Pressure and Velocity Distributions in Pulsating Laminar Pipe Flow

Abstract

Dimensionless approximate solution for slightly compressible fluid flow are derived from the exact solutions of the fundamental linear equations for unsteady viscous compressible flow, and shown to be reasonable within the region w'≤3c' and c'≥3.375×104(w'=R2w/v, c'=Rc/v ; w, angular frequency ; c, speed of sound ; R, pipe radius ; v, kinematic viscosity). In this region radial velocity and cross-sectional variation of pressure are shown to be negligibly small. Pressure and velocity of air and water flow pulsating through a vertical pipe by means of a piston are measured by the use of a strain-gauge-type pressure transducer and a hot-wire anemometer, respectively. Comparisons of experimental results with approximate solutions show that cross-sectional distribution of oscillating velocities agree closely with the theoretical value within the frequency range 0.02 ≲ f ≲ 12 Hz, independently of Reynolds number, piston amplitude, pipe radius, and fluid, and that oscillating pressure distribution within the pipe and oscillating velocity distribution along the pipe axis also agree well with the theoretical values.