Abstract
This paper deals with the measurement of instantaneous oil flow rate for laminar pulsating flow in a pipeline using a venturi meter.
Assuming that the flow is axisymmetric, laminar, incompressible and sinusoidal and that streamlines in the convergent tube are rectilinear, equations between flow rate and differential pressure were obtained theoretically from Navier-Stokes equations of motion and continuity equation by expressing the velocity profile in the cross section as power series of radial coordinate.
In order to satisfy the assumption mentioned above, in designing the venturi meter, the taper of the convergent tube was made much smaller than that of ordinary venturi meters.
Differential pressure was measured by a diffused type semiconductor differential pressure transducer.
Experimental results agreed fairly well with the theory. The relation between time-mean differential pressure and Reynolds number and Bode diagram of flow rate amplitude with respect to differential pressure amplitude were obtained.
Consequently, the theory developed in this paper can be considered to be accurate to obtain the approximately sinusoidal flow rate from measured differential pressure at Reynolds number up to 450, at Strouhal number up to 0.56 and at flow rate amplitude ratios up to 0.2, if one uses a venturi meter with small taper of the convergent tube.
The velocity profile in the cross section of the convergent tube was found to be quite different from that of laminar pulsating flow in a circular tube, even if convergent angle is very small.
When flow rate amplitude is less than 0.2 times average flow rate, time-mean differential pressure is scarcely dependent upon flow rate amplitude.
