Some Aspects of the Measurement of Oscillatory Hydraulic Flow Including Nonlinear Effects

Abstract

The venturi-type flowmeter is simulated by a model capable of analysis under nonsteady flow conditions. Nonlinear effects and the effect of inertia are included in the model chosen. The basic parameter in nonsteady flowmetering is shown to be a nondimensional frequency defined as the Strouhal number. The errors due to neglecting inertial forces in the flowmeter model have been calculated as a function of the Strouhal number. The analysis indicates that for a venturi type of meter the error in average flow rate calculated (neglecting inertia) is likely to be small for many practical cases. However, the phase lag and change in response, due to inertia, are likely to be important when an estimate of instantaneous flow is required. NomenclatureA -cross-sectional area d = diameter of straight section of meter / = friction factor A/ = maximum deviation of friction factor from steady state value under oscillatory conditions fi(a, ck/di) = function of half-angle a and diameter ratio d 2 /di of flowmeter FR(oi) = frequency response of the flowmeter Gi(Ns) = special function of Strouhal number (*2{Ns) = special function of Strouhal number IR = ratio of inertia in the convergent section of the flowmeter to the inertia in the straight throat section J = inertia factor of flowmeter = (2Li/u 2 , s .s.)K* K = steady state flow coefficient of meter 1 L L t N s V Ap T t u x a v> -m+f length actual length of straight section or throat in flowmeter Strouhal number (cf. Equation [20]) pressure pressure drop across meter steady state pressure drop due to friction in flowmeter period of oscillation time flow velocit}^ distance in direction of flow half-angle of conical convergence section of flowmeter (degrees)