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# Calculation of Differential Pressure controller

dPconst : Differential pressure to maintain
bar
dP : Permissible pressure loss on the control valve
bar
P1 : Pressure before the valve
bar
Tmax : Maximum water temperature
°C
G : Water flow rate
m³/h

## Calculation methodology

The calculation of a Differential Pressure Controller involves determining the required flow capacity, the necessary adjustment range, and checking for possible noise and cavitation.

## Calculation of flow capacity Kvs

The dependence of pressure drop on water flow through the differential pressure controller is called flow capacity - Kvs.

Kvs is the flow capacity, numerically equal to the flow rate of water in m³/h, through a fully open differential pressure controller valve, at which the pressure drop on it is 1 bar.

Kv is the same for a partially open valve of the differential pressure controller.

Knowing that when the flow rate of water changes 'n' times, the pressure drop on the regulator changes 'n²' times, it is easy to determine the necessary value of Kv for the differential pressure controller by substituting the calculated flow rate and excess pressure into the equation.

Some manufacturers recommend selecting a differential pressure controller with the nearest larger Kvs value to the obtained Kv value. This selection approach allows for more accurate regulation of water flow below the setpoint, but does not allow for an increase in flow. We recommend selecting differential pressure controllers so that the required flow capacity value is in the range of 40 to 70% of the valve stroke. A differential pressure controller calculated in this way can significantly reduce water flow with sufficient accuracy and slightly increase it as well.

As a result of the selection process, the percentage of valve opening of the differential pressure controller at which the set excess pressure is throttled at the given water flow rate is provided.

## Selection of setting range

The setting range of the differential pressure controllerr depends on the spring compression force. Some differential pressure controllers are equipped with only one spring and have only one setting range, while others can be equipped with springs of different stiffness and have several setting ranges. The pressure differential that the regulator will maintain should be in the middle third of the setting range.

The aforementioned selection algorithm outputs a list of regulators in which the specified differential pressure falls within the range of 20 to 80% of the range of maintained differential pressure.

## Cavitation calculation for the regulator

Cavitation is the formation of vapor bubbles in a water flow that occurs when the pressure in the flow drops below the saturation pressure of water vapor. The effect of increasing flow velocity and reducing pressure in a flow that occurs when the flow area is narrowed is described by Bernoulli's equation. The flow area of the differential pressure controller is precisely this narrowing, in which the pressure can drop to the saturation pressure and is the most likely place for cavitation to occur. Vapor bubbles are unstable; they suddenly appear and disappear, which leads to the erosion of metal particles from the regulator components, which inevitably causes premature wear. In addition to wear, cavitation leads to increased noise during the operation of the regulator.

The main factors that affect cavitation are:

• Water temperature - the higher it is, the more likely cavitation is to occur.
• Water pressure - the higher it is before the differential pressure controller, the less likely cavitation is to occur.
• Throttling pressure - the higher it is, the more likely cavitation is to occur.
• Cavitation characteristic of the regulator - determined by the features of the throttling element of the regulator. The cavitation coefficient is different for different types of regulators and should be indicated in their technical specifications, but since most manufacturers do not indicate this value...

After checking for cavitation, the following results are possible:

• 'No' - cavitation will definitely not occur.
• 'Possible' - cavitation may occur on the valves of some constructions, it is recommended to change one of the aforementioned factors that affect cavitation.
• 'Yes' - cavitation will definitely occur, change one of the factors that affect cavitation.

## Calculation for Noise Generation

A high flow velocity in the inlet of a pressure regulator can cause high noise levels. For most rooms where differential pressure controllers are installed, the permissible noise level is 35-40 dBA, which corresponds to a velocity of approximately 3 m/s at the inlet of the valve. Therefore, when selecting a differential pressure controller, it is recommended not to exceed the aforementioned velocity.

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