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Differential Pressure Mass Flow Meter Operation - Focus on Microfluidic Control Technology

Poiseuille's law is usually used for internal compensation laminar flow (ICL) calculation. First, there is a special pipeline channel. We call it laminar flow element (LFE). LFE will force gas molecules to pass in parallel along the pipeline, almost The pressure difference at both ends was measured in the laminar flow region after elimination of turbulence. According to Poiseuille's law, the relationship between flow and pressure difference is as follows:
Q = (P1 - P2)π r4 / 8ηL
Q = volume flow
P1 = inlet static pressure
P2 = outlet static pressure
r = pipe radius
η = absolute viscosity of the fluid
L = pipe length
Since π, r, and L are constants, the above formula can be simplified to:
Q = K(Δ P/η)
In this formula, K is a constant determined by the geometry of the pipe, so a simpler linear relationship between volume flow, pressure difference and absolute viscosity is obtained.
The change of gas temperature will affect the viscosity, so it is necessary to measure the temperature to determine η. Most pressure-pressure equipments do this step by manually looking up the table (gas viscosity table at a known temperature), and the internal compensation layer is used. Flow meters & flow controllers are implemented with a separate temperature sensor and a microprocessor.
Now we only know the volumetric flow rate. For devices that use internal compensation to measure the laminar flow principle, additional measurements are required to determine the gas mass flow. The relationship between mass flow and volume flow is as follows:
Quality = Volume × Density Correction Factor
According to the ideal gas law, the gas density is affected by its temperature and absolute pressure. The relationship between density and temperature is as follows:
Ρa / ρs = Ts / Ta
Ρa = Actual gas density
Ta = actual absolute temperature
Ρs = gas density under standard conditions
Ts = absolute temperature under standard conditions
°K = °C +273.15
The relationship between density and absolute pressure is as follows:
Ρa / ρs = Pa / Ps
Ρa = Actual gas density
Pa = Actual absolute pressure
Ρs = gas density under standard conditions
Ps = absolute pressure under standard conditions
From this it can be seen that to obtain mass flow, two correction factors must be considered: the effect of temperature on density and the effect of absolute pressure on density, which can be expressed by the following formula:
M = Q(Ts / Ta)( Pa / Ps)
In the internal compensation laminar flow device, there is an independent absolute pressure sensor in the laminar flow area. Both the absolute pressure signal and the absolute temperature signal are transmitted to the microprocessor and the mass flow is calculated.
The above calculation requires reference to temperature values Ts and pressure values Ps under standard operating conditions (STP). Standard operating conditions (STP) usually refer to sea level, but there is no single standard. For example, the commonly used standard operating conditions are as follows:
0 °C, 14.696 PSIA
25 °C, 14.696 PSIA
0 °C, 760 mmHG
It is worth noting that the unit of mass is usually grams, kilograms, etc., while the units of mass flow are SLPM (standard liters per minute), SCCM (standard milliliters per minute) or SCFH (standard cubic feet per hour). As long as you know the standard working conditions of the equipment calibration and the density of the measured gas under standard operating conditions, you can calculate how many grams per minute or how many kilograms per hour. for example:
A known:
Gas = Helium
M = 250 SCCM
STP = 25 °C, 14.696 PSIA
Gas density = 0.166 g/L
Actual mass flow = M × STP gas density
Actual mass flow = 250 SCCM × (1L / 1000cm3) × 0.166 g/L
Actual mass flow = 0.0409 g/min (helium)

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