A concept of the laminar flowmeter is based on the well-known relationship between laminar flow rate of fluid $Q$ through a measuring element of length $L$ and pressure drop $ΔP$. Usually the measuring element is a capillary tube, capillary tube bundle, parallel plate bundle, or concentric annular duct (Fig. 1).

The pressure drop in the measuring element (“long duct”) consists of two components:
$ΔP=CρνL2ADh2Q+K∞ρ2A2Q2$
1
where: $C$ is a constant (depends on a duct cross-section shape), $A$ is the duct cross-sectional area, $Dh$ is the hydraulic diameter of the duct, $K∞$ is the incremental pressure drop number in a fully developed flow region (depends both on the duct cross-section shape and on the inflow...
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