Flow coefficient

Last updated

The flow coefficient of a device is a relative measure of its efficiency at allowing fluid flow. It describes the relationship between the pressure drop across an orifice valve or other assembly and the corresponding flow rate.

Contents

Mathematically the flow coefficient Cv (or flow-capacity rating of valve) can be expressed as :

where:

Q is the rate of flow (expressed in US gallons per minute),
SG is the specific gravity of the fluid (for water = 1),
ΔP is the pressure drop across the valve (expressed in psi).

In more practical terms, the flow coefficientCv is the volume (in US gallons) of water at 60 °F (16 °C) that will flow per minute through a valve with a pressure drop of 1 psi (6.9 kPa) across the valve.

The use of the flow coefficient offers a standard method of comparing valve capacities and sizing valves for specific applications that is widely accepted by industry. The general definition of the flow coefficient can be expanded into equations modeling the flow of liquids, gases and steam using the discharge coefficient.

For gas flow in a pneumatic system the Cv for the same assembly can be used with a more complex equation. [1] [2] Absolute pressures (psia) must be used for gas rather than simply differential pressure.

For air flow at room temperature, when the outlet pressure is less than 1/2 the absolute inlet pressure, the flow becomes quite simple (although it reaches sonic velocity internally). With Cv = 1.0 and 200 psia inlet pressure the flow is 100 standard cubic feet per minute (scfm). The flow is proportional to the absolute inlet pressure, so the flow in scfm would equal the Cv flow coefficient if the inlet pressure were reduced to 2 psia and the outlet were connected to a vacuum with less than 1 psi absolute pressure (1.0 scfm when Cv = 1.0, 2 psia input).

Flow factor

The metric equivalent flow factor (Kv) is calculated using metric units :

where [3]

Kv is the flow factor (expressed in m3·h−1).
Q is the flowrate (expressed in cubic metres per hour m3·h−1),
SG is the specific gravity of the fluid (for water = 1),
P is the differential pressure across the device (expressed in bar).

Kv can be calculated from Cv using the equation: [4]

The kv factor or value as it is also called is defined in VDI/VDE Richtlinien No. 2173. [5] A simplified version of the definition is: The kv factor of a valve indicates "The water flow in m3/h, at a pressure drop across the valve of 1 kgf/cm2 when the valve is completely open. The complete definition also says that the flow medium must have a density of 1000 kg/m3 and a kinematic viscosity of 10−6 m2/s. e.g. water[ clarify ]

Related Research Articles

<span class="mw-page-title-main">Enthalpy</span> Measure of energy in a thermodynamic system

Enthalpy, a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant pressure, which is conveniently provided by the large ambient atmosphere. The pressure–volume term expresses the work required to establish the system's physical dimensions, i.e. to make room for it by displacing its surroundings. The pressure-volume term is very small for solids and liquids at common conditions, and fairly small for gases. Therefore, enthalpy is a stand-in for energy in chemical systems; bond, lattice, solvation and other "energies" in chemistry are actually enthalpy differences. As a state function, enthalpy depends only on the final configuration of internal energy, pressure, and volume, not on the path taken to achieve it.

<span class="mw-page-title-main">Pressure</span> Force distributed over an area

Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure is the pressure relative to the ambient pressure.

<span class="mw-page-title-main">Vapor pressure</span> Pressure exerted by a vapor in thermodynamic equilibrium

Vapor pressure is defined as the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases at a given temperature in a closed system. The equilibrium vapor pressure is an indication of a liquid's thermodynamic tendency to evaporate. It relates to the balance of particles escaping from the liquid in equilibrium with those in a coexisting vapor phase. A substance with a high vapor pressure at normal temperatures is often referred to as volatile. The pressure exhibited by vapor present above a liquid surface is known as vapor pressure. As the temperature of a liquid increases, the attractive interactions between liquid molecules become less significant in comparison to the entropy of those molecules in the gas phase, increasing the vapor pressure. Thus, liquids with strong intermolecular interactions are likely to have smaller vapor pressures, with the reverse true for weaker interactions.

<span class="mw-page-title-main">Bernoulli's principle</span> Principle relating to fluid dynamics

Bernoulli's principle is a key concept in fluid dynamics that relates pressure, speed and height. Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure or the fluid's potential energy. The principle is named after the Swiss mathematician and physicist Daniel Bernoulli, who published it in his book Hydrodynamica in 1738. Although Bernoulli deduced that pressure decreases when the flow speed increases, it was Leonhard Euler in 1752 who derived Bernoulli's equation in its usual form.

In fluid dynamics, the Darcy–Weisbach equation is an empirical equation that relates the head loss, or pressure loss, due to friction along a given length of pipe to the average velocity of the fluid flow for an incompressible fluid. The equation is named after Henry Darcy and Julius Weisbach. Currently, there is no formula more accurate or universally applicable than the Darcy-Weisbach supplemented by the Moody diagram or Colebrook equation.

<span class="mw-page-title-main">Electro-osmosis</span>

Electroosmotic flow is the motion of liquid induced by an applied potential across a porous material, capillary tube, membrane, microchannel, or any other fluid conduit. Because electroosmotic velocities are independent of conduit size, as long as the electrical double layer is much smaller than the characteristic length scale of the channel, electroosmotic flow will have little effect. Electroosmotic flow is most significant when in small channels. Electroosmotic flow is an essential component in chemical separation techniques, notably capillary electrophoresis. Electroosmotic flow can occur in natural unfiltered water, as well as buffered solutions.

An orifice plate is a device used for measuring flow rate, for reducing pressure or for restricting flow.

<span class="mw-page-title-main">Hydraulic head</span> Specific measurement of liquid pressure above a vertical datum

Hydraulic head or piezometric head is a specific measurement of liquid pressure above a vertical datum.

<span class="mw-page-title-main">Solenoid valve</span> Electromechanical valve

A solenoid valve is an electromechanically operated valve.

<span class="mw-page-title-main">Centrifugal pump</span> Pump used to transport fluids by conversion of rotational kinetic energy

Centrifugal pumps are used to transport fluids by the conversion of rotational kinetic energy to the hydrodynamic energy of the fluid flow. The rotational energy typically comes from an engine or electric motor. They are a sub-class of dynamic axisymmetric work-absorbing turbomachinery. The fluid enters the pump impeller along or near to the rotating axis and is accelerated by the impeller, flowing radially outward into a diffuser or volute chamber (casing), from which it exits.

Standard cubic feet per minute (SCFM) is the molar flow rate of a gas expressed as a volumetric flow at a "standardized" temperature and pressure thus representing a fixed number of moles of gas regardless of composition and actual flow conditions. It is related to the mass flow rate of the gas by a multiplicative constant which depends only on the molecular weight of the gas. There are different standard conditions for temperature and pressure, so care is taken when choosing a particular standard value. Worldwide, the "standard" condition for pressure is variously defined as an absolute pressure of 101,325 pascals, 1.0 bar, 14.73 psia, or 14.696 psia and the "standard" temperature is variously defined as 68 °F, 60 °F, 0 °C, 15 °C, 20 °C, or 25 °C. The relative humidity is also included in some definitions of standard conditions.

In a hydraulic circuit, net positive suction head (NPSH) may refer to one of two quantities in the analysis of cavitation:

  1. The Available NPSH (NPSHA): a measure of how close the fluid at a given point is to flashing, and so to cavitation. Technically it is the absolute pressure head minus the vapour pressure of the liquid.
  2. The Required NPSH (NPSHR): the head value at the suction side required to keep the fluid away from cavitating.

The Hazen–Williams equation is an empirical relationship which relates the flow of water in a pipe with the physical properties of the pipe and the pressure drop caused by friction. It is used in the design of water pipe systems such as fire sprinkler systems, water supply networks, and irrigation systems. It is named after Allen Hazen and Gardner Stewart Williams.

<span class="mw-page-title-main">Air flow bench</span> Device for testing internal aerodynamics of engine parts

An air flow bench is a device used for testing the internal aerodynamic qualities of an engine component and is related to the more familiar wind tunnel.

Pressure drop is defined as the difference in total pressure between two points of a fluid carrying network. A pressure drop occurs when frictional forces, caused by the resistance to flow, act on a fluid as it flows through a conduit. This friction converts some of the fluid’s hydraulic energy to thermal energy. Since the thermal energy cannot be converted back to hydraulic energy, the fluid experiences a drop in pressure, as is required by conservation of energy.

In fluid dynamics, the Oseen equations describe the flow of a viscous and incompressible fluid at small Reynolds numbers, as formulated by Carl Wilhelm Oseen in 1910. Oseen flow is an improved description of these flows, as compared to Stokes flow, with the (partial) inclusion of convective acceleration.

In a nozzle or other constriction, the discharge coefficient is the ratio of the actual discharge to the ideal discharge, i.e., the ratio of the mass flow rate at the discharge end of the nozzle to that of an ideal nozzle which expands an identical working fluid from the same initial conditions to the same exit pressures.

In engineering, physics, and chemistry, the study of transport phenomena concerns the exchange of mass, energy, charge, momentum and angular momentum between observed and studied systems. While it draws from fields as diverse as continuum mechanics and thermodynamics, it places a heavy emphasis on the commonalities between the topics covered. Mass, momentum, and heat transport all share a very similar mathematical framework, and the parallels between them are exploited in the study of transport phenomena to draw deep mathematical connections that often provide very useful tools in the analysis of one field that are directly derived from the others.

Compressor characteristic is a mathematical curve that shows the behaviour of a fluid going through a dynamic compressor. It shows changes in fluid pressure, temperature, entropy, flow rate etc.) with the compressor operating at different speeds.

Morris Muskat et al. developed the governing equations for multiphase flow in porous media as a generalisation of Darcy's equation for water flow in porous media. The porous media are usually sedimentary rocks such as clastic rocks or carbonate rocks.

References

  1. "Valve Sizing" (PDF). Technical Bulletin. Swagelok. Retrieved 21 April 2020.
  2. "Cv Calculator". Generant. Retrieved 21 April 2020.
  3. Boysen, Herman. "kV: what, why, how, whence?" (PDF). Technical paper. Danfoss. Danfoss. Retrieved 21 April 2020.
  4. "Control Valve Sizing". Control Valve Handbook (PDF) (5th ed.). Emerson Electric. September 2019. Retrieved 26 February 2022.
  5. Strömungstechnische Kenngrößen von Stellventilen und deren Bestimmung [Fluidic characteristic quantities of control valves and their determination](PDF) (Standard). VDI, VDE. September 2007. 2173. Retrieved 17 April 2020.

See also