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Theory of Operations |
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One methodology for an Internally Compensated Laminar (ICL) unit is based on the physics of the Poiseuille Equation.
First an internal restriction is created. This restriction is known as a Laminar Flow Element (LFE).
The LFE forces the gas molecules to move in parallel paths along the length of the passage, nearly eliminating flow turbulence (Figure 1).
The differential pressure drop is measured within the laminar region.
The Poiseuille Equation quantifies the relationship between pressure drop and flow as:
Q = (P1 - P2)π r4 / 8ηL
Where:
Q = Volumetric Flow Rate
P1 = Static pressure at the inlet
P2 = Static pressure at the outlet
r = Hydraulic Radius of the restriction
η = (eta) absolute viscosity of the fluid
L = Length of the restriction
Since π, r and L are constant, the equation can be rewritten as:
Q = K(Δ P/η)
In this equation, K is a constant factor determined by the geometry of the restriction. It shows
the linear relationship between volumetric flow rate (Q), differential pressure (ΔP), and
absolute viscosity (η) in a simpler form.
Changes in gas temperature affect the absolute viscosity of the gas. This requires a temperature
measurement to determine the value of η. For most DP devices this is done by manually referencing
charts that indicate the viscosity properties of the gas at given temperatures. In an ICL device this
reference is performed internally through the use of a discrete temperature sensor and a microprocessor.
At this point only the volumetric flow rate has been determined. For an ICL device to address the range
limitations of thermal devices, additional measurements must be taken to determine the actual mass flow
rate of the gas. The relationship between volume flow and mass flow is:
Mass = Volume * Density Correction Factor
Ideal gas laws show us that the density of a gas is affected by its temperature and absolute pressure.
Using ideal gas laws, the effect of temperature on density is:
ρa / ρs = Ts / Ta
Where:
ρa = Density @ Flow Condition
Ta = Absolute Temperature @ Flow Condition in Kelvin
ρs = Density @ Standard Condition
Ts = Absolute Temperature @ Standard Condition in Kelvin
°K = °C +273.15 (to find Kelvin)
And the effect of absolute pressure on density is:
ρa / ρs = Pa / Ps
Where:
ρa = Density @ Flow Condition
Pa = Flow Absolute Pressure
ρs = Density @ Standard Condition
Ps = Absolute Pressure @ Standard Condition
Therefore, in order to determine the mass flow rate (M), two correction factors must be
applied to volumetric flow rate: temperature effect on density, and absolute pressure
effect on density. This can be written as:
M = Q(Ts / Ta)( Pa / Ps)
In an ICL flowmeter a discrete absolute pressure sensor is also placed in the laminar region of
the flow stream. This information is sent to the microprocessor and is combined with the data
from the discrete absolute temperature sensor for the appropriate calculations to determine mass flow.
Performing these calculations requires reference to some standard temperature and pressure (STP) as
indicated by variables Ts and Ps. STP is usually defined at sea level conditions, but no single
standard exists for this convention. Examples of common reference conditions include:
0 °C and 14.696 PSIA
25 °C and 14.696 PSIA
0 °C and 760 torr (mmHG)
It is relevant to note, while the correct units for mass are expressed in grams, kilograms, etc., it
has become standard that the mass flow rate is specified in SLPM (standard liters per minute), SCCM
(standard cubic centimeters per minute) or SCFH (standard cubic feet per hour). By knowing the STP
calibration of the device and the density of a particular gas at that STP, it is possible to determine
the flow rate in grams per minute, kilograms per hour, etc. For example:
Given:
Gas = Helium
M = 250 SCCM
STP = 25 °C and 14.696 PSIA
Gas Density = 0.166 Grams per Liter
True Mass Flow = M * Gas Density at STP
True Mass Flow = (250 SCCM)(1 liter per 1000 CC)(0.1636 grams per liter)
True Mass Flow = 0.0409 Grams per Minute of Helium
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WHAT'S NEW |
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| We've moved! |
Alicat Scientific moved to its new facility on June 11th 2009.
Our new address is:
7641 N. Business Park Drive
Tucson, AZ 85743
Please update your address books.
New communication protocols!
Alicat flow and pressure instruments can now be ordered with RS-485 or PROFIBUS.
Now quoting units with DeviceNet communications. |
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Technical Info. |
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| Technical FAQ |
 Get answers to common technical questions.
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| Theory of Operations |
Learn how our devices work.
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| Documents |
 Download Operating Manuals, Specification Sheets, Application Notes and more.
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