# Kv value

Physical key figure
Surname Flow factor,
flow coefficient
Formula symbol ${\ displaystyle K _ {\ mathrm {v}}}$
dimension ${\ displaystyle \ mathrm {\ frac {m ^ {3}} {h}}}$
definition ${\ displaystyle K _ {\ mathrm {v}} = Q \ cdot {\ sqrt {{\ frac {1 \ \ mathrm {bar}} {\ Delta p}} \ cdot {\ frac {\ rho} {1000 \ { \ frac {\ mathrm {kg}} {\ mathrm {m} ^ {3}}}}}}}}$
 ${\ displaystyle Q}$ Volume flow in${\ displaystyle \ mathrm {\ tfrac {m ^ {3}} {h}}}$ ${\ displaystyle \ Delta p}$ Pressure difference in${\ displaystyle \ mathrm {bar}}$ ${\ displaystyle \ rho}$ Density of the fluid in${\ displaystyle \ mathrm {\ tfrac {kg} {m ^ {3}}}}$
scope of application Dimensioning of valves

The Kv value is also called flow factor or flow coefficient referred. It is a measure of the achievable throughput of a liquid or a gas through a valve and is used for the selection and dimensioning of valves. The value is given in the unit m³ / h and can be interpreted as the effective cross-section.

## definition

The Kv value corresponds to the water flow through a valve (in m³ / h) at a pressure difference of about one bar (exactly 0.98 bar) and a water temperature of 5 ° C - 30 ° C. Depending on the valve size, it is often given in l / min.

A Kv value only applies to the associated stroke (degree of opening) of a valve. The Kv value of a valve at the nominal stroke (100% degree of opening) is called the Kvs value. The maximum possible throughput of a valve can be determined using the Kvs value .

Example: A permanently adjustable regulating valve with five setting stages has a different Kv value for each individual stage, but only one Kvs value, namely the flow rate at the highest stage.

That means z. B. with valves that the Kvs value is used to express the maximum possible throughput of any valve. It identifies and differentiates valves based on their capacity and, according to DIN IEC 5314, amounts to: the value with the valve fully open K100 with a tolerance of ± 10%.

The determination of the Kv value is regulated in the technical rule VDI / VDE 2173, Fluidic parameters of control valves and their determination .

For liquids, the minimum required Kv value for a valve is determined from the required operating data for the application using the following equation, if the pressure loss is between 0.35 and 1 bar:

${\ displaystyle K _ {\ mathrm {v}} = Q \ cdot {\ sqrt {{\ frac {1 \ \ mathrm {bar}} {\ Delta p}} \ cdot {\ frac {\ rho} {1000 \ { \ frac {\ mathrm {kg}} {\ mathrm {m} ^ {3}}}}}}}}$
Density of water as a function of temperature

With:

• ${\ displaystyle K _ {\ mathrm {v}}}$ = Flow coefficient
• ${\ displaystyle Q}$ = Volume flow
• ${\ displaystyle \ Delta p}$ = Pressure difference (inlet pressure - outlet pressure)
• ${\ displaystyle \ rho}$= Density of the fluid

For water with a density of , the formula simplifies to: ${\ displaystyle \ rho = 1000 \, \ mathrm {kg / m ^ {3}}}$

${\ displaystyle K _ {\ mathrm {v}} = Q \ cdot {\ sqrt {\ frac {1 \ \ mathrm {bar}} {\ Delta p}}}}$

Strictly speaking, this relationship only applies to cold water, since the density decreases with increasing temperature. Water at 100 ° C has a density that is approx. 4% lower.

If the Kv value is known, the throughput can be determined for any density and pressure difference. The following generally applies (assuming incompressibility )

${\ displaystyle {\ text {Volume flow}} \ sim {\ sqrt {\ frac {\ text {Pressure difference}} {\ text {Density}}}}.}$

This means for example:

• at 4 times the pressure difference, the volume flow doubles .
• at 4 times the density, the volume flow is halved or the mass flow is doubled .

In non-metric systems, a Cv value is often given (flow coefficient value). This describes the water flow in US gallons per minute (USG / min). Converted, the Cv value corresponds approximately to 1,165 times the Kv value. (Kv = Cv x 0.857).

For gases such as natural gas , calculations are often made with the K G value instead of the Kv value . The K G value relates to natural gas with a density ratio of d = 0.64 corresponding to a standard density of = 0.82752 (approx. 0.83) kg / m 3 at p 1 = 2 bar (absolute), p 2 = 1 bar (absolute) and a gas inlet temperature of t u = 15 ° C or T u = 288.15 K, in accordance with the European standards EN 334 for gas pressure regulators and EN 14382 for safety shut-off devices. The K G value is given in the unit (m³ / h) / bar. ${\ displaystyle \ rho _ {n}}$

The conversion results in K G = 33.62 x Kv.

## General fluidic representation and use of the Kv value

The valve coefficient Cv, introduced in 1953 by Mason-Neilan Regulator Co., Boston, quickly established itself in the field of control engineering with metric units of measurement as the Kv value and found its way into the above-mentioned standards. In contrast, it is not used in general fluid mechanics. This is likely mainly due to the above definition as a tailored size equation. The representation of the Kv value as a flow coefficient is more generally valid as follows:

${\ displaystyle K _ {\ mathrm {v}} = Q \ cdot {\ sqrt {\ frac {\ rho} {\ Delta p}}}}$

If the sizes are used in SI units, the Kv value has the dimension of an area. From a physical point of view, this is to be understood as a corrected flow area that is smaller than the geometrically narrowest cross-section due to the constriction of the jet, vortex formation, etc. However, even with the introduction of the SI units, this universally valid, scientifically correct representation has not prevailed.

The conversion between the Kv value in m³ / h defined above and the generally applicable Kv value in mm² applies for water (at 1 bar pressure difference and a density of 1000 kg / m³):

${\ displaystyle \ {K _ {\ mathrm {v}} \} _ {\ mathrm {m ^ {3} / h}} = {\ frac {9} {250}} \ cdot \ {K _ {\ mathrm {v }} \} _ {\ mathrm {mm ^ {2}}}}$

The Kv value enables a simple calculation of series and parallel connections of flow resistances or valves to a resulting total Kv value and the conversion to the pressure loss coefficient .

## Single receipts

1. ^ Roos, Hans: Hydraulics of the water heating; 5th ed .; Oldenbourg-Industrieverl .; 2002; Quote p. 14 above: "According to VDI / VDE guideline 2173, the Kv value of a valve is defined as the flow rate in m³ / h of water that [...] flows through the valve"
2. http://www.buerkert.de/DEU/737.html
3. http://www.fas.ch/info_tech_kv.asp?sectionID=t&Langue=deutsch
4. VDI / VDE 2173
5. Burkhardt, Wolfgang; Kraus, Roland: Project planning of hot water heating systems; 7th edition; Oldenbourg-Industrieverl .; 2005; P. 311 f.
6. ^ Roos, Hans: Hydraulics of the water heating; 5th ed .; Oldenbourg-Industrieverl .; 2002; P. 15, formula 1.20
7. Bürkert fluidics calculator. Retrieved January 14, 2019 .
8. Bernd Glück: "Hydrodynamic and gas-dynamic pipe flow, pressure losses" . Download, page 61 ff.