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+Kρ2A2Q2
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...
1.
Shah
,
R. K.
, and
London
,
A. L.
, 1978, Supplement 1: “
Laminar Flow Forced Convection in Ducts
,”
Advances in Heat Transfer
,
Academic Press
,
New York
, pp.
41
42
,
168
169
,
287
289
.
2.
Guide to the Expression of Uncertainty in Measurements
, 1993, ISO/IEC/OIML/BIPM,
Int. Organization for Standardization (ISO)
, Switzerland (
1st ed.
).
3.
Beavers
,
G. S.
,
Sparrow
,
E. M.
, and
Magnuson
,
R. A.
, 1970, “
Experiments on the Breakdown of Laminar Flow in a Parallel-Plate Channel
,”
Int. J. Heat Mass Transfer
0017-9310,
13
, pp.
809
815
.
4.
Sparrow
,
E. M.
, and
Lin
,
S. H.
, 1964, “
The Developing Laminar Flow and Pressure Drop in the Entrance Region of Annular Ducts
,”
J. Basic Eng.
0021-9223,
86
, pp.
827
834
.
5.
Chen
,
R.-Y.
, 1973, “
Flow in the Entrance Region at Low Reynolds Number
,”
ASME Trans. J. Fluids Eng.
0098-2202,
95
, pp.
153
158
.
6.
Shah
,
R. K.
, 1978, “
A Correlation for Laminar Hydrodynamic Entry Length Solutions for Circular and Noncircular Ducts
,”
ASME Trans. J. Fluids Eng.
0098-2202,
100
, pp.
177
179
.
7.
Atkinson
,
B.
,
Brockleband
,
M. P.
,
Card
,
C. H.
, and
Smith
,
J. M.
, 1969, “
Low Reynolds Number Developing Flows
,”
AIChE J.
0001-1541,
15
, pp.
548
553
.
8.
Heaton
,
H. S.
,
Reynolds
,
W. C.
, and
Kays
,
W. M.
, 1961, “
Heat Transfer in Annular Passages. Simultaneous Development of Velocity and Temperature Fields in Laminar Flow
,”
Int. J. Heat Mass Transfer
0017-9310,
7
, pp.
763
781
.
9.
Coney
,
J. E. R.
, and
El-Shaarawi
,
M. A. I.
, 1975, “
Developing Laminar Radial Velocity Profiles and Pressure Drop in the Entrance Region of Concentric Annuli
,”
Nucl. Sci. Eng.
0029-5639,
57
, pp.
169
174
.
You do not currently have access to this content.