4

b) 90 ° bend: ξ = 0.17

c) a tee for a straight passage:

Section 2-2 ':

a) a tee on a branch

Section 2-3:

a) 90 ° bend: ξ = 0.17

b) a tee for a straight passage:

ξ = 0,25

Section 3-3 ':

a) a tee on a branch

Section 3-4:

a) 90 ° bend: ξ = 0.17

b) a tee for a straight passage:

Section 4-4 ':

a) a tee on a branch

Section 4-5:

a) a tee for a straight pass:

Section 5-5 ':

a) a tee on a branch

Section 5-6:

a) 90 ° bend: ξ = 0.17

b) a tee for a straight passage:

Section 6-6 ':

a) a tee on a branch

Section 6-7:

a) a tee for a straight pass:

ξ = 0,15

Section 7-8:

a) a tee for a straight pass:

ξ = 0,25

Section 8-9:

a) 2 bends 90 °: ξ = 0.17

b) a tee for a straight passage:

Section 10-11:

a) 90 ° bend: ξ = 0.17

b) at the exit: ξ = 1.4

Section 12-13:

a) at the exit: ξ = 1.4

b) 90 ° bend: ξ = 0.17

c) a tee for a straight passage:

Section 13-13 '

a) a tee on a branch

Section 7-13:

a) 90 ° bend: ξ = 0.17

b) a tee for a straight passage:

ξ = 0,25

c) a tee on a branch:

ξ = 0,8

Section 14-15:

a) at the exit: ξ = 1.4

b) 90 ° bend: ξ = 0.17

c) a tee for a straight passage:

Section 15-15 ':

a) a tee on a branch

Section 15-16:

a) 2 bends 90 °: ξ = 0.17

b) a tee for a straight passage:

ξ = 0,25

Section 16-16 ':

a) a tee on a branch

Section 8-16:

a) a tee for a straight pass:

ξ = 0,25

b) a tee on a branch:

Aerodynamic calculation of the supply air system P1

Consumption, L, m³ / h

Length, l, m

Duct dimensions

Air speed V, m / s

Losses per 1 m of section length R, Pa

Coeff. roughness m

Friction loss Rlm, Pa

Sum of CMR, Σξ

Dynamic pressure Рд, Pa

Losses on local resist, Z

Pressure loss in the section, ΔР, Pa

Sectional area F, m2

Equivalent diameter

Let's perform the discrepancy of the supply system P1, which should be no more than 10%.

Since the discrepancy exceeds the permissible 10%, it is necessary to install a diaphragm.

I set the diaphragm in the section 7-13, V = 8.1 m / s, Р С = 20.58 Pa

Therefore, for an air duct with a diameter of 450, I install a diaphragm with a diameter of 309.

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