# Hydraulic calculation of the heating system

## Recommendation points

Today we will analyze how to make a hydraulic calculation of the heating system. Indeed, to this day, the practice of designing heating systems on a whim is spreading. This is a fundamentally wrong approach: without preliminary calculation, we raise the bar for material consumption, provoke abnormal operating modes and lose the opportunity to achieve maximum efficiency.

## Goals and objectives of hydraulic calculation

From an engineering point of view, a liquid heating system seems to be a rather complex complex, including devices for generating heat, transporting it and releasing it in heated rooms. The ideal operating mode of the hydraulic heating system is considered to be one in which the coolant absorbs maximum heat from the source and transfers it to the room atmosphere without loss during movement. Of course, such a task seems completely unattainable, but a more thoughtful approach allows you to predict the behavior of the system in various conditions and as close as possible to the benchmarks. This is the main goal of designing heating systems, the most important part of which is rightfully considered to be hydraulic calculation..

The practical goals of hydraulic design are:

1. Understand at what speed and in what volume the coolant moves in each node of the system.
2. Determine what effect a change in the operating mode of each device has on the entire complex as a whole.
3. Establish what capacity and operating characteristics of individual units and devices will be sufficient for the heating system to perform its functions without a significant increase in cost and ensuring an unreasonably high safety margin.
4. Ultimately – to ensure a strictly metered distribution of heat energy in various heating zones and to ensure that this distribution is maintained with high constancy.

We can say more: without at least basic calculations, it is impossible to achieve acceptable stability and long-term use of equipment. Modeling the operation of a hydraulic system, in fact, is the basis on which all further design development is based..

## Types of heating systems

Engineering tasks of this kind are complicated by the great variety of heating systems, both in terms of scale and configuration. There are several types of heating interchanges, each of which has its own laws:

1. Two-pipe dead-end systemsa – the most common version of the device, well suited for organizing both central and individual heating circuits.

2. One-pipe system or “Leningradka”is considered the best way to build civil heating complexes with a thermal power of up to 30-35 kW.

One-pipe heating system with forced circulation: 1 – heating boiler; 2 – security group; 3 – heating radiators; 4 – Mayevsky crane; 5 – expansion tank; 6 – circulation pump; 7 – drain

3. Twin-pipe system of passing type– the most material-intensive type of decoupling of heating circuits, characterized by the highest known stability of operation and the quality of distribution of the coolant.

Two-pipe associated heating system (Tichelman loop)

4. Beam layoutis in many ways similar to a two-pipe ride, but at the same time all the controls of the system are placed at one point – to the manifold assembly.

Radiation heating circuit: 1 – boiler; 2 – expansion tank; 3 – feed manifold; 4 – heating radiators; 5 – return manifold; 6 – circulation pump

Before getting down to the applied side of the calculations, there are a couple of important caveats to make. First of all, you need to learn that the key to a good calculation lies in understanding the principles of fluid systems at an intuitive level. Without this, consideration of each individual solution turns into an interweaving of complex mathematical calculations. The second is the practical impossibility of presenting more than basic concepts within one review; for more detailed explanations, it is better to refer to such literature on the calculation of heating systems:

• V. Pyrkov “Hydraulic regulation of heating and cooling systems. Theory and Practice “2nd edition, 2010.
• R. Jaushovets “Hydraulics – the heart of water heating”.
• Boiler room hydraulics manual from De Dietrich.
• A. Saveliev “Heating at home. Calculation and installation of systems “.

## Determination of flow rate and speed of movement of the coolant

The most well-known method for calculating hydraulic systems is based on data from a heat engineering calculation, which determines the rate of replenishment of heat losses in each room and, accordingly, the thermal power of the radiators installed in them. At first glance, everything is simple: we have the total value of the thermal power and then dose the flow of the heat carrier to each heating device. For greater convenience, an axonometric sketch of the hydraulic system is pre-built, which is annotated with the required power indicators of radiators or loops of a water heated floor..

Axonometric diagram of the heating system

The transition from heat engineering to hydraulic calculation is carried out by introducing the concept of mass flow, that is, a certain mass of coolant supplied to each section of the heating circuit. The mass flow is the ratio of the required thermal power to the product of the specific heat capacity of the coolant by the temperature difference in the supply and return pipelines. Thus, on the sketch of the heating system, key points are marked for which the nominal mass flow is indicated. For convenience, the volumetric flow is determined in parallel, taking into account the density of the heat carrier used.

G = Q / (c (t2 – t1))

• G – coolant flow rate, kg / s
• Q – required thermal power, W
• c – specific heat capacity of the coolant, for water taken as 4200 J / (kg ° C)
• ?T = (t2 – t1) – temperature difference between supply and return, ° С

The logic here is simple: to deliver the required amount of heat to the radiator, you must first determine the volume or mass of the coolant with a given heat capacity passing through the pipeline per unit of time. To do this, it is required to determine the speed of movement of the coolant in the circuit, which is equal to the ratio of the volumetric flow to the cross-sectional area of ​​the internal passage of the pipe. If the speed is calculated relative to the mass flow, the value of the coolant density must be added to the denominator:

V = G / (? F)

• V – speed of movement of the coolant, m / s
• G – coolant flow rate, kg / s
• ? – the density of the coolant, for water you can take 1000 kg / m3
• f – cross-sectional area of ​​the pipe, is found by the formula ?­R2, where r is the inner diameter of the pipe divided by two

The data on the flow rate and speed are necessary to determine the nominal size of the decoupling pipes, as well as the flow and head of circulation pumps. Forced circulation devices must create excess pressure to overcome the hydrodynamic resistance of pipes and shut-off and control valves. The greatest difficulty is the hydraulic calculation of systems with natural (gravitational) circulation, for which the required excess pressure is calculated according to the speed and degree of volumetric expansion of the heated coolant.

The calculation of the parameters according to the ratios described above would be sufficient for ideal models. In real life, both the volumetric flow and the speed of the coolant will always differ from the calculated ones at different points of the system. The reason for this is the hydrodynamic resistance to the movement of the coolant. It is due to a number of factors:

1. Friction forces of the coolant against the pipe walls.
2. Local resistances to the flow formed by fittings, taps, filters, thermostatic valves and other fittings.
3. The presence of branching connecting and branching types.
4. Turbulent eddies in corners, constrictions, expansions, etc..

The problem of finding the pressure drop and velocity in different parts of the system is rightfully considered the most difficult; it lies in the field of calculations of hydrodynamic media. Thus, the forces of friction of the fluid against the inner surfaces of the pipe are described by a logarithmic function that takes into account the roughness of the material and the kinematic viscosity. Calculations of turbulent eddies are even more complicated: the slightest change in the profile and shape of the channel makes each situation unique. To facilitate calculations, two reference factors are introduced:

1. Kvs– characterizing the throughput of pipes, radiators, separators and other areas close to linear.
2. TOms– determining local resistance in various fittings.

These factors are indicated by the manufacturers of pipes, valves, valves, filters for each individual product. It is quite easy to use the coefficients: to determine the head loss, Kms is multiplied by the ratio of the square of the speed of movement of the coolant to the double value of the acceleration due to gravity:

?hms = Kms (V2/ 2g)or ?pms = Kms (? V2/ 2)

• ?hms – head loss on local resistances, m
• ?pms – pressure loss on local resistances, Pa
• TOms – coefficient of local resistance
• g – acceleration of gravity, 9.8 m / s2
• ? – the density of the coolant, for water 1000 kg / m3

The head loss in linear sections is the ratio of the channel capacity to the known capacity factor, and the result of the division must be raised to the second power:

P = (G / Kvs)2

• P – head loss, bar
• G – the actual flow rate of the coolant, m3/hour
• Kvs – throughput, m3/hour

## Pre-balancing the system

The most important final goal of the hydraulic calculation of the heating system is the calculation of such values ​​of throughput at which a strictly metered amount of coolant with a certain temperature enters each part of each heating circuit, which ensures the normalized heat release on the heating devices. This task seems difficult only at first glance. In fact, balancing is done by flow restricting control valves. For each valve model, both the Kvs factor for the fully open position and the Kv factor curve for different degrees of opening of the control stem are indicated. By changing the throughput of the valves, which, as a rule, are installed at the connection points of heating devices, it is possible to achieve the desired distribution of the coolant, and therefore the amount of heat transferred by it.

There is, however, a small nuance: when the throughput changes at one point in the system, not only the actual flow rate in the section under consideration changes. Due to a decrease or increase in the flow, the balance in all other circuits changes to some extent. If we take, for example, two radiators with different thermal power, connected in parallel with the oncoming movement of the coolant, then with an increase in the throughput of the device that is the first in the circuit, the second will receive less coolant due to an increase in the difference in hydrodynamic resistance. On the contrary, when the flow rate decreases due to the control valve, all other radiators further down the chain will receive a larger volume of the coolant automatically and will need additional calibration. Each type of wiring has its own balancing principles.

## Software systems for calculations

Obviously, manual calculations are only justified for small heating systems with a maximum of one or two circuits with 4–5 radiators in each. More complex heating systems with a thermal power of over 30 kW require an integrated approach to the calculation of hydraulics, which expands the range of tools used far beyond pencil and sheet of paper.

Danfoss C.O. 3.8

Today, there is a fairly large number of software provided by the largest manufacturers of heating equipment, such as Valtec, Danfoss or Herz. In such software packages, the same methodology is used to calculate the behavior of hydraulics, which was described in our review. First, an exact copy of the projected heating system is modeled in the visual editor, for which data on the heat output, type of heat carrier, length and height of pipe drops, used fittings, radiators and underfloor heating coils are indicated. The program library contains a wide range of hydraulic devices and fittings; for each product, the manufacturer has predetermined the operating parameters and base coefficients. If desired, you can add third-party samples of devices, if the required list of characteristics is known for them.

At the end of the work, the program makes it possible to determine the appropriate nominal pipe bore, select the sufficient flow and pressure of the circulation pumps. The calculation is completed by balancing the system, while during the simulation of the operation of the hydraulics, the dependences and the effect of changes in the throughput of one unit of the system on all others are taken into account. Practice shows that mastering and using even paid software products turns out to be cheaper than if the calculations were entrusted to contracted specialists..

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