Critical Reynolds Number in Constant-Acceleration Pipe Flow

Abstract

Experimental investigation has been carried out to understand the transition to turbulence in constant-acceleration pipe flow. A fluid initially at rest in a circular pipe is accelerated at a constant acceleration. The transition to turbulence is judged on the basis of the output signal of a hot-wire anemometer or laser Doppler velocimetry in addition to flow visualization. The critical Reynolds number,Re_tr(=u_mD⁄v), is highly increased beyond that of approximately 3000 in steady pipe flows, where u_m is the cross-sectional mean velocity, D is the pipe diameter, and v is the kinematic viscosity of fluid. The following empirical equation is proposed for the critical Reynolds number.Re_tr=1.33[D(a⁄v²)^1⁄3]^1.86 where a is the acceleration.