Inherently Linear Annular-Duct-Type Laminar Flowmeter

Abstract

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 conditions , L is the distance between the flowmeter pressure taps, is fluid density, and is fluid kinematic viscosity. The first component on the right-hand side of Eq. 1 is the pressure drop in the fully developed flow. The second one describes some additional pressure drop due to momentum change and accumulated increment in wall shear between developing flow and developed flow 1 . It is seen that the relationship between produced differential pressure P and flow rate Q is not linear. As a result, in the majority of commercial laminar flowmeters, to obtain precise Q values software corrections are required. In some of the commercial “laminar flow elements” the entrance effect is ignored as a relatively low one. In order to eliminate the necessity of reading corrections and to achieve inherent linearity the second term of Eq. 1 must be removed. It can be done by locating the first pressure tap P1 at the beginning of the fully developed flow region. As the entrance length Le increases with the Reynolds number Re=DhQ / A , the distance between the duct entrance and the pressure tap P1 should not be shorter than the entrance length for the maximum flow rate, i.e., for the laminar-turbulent transition Reynolds number. The main aim of this work was to determine the design recommendation for the inherently linear laminar annular-duct flowmeter. The pressure distribution along the annular duct was measured. The entrance lengths for various inlet conditions and Reynolds numbers were investigated.