# Operating principle: Laminar differential pressure mass flow technology

Most Alicat mass flow instruments use laminar differential pressure technology to measure highly accurate mass flow rates for over 98 gases.

## How Alicat devices measure mass flow rate

There are four simple steps an Alicat differential pressure device uses to calculate a mass flow rate.

1. Convert turbulent flow into smooth laminar flow
2. Measure the pressure drop across a flow channel
3. Calculate the volumetric flow rate
4. Calculate a standardized mass flow rate

This video gives a quick overview of this process:

### Calculating volumetric flow rate

Alicat devices contain a flow passage called a laminar flow element (LFE) that converts all turbulent flow into laminar flow. The instrument first measures the differential pressure drop across the LFE, and then uses the Poiseuille Equation to calculate a volumetric flow rate.

Poiseuille equation

Volumetric flow = (P1-P2)πr4/8ηL = K(ΔP)/η

P1 = Static pressure at the inlet; P2 = Static pressure at the outlet; r = Hydraulic radius of the restriction; η = Absolute viscosity of the fluid; L = Length of the restriction

The Poiseuille equation shows the linear relationship between volumetric flow rate, differential pressure (ΔP), and absolute viscosity (η). In the simplified equation, K is a constant that encompasses the geometric factors of the LFE.

### Calculating mass flow rate

Laminar DP mass flow instruments use the volumetric flow rate and a series of density correction factors to calculate a mass flow rate.

Density correction factors

1. Temperature density correction = Ts/Ta

Ta = Absolute temperature at flow conditions; Ts = Absolute temperature at standard conditions (STP)

2. Pressure density correction= Pa/Ps

Pa = Absolute pressure at flow conditions; Ps = Absolute pressure at standard conditions (STP)

3. Compressibility = Zs/Za

Za = Compressibility at flow conditions; Zs = Compressibility at standard conditions (STP)

When combined, you can produce an equation that uses volumetric flow, temperature, pressure, and gas compressibility to calculate a mass flow rate.

Mass flow rate equation

Mass flow = (Volumetric flow)(Ts/Ta)(Pa/Ps)(Zs/Za)

(Ts/Ta)(Pa/Ps)(Zs/Za) = Density correction factors

In an Alicat mass flow device, a discrete absolute pressure sensor is 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 to make the correct mass flow calculations.