For velocities and pipe diameters above a threshold, actual fluid flow is not laminar but turbulent, leading to larger pressure drops than calculated by the Hagen–Poiseuille equation. The assumptions of the equation are that the fluid is incompressible and Newtonian the flow is laminar through a pipe of constant circular cross-section that is substantially longer than its diameter and there is no acceleration of fluid in the pipe.
The theoretical justification of the Poiseuille law was given by George Stokes in 1845.
It was experimentally derived independently by Jean Léonard Marie Poiseuille in 1838 and Gotthilf Heinrich Ludwig Hagen, and published by Poiseuille in 1840–. It can be successfully applied to air flow in lung alveoli, or the flow through a drinking straw or through a hypodermic needle. In case mass flow rates are expressed in volumetric flow units, the reference temperature and pressure conditions of the instruments flow unit is always mentioned on the calibration certificate of Bronkhorst.In nonideal fluid dynamics, the Hagen–Poiseuille equation, also known as the Hagen–Poiseuille law, Poiseuille law or Poiseuille equation, is a physical law that gives the pressure drop in an incompressible and Newtonian fluid in laminar flow flowing through a long cylindrical pipe of constant cross section. These instruments are used, for example, to measure the amount of colouring agent, flavouring agent and acid that is supplied to a candy production process. They effectively measure the flow velocity, which multiplied by the tube cross-section inside the device results in volumetric liquid flow rates. The ES-FLOW instruments measure and control volumetric liquid flow rates using ultrasound.Mass flow rates for liquids are expressed directly in mass units like grams per hour (g/h), virtually independent of temperature and pressure fluctuations. Bronkhorst mini CORI-FLOW instruments are applied in, for example, mRNA vaccine production for accurately and reproducibly measuring liquid vaccine ingredients.With very short response times - due to TCS (chip sensor) technology for the manufacturing of highly compact instruments that can measure and control gas pressure in addition to mass flow rate. Also the new FLEXI-FLOW instruments work according to the thermal mass flow measurement principle.
The EL-FLOW Select mass flow controllers are used to supply air into the production of ice cream, called aeration. Mass flow rates are typically expressed in ml n/min and l n/min.These values resemble average temperature and pressure conditions at sea level.Įxamples of mass flow & volume flow instruments As an alternative, a temperature of 20☌ and a pressure of 1 atm (1.013 bar) are used to refer to European standard reference conditions, indicated by the subscript s in the volumetric units (ml s/min, m 3 s/h).This corresponds to the prefix "s" in sccm (standard cubic centimetres per minute) or slm (standard litre per minute), which refers to American standard conditions at a temperature of 0☌ (32☏) and an absolute pressure of 1 atm (1.013 bar, 14.69 psia).The subscript n represents normal reference conditions in European style. When the mass flow rate is expressed with subscript n as in ml n/min or m3 n/h, this means that a fluid density at a temperature of 0 ☌ and a pressure of 1 atm (1.013 bar) are selected for conversion from mass flow rate to volumetric flow rate.The following reference conditions are used by Bronkhorst: Worldwide, there are quite a lot of these standard reference conditions for conversion. That’s fine, and to use density in converting mass flow to volume flow, we must pick a set of specific pressure and temperature conditions at which we use the density value for the gas. Most users, however, think and work in units of volume. Why use volumetric units for mass flow rates?įollowing the logic above, a mass flow rate should be expressed in units of mass such as g/h, mg/s, etc.
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