An example of calculating the pressure in the ventilation network. Calculation of resistance in ventilation systems. Network elements and local resistances
- The performance of a system serving up to 4 rooms.
- Dimensions of air ducts and air distribution grilles.
- Air line resistance.
- Heater power and estimated electricity costs (when using an electric heater).
If you need to choose a model with humidification, cooling or recuperation, use the calculator on the Breezart website.
An example of calculating ventilation using a calculator
In this example, we will show how to calculate supply ventilation for 3 room apartment in which a family of three lives (two adults and a child). During the day, relatives sometimes come to them, so up to 5 people can stay in the living room for a long time. The ceiling height of the apartment is 2.8 meters. Room parameters:
We will set the consumption rates for the bedroom and the nursery in accordance with the recommendations of SNiP - 60 m³ / h per person. For the living room, we will limit ourselves to 30 m³ / h, since a large number of there are not many people in this room. According to SNiP, such air flow is acceptable for rooms with natural ventilation (you can open a window for ventilation). If we also set an air flow rate of 60 m³/h per person for the living room, then the required performance for this room would be 300 m³/h. The cost of electricity to heat this amount of air would be very high, so we made a compromise between comfort and economy. To calculate the air exchange by the multiplicity for all rooms, we will choose a comfortable double air exchange.
The main air duct will be rectangular rigid, the branches will be flexible and soundproof (this combination of duct types is not the most common, but we chose it for demonstration purposes). For additional cleaning of the supply air, a carbon-dust fine filter of the EU5 class will be installed (we will calculate the network resistance with dirty filters). Air velocities in ducts and allowable level we leave the noise on the gratings equal to the recommended values, which are set by default.
Let's start the calculation by drawing up a diagram of the air distribution network. This scheme will allow us to determine the length of the ducts and the number of turns that can be both in the horizontal and vertical plane (we need to count all the turns at a right angle). So our schema is:
The resistance of the air distribution network is equal to the resistance of the longest section. This section can be divided into two parts: the main duct and the longest branch. If you have two branches of approximately the same length, then you need to determine which one has more resistance. To do this, we can assume that the resistance of one turn is equal to the resistance of 2.5 meters of the duct, then the branch with the maximum value (2.5 * number of turns + duct length) will have the greatest resistance. It is necessary to select two parts from the route in order to be able to set different type ducts and different air speeds for the main section and branches.
In our system, balancing throttle valves are installed on all branches, allowing you to adjust the air flow in each room in accordance with the project. Their resistance (open) is already taken into account as it is a standard element ventilation system.
The length of the main air duct (from the air intake grille to the branch to room No. 1) is 15 meters, there are 4 right-angle turns in this section. The length of the supply unit and the air filter can be ignored (their resistance will be taken into account separately), and the silencer resistance can be taken equal to the resistance of an air duct of the same length, that is, simply consider it a part of the main air duct. The longest branch is 7 meters long and has 3 right angle bends (one at the branch, one at the duct and one at the adapter). Thus, we have set all the necessary initial data and now we can proceed to the calculations (screenshot). The calculation results are summarized in tables:
Calculation results for roomsResults of the calculation of general parameters
| Type of ventilation system | Plain | VAV |
| Performance | 365 m³/h | 243 m³/h |
| Cross-sectional area of the main air duct | 253 cm² | 169 cm² |
| Recommended main duct dimensions | 160x160mm 90x315mm 125x250mm |
125x140mm 90x200mm 140x140mm |
| Air network resistance | 219 Pa | 228 Pa |
| Heater power | 5.40 kW | 3.59 kW |
| Recommended Supply unit | Breezart 550 Lux (in 550 m³/h configuration) |
Breezart 550 Lux (VAV) |
| Maximum performance recommended PU |
438 m³/h | 433 m³/h |
| Electric power heater PU | 4.8 kW | 4.8 kW |
| Average monthly electricity costs | 2698 rubles | 1619 rubles |
Calculation of the air duct network
- For each room (subsection 1.2), the performance is calculated, the cross-section of the duct is determined, and a suitable duct of standard diameter is selected. According to the Arktos catalog, the dimensions of distribution grids with a given noise level are determined (data for the AMN, ADN, AMR, ADR series are used). You can use other gratings with the same dimensions - in this case, there may be a slight change in the noise level and network resistance. In our case, the gratings for all rooms turned out to be the same, since at a noise level of 25 dB(A) the permissible air flow through them is 180 m³/h (there are no smaller gratings in these series).
- The sum of the air flow rates for all three rooms gives us the total system performance (subsection 1.3). When using a VAV system, the system performance will be one third lower due to the separate adjustment of the air flow in each room. Next, the cross section of the main duct is calculated (in the right column - for VAV systems) and suitable rectangular air ducts are selected (usually several options are given with different aspect ratios). At the end of the section, the resistance of the air duct network is calculated, which turned out to be very large - this is due to the use of a fine filter in the ventilation system, which has a high resistance.
- We have received all the necessary data to complete the air distribution network, with the exception of the size of the main air duct between branches 1 and 3 (this parameter is not calculated in the calculator, since the network configuration is not known in advance). However, the cross-sectional area of this section can be easily calculated manually: from the cross-sectional area of the main duct, you need to subtract the cross-sectional area of \u200b\u200bbranch No. 3. Having obtained the cross-sectional area of \u200b\u200bthe duct, its size can be determined by.
Calculation of heater power and selection of air handling unit
The recommended Breezart 550 Lux model has programmable parameters (capacity and power of the heater), therefore, the performance that should be selected when setting up the remote control is indicated in brackets. It can be seen that the maximum possible power of the heater of this launcher is 11% lower than the calculated value. The lack of power will be noticeable only at outdoor temperatures below -22 ° C, and this does not happen often. In such cases, the air handling unit will automatically switch to a lower speed to maintain the set outlet temperature (Comfort function).
In the calculation results, in addition to the required performance of the ventilation system, the maximum performance of the PU for a given network resistance is indicated. If this performance turns out to be noticeably higher than the required value, you can take advantage of the programmatic limitation of the maximum performance, which is available for all Breezart ventilation units. For a VAV system, the maximum performance is indicated for reference, since its performance is adjusted automatically during the operation of the system.
Calculation of the cost of operation
This section calculates the cost of electricity used to heat the air in cold period of the year. The costs for a VAV system depend on its configuration and mode of operation, so they are assumed to be equal to the average value: 60% of the costs of a conventional ventilation system. In our case, you can save money by reducing the air consumption at night in the living room, and during the day in the bedroom.
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However, at high relative flow rates in the branch, the CMR changes very sharply, therefore, in this area, the considered tables are manually interpolated with difficulty and with a significant error. In addition, in the case of using MS Excel spreadsheets, it is again desirable to have formulas for directly calculating the CMR through the ratio of costs and sections. At the same time, such formulas should be, on the one hand, quite simple and convenient for mass design and use in the educational process, but at the same time, they should not give an error that exceeds the usual accuracy of engineering calculations. Previously, a similar problem was solved by the author in relation to the resistances encountered in water heating systems. Let us now consider this question for mechanical systems V and KV. Below are the results of data approximation for unified tees (branch nodes) per pass. The general form of dependencies was chosen based on physical considerations, taking into account the convenience of using the obtained expressions while ensuring an acceptable deviation from tabular data:
❏ for supply tees, with Loʹ ≤ 0.7 and fnʹ ≥ 0.5: and with Loʹ ≤ 0.4, a simplified formula can be used:
❏ for exhaust tees: 
It is easy to see that the relative area of the passage fnʹ during injection or, respectively, the branch foʹ during suction affects the CMR in the same way, namely, with an increase in fnʹ or foʹ, the resistance will decrease, and the numerical coefficient for the indicated parameters in all the above formulas is the same, namely (-0.25). In addition, for both supply and exhaust tees, when the air flow in the branch changes, the relative minimum of the CMR occurs at the same level Loʹ = 0.2. These circumstances indicate that the expressions obtained, despite their simplicity, sufficiently reflect the general physical laws underlying the influence of the studied parameters on pressure losses in tees of any type. In particular, the larger fnʹ or foʹ, i.e. the closer they are to unity, the less the flow structure changes during the passage of resistance, and hence the smaller the CMR. For the Loʹ value, the dependence is more complex, but here, too, it will be common to both modes of air movement.
An idea of the degree of correspondence between the found ratios and the initial values of the CMR is given in Fig. . 1, which shows the results of processing table 22.37 for KMS unified tees (branch nodes) for a round and rectangular passage during injection. Approximately the same picture is obtained for the approximation of Table. 22.38 using formula (3). Note that although in the latter case we are talking about round section, it is easy to make sure that expression (3) quite successfully describes the data in Table. 22.39, already related to rectangular nodes. 
The error of the formulas for CMS is mainly 5-10% (up to a maximum of 15%). Somewhat higher deviations can be given by expression (3) for suction tees, but even here it can be considered satisfactory, given the complexity of changing the resistance in such elements. In any case, the nature of the dependence of the CMR on the factors influencing it is reflected here very well. In this case, the obtained ratios do not require any other initial data, except for those already available in the aerodynamic calculation table. Indeed, it must explicitly indicate both the air flow rates and the cross-sections in the current and in the neighboring section, which are included in the listed formulas. This especially simplifies calculations when using MS Excel spreadsheets.
At the same time, the formulas given in this paper are very simple, illustrative and easily accessible for engineering calculations, especially in MS Excel, and also in the learning process. Their use makes it possible to abandon the interpolation of tables while maintaining the accuracy required for engineering calculations, and directly calculate KMS tees per passage at a wide variety of ratios of cross sections and air flow rates in the trunk and branches. This is quite sufficient for the design of V and HF systems in most residential and public buildings.
1. A.D. Altshul, L.S. Zhivotovsky, L.P. Ivanov. Hydraulics and aerodynamics. — M.: Stroyizdat, 1987.
2. Designer's guide. Internal sanitary devices. Part 3. Ventilation and air conditioning. Book. 2 / Ed. N.N. Pavlov and Yu.I. Schiller. — M.: Stroyizdat, 1992.
3. O.D. Samarin. On the calculation of pressure losses in the elements of water heating systems // Journal of S.O.K., No. 2/2007.
The basis for the design of any engineering networks is the calculation. In order to correctly design a network of supply or exhaust air ducts, it is necessary to know the parameters of the air flow. In particular, it is required to calculate the flow rate and pressure loss in the channel for correct selection fan power.
In this calculation, an important role is played by such a parameter as dynamic pressure on the walls of the duct.
Behavior of the medium inside the air duct
The fan, which creates an air flow in the supply or exhaust duct, informs this flow potential energy. In the process of movement in the limited space of the pipe, the potential energy of the air is partially converted into kinetic energy. This process occurs as a result of the action of the flow on the walls of the channel and is called dynamic pressure.
In addition to it, there is also static pressure, this is the effect of air molecules on each other in a stream, it reflects its potential energy. The kinetic energy of the flow is reflected by the dynamic impact indicator, which is why this parameter is involved in the calculations.
At a constant air flow, the sum of these two parameters is constant and is called full pressure. It can be expressed in absolute and relative units. The reference point for absolute pressure is full vacuum, while relative pressure is considered starting from atmospheric, that is, the difference between them is 1 atm. As a rule, when calculating all pipelines, the value of the relative (excessive) impact is used.
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The physical meaning of the parameter
If we consider straight sections of air ducts, the sections of which decrease at a constant air flow, then an increase in the flow rate will be observed. In this case, the dynamic pressure in the air ducts will increase, and the static pressure will decrease, the magnitude of the total impact will remain unchanged. Accordingly, in order for the flow to pass through such a narrowing (confuser), it should initially be given the required amount of energy, otherwise the flow rate may decrease, which is unacceptable. By calculating the magnitude of the dynamic impact, you can find out the number of losses in this confuser and choose the right power ventilation unit.
The reverse process will occur in the case of an increase in the channel cross section at a constant flow rate (diffuser). The speed and dynamic impact will begin to decrease, the kinetic energy of the flow will turn into potential. If the pressure developed by the fan is too high, the flow rate in the area and throughout the system may increase.
Depending on the complexity of the scheme, ventilation systems have many turns, tees, narrowings, valves and other elements called local resistances. The dynamic effect in these elements increases depending on the angle of attack of the flow on inner wall pipes. Some parts of the systems cause a significant increase in this parameter, for example, fire dampers in which one or more dampers are installed in the flow path. This creates increased flow resistance in the area, which must be taken into account in the calculation. Therefore, in all of the above cases, you need to know the value of the dynamic pressure in the channel.
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Parameter calculations by formulas
On a straight section, the speed of air movement in the duct is unchanged, and the magnitude of the dynamic impact remains constant. The latter is calculated by the formula:
Rd = v2γ / 2g
In this formula:
- Pd is the dynamic pressure in kgf/m2;
- V is the air velocity in m/s;
- γ is the specific mass of air in this area, kg/m3;
- g is the acceleration due to gravity, equal to 9.81 m/s2.
You can get the value of dynamic pressure in other units, in Pascals. There is another version of this formula for this:
Pd = ρ(v2 / 2)
Here ρ is the air density, kg/m3. Since there are no conditions in ventilation systems for compressing the air to such an extent that its density changes, it is assumed to be constant - 1.2 kg/m3.
Further, it is necessary to consider how the magnitude of the dynamic action is involved in the calculation of the channels. The meaning of this calculation is to determine the losses in the entire supply or exhaust ventilation to select the fan pressure, its design and engine power. The calculation of losses takes place in two stages: first, the losses due to friction against the channel walls are determined, then the drop in the power of the air flow in local resistances is calculated. The dynamic pressure parameter is involved in the calculation at both stages.
Friction resistance per 1 m of the round channel is calculated by the formula:
R = (λ / d) Rd, where:
- Pd is the dynamic pressure in kgf/m2 or Pa;
- λ is the friction resistance coefficient;
- d is the duct diameter in meters.
Friction losses are determined separately for each section with different diameters and flow rates. The resulting value of R is multiplied by the total length of the channels of the calculated diameter, the losses on local resistances are added and get general meaning for the whole system:
HB = ∑(Rl + Z)
Here are the options:
- HB (kgf/m2) - total losses in the ventilation system.
- R is the friction loss per 1 m of the circular channel.
- l (m) is the length of the section.
- Z (kgf / m2) - losses in local resistances (bends, crosses, valves, and so on).
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Determination of parameters of local resistances of the ventilation system
The magnitude of the dynamic impact also takes part in determining the Z parameter. The difference with the straight section is that in different elements of the system the flow changes its direction, branches, converges. In this case, the medium interacts with the inner walls of the channel not tangentially, but at different angles. To take this into account, a trigonometric function can be introduced into the calculation formula, but there are a lot of difficulties. For example, when passing a simple 90⁰ bend, the air turns and presses against the inner wall at least three different angles (depending on the design of the bend). There are a lot of more complex elements in the duct system, how to calculate the losses in them? There is a formula for this:
- Z = ∑ξ Rd.
In order to simplify the calculation process, a dimensionless coefficient of local resistance has been introduced into the formula. For each element of the ventilation system, it is different and is a reference value. The values of the coefficients were obtained by calculations or empirically. Many manufacturing plants that produce ventilation equipment conduct their own aerodynamic studies and product calculations. Their results, including the coefficient of local resistance of an element (for example, a fire damper), are entered in the product passport or placed in the technical documentation on their website.
To simplify the process of calculating the losses of ventilation ducts, all values of the dynamic impact for different speeds are also calculated and summarized in tables, from which they can be simply selected and inserted into the formulas. Table 1 lists some values for the most commonly used air velocities in air ducts.
The scheme of the supply ventilation system is shown in Figure 23. and includes the following main elements: 1 - air inlets for outside air intake; 2- fan with devices for cleaning 3, cooling 4, drying, humidification and heating 5 of the outside air; 6 air duct system through which the supply air from the fan is directed to the premises.
1 - air inlets, 2 - fan with devices for cleaning 3, cooling 4, dehumidification, humidification and heating 5 of outside air, 6 - air ducts
Figure 23. Scheme of the supply ventilation unit
Aerodynamic calculation of air ducts is reduced to sizing cross section duct and to the calculation of pressure losses in the network.
The initial data for its implementation are:
values of air flow in each section V (m 3 / hour); section length Li (m); limit values of air movement speeds in sections w i (m/s); as well as the values of the local resistance coefficients Z i .
Calculation of cross-sections of individual sections of air ducts (fк) at a selected air speed and a certain flow rate is carried out according to the formula:
where V is the flow rate of air passing through the considered section, m 3 / h;
ω - air speed in the same section, m/s.
When calculating the discharge air ducts, the air velocity in them is taken in the range from 6 to 12 m/s. The air velocity at the outlet of the gratings for wagons with cooling units should not exceed 0.25 m/s. In the absence of cooling, the speed of air exit from the ventilation grill should be 0.3-0.6 m/s in winter and 1.2-1.5 m/s in summer.
When calculating hydraulic losses in air ducts, it should be taken into account that the fan performs two tasks during its operation:
Transfers air from a state of rest to a state of motion with a certain speed w;
It overcomes the frictional resistance that occurs in the duct when air moves at a speed w.
The scheme of the supply ventilation unit and the pressure diagram in the air ducts is shown in Figure 24. To move air along a straight section of the discharge air duct at a speed w 2, the fan must provide the total pressure (N p), which is the sum of the dynamic (speed) and static pressure H st.
, (2.3)
Dynamic pressure is due to the presence of a moving mass of air with a speed w 2 and is determined from the expression:
where - air density kg / m 3;
v - air velocity in the duct, m/s;
g - acceleration of gravity m / s 2.
Static pressure is necessary to overcome the resistance to the movement of air flow along the length of the duct (), as well as to overcome local resistance (Z 2).
, (2.5)
where R is the pressure loss per unit length of the duct;
L is the length of the duct, m.
The total pressure loss H p in the suction and discharge ducts is:
, (2.6)
where Rv and Rn are friction losses per 1 running meter of the length of the suction and discharge ducts, respectively, mm. water. Art.;
l B and l H - respectively, the length of the suction and discharge duct, m;
Z in and Z n - pressure losses in local resistances, respectively, of the suction and discharge duct, mm. water. Art.
The pressure loss per unit length of a circular duct is determined by the formula:
, (2.7)
where λ is the coefficient of resistance to air friction against the walls;
d - duct diameter, m.
For rectangular air ducts with sides a and b, the pressure loss per unit length will be:
, (2.8)
The value of the friction resistance coefficient λ depends on the mode of air movement, characterized by the Reynolds number, and on the condition of the internal surfaces of the air duct. The Reynolds number, as is known, is determined from the expression.
The resistance to the passage of air in a ventilation system is mainly determined by the speed of air movement in this system. As the speed increases, so does the resistance. This phenomenon is called pressure loss. The static pressure created by the fan causes the air to move in the ventilation system, which has a certain resistance. The higher the resistance of such a system, the lower the air flow moved by the fan. The calculation of friction losses for air in air ducts, as well as the resistance of network equipment (filter, silencer, heater, valve, etc.) can be made using the appropriate tables and diagrams specified in the catalog. The total pressure drop can be calculated by summing the resistance values of all elements of the ventilation system.
Determining the speed of air movement in the ducts:
V= L / 3600*F (m/s)
where L– air consumption, m3/h; F is the cross-sectional area of the channel, m2.
Pressure loss in a duct system can be reduced by increasing the cross section of the ducts to ensure relatively uniform air velocity throughout the system. In the image we see how it is possible to achieve a relatively uniform air velocity in the duct network with minimal pressure loss.
In systems with a large length of air ducts and a large number of ventilation grilles, it is advisable to place the fan in the middle of the ventilation system. This solution has several advantages. On the one hand, pressure losses are reduced, and on the other hand, smaller ducts can be used.
An example of calculating the ventilation system:
The calculation must begin with a sketch of the system, indicating the location of the air ducts, ventilation grilles, fans, as well as the lengths of the air duct sections between the tees, then determine the air flow in each section of the network.
Let's find out the pressure loss for sections 1-6, using the graph of pressure loss in round ducts, we will determine the required diameters of the ducts and the pressure loss in them, provided that it is necessary to provide an acceptable air speed.
Plot 1: the air flow will be 220 m3/h. We take the diameter of the air duct equal to 200 mm, the speed is 1.95 m / s, the pressure loss will be 0.2 Pa / m x 15 m = 3 Pa (see the diagram for determining pressure losses in air ducts).
Plot 2: let's repeat the same calculations, not forgetting that the air flow through this section will already be 220+350=570 m3/h. We take the diameter of the duct equal to 250 mm, the speed is 3.23 m/s. The pressure loss will be 0.9 Pa / m x 20 m = 18 Pa.
Plot 3: the air flow through this section will be 1070 m3/h. We take the diameter of the duct equal to 315 mm, the speed is 3.82 m/s. The pressure loss will be 1.1 Pa / m x 20 \u003d 22 Pa.
Plot 4: the air flow through this section will be 1570 m3/h. We take the diameter of the duct equal to 315 mm, the speed is 5.6 m/s. The pressure loss will be 2.3 Pa x 20 = 46 Pa.
Plot 5: the air flow through this section will be 1570 m3/h. We take the diameter of the duct equal to 315 mm, the speed is 5.6 m/s. The pressure loss will be 2.3 Pa / m x 1 \u003d 2.3 Pa.
Plot 6: the air flow through this section will be 1570 m3/h. We take the diameter of the duct equal to 315 mm, the speed is 5.6 m/s. The pressure loss will be 2.3 Pa x 10 = 23 Pa. The total pressure loss in the air ducts will be 114.3 Pa.
When the calculation of the last section is completed, it is necessary to determine the pressure losses in the network elements: in the silencer СР 315/900 (16 Pa) and in check valve KOM 315 (22 Pa). We also determine the pressure loss in the outlets to the grids (the resistance of the 4 outlets in total will be 8 Pa).
Determination of pressure losses at duct bends
The graph allows you to determine the pressure loss in the outlet, based on the bending angle, diameter and air flow.
Example. Let us determine the pressure loss for a 90° outlet with a diameter of 250 mm at an air flow rate of 500 m3/h. To do this, we find the intersection of the vertical line corresponding to our air flow with a slash characterizing a diameter of 250 mm, and on the vertical line on the left for a 90 ° outlet, we find the pressure loss, which is 2Pa.
We accept for installation ceiling diffusers of the PF series, the resistance of which, according to the schedule, will be 26 Pa.
Determination of pressure losses on bends of air ducts.
