Sprinkler Head Revisited: Momentum, Forces, and Flows in Machian Propulsion

TL;DR

This paper explains Machian propulsion, where devices that suck in and expel fluid move in the same direction as if only expelled, by analyzing momentum transfer and flow dynamics.

Contribution

It provides a comprehensive, conservation-based explanation of Machian propulsion, unifying previous separate analyses of different devices.

Findings

Flow shape analysis is more subtle than conservation arguments.

Machian propulsion involves efficient momentum transfer through outflow.

Applications range from microengineering to astrophysics.

Abstract

Many experimenters, starting with Ernst Mach in 1883, have reported that if a device alternately sucks in and then expels a surrounding fluid, it moves in the same direction as if it only expelled fluid. This surprising phenomenon, which we call "Machian propulsion," is explained by conservation of momentum: the outflow efficiently transfers momentum away from the device and into the surrounding medium, while the inflow can do so only by viscous diffusion. However, many previous theoretical discussions have focused instead on the difference in the shapes of the outflow and the inflow. Whereas the argument based on conservation is straightforward and complete, the analysis of the shapes of the flows is more subtle and requires conservation in the first place. Our discussion covers three devices that have usually been treated separately: the reverse sprinkler (also called the inverse, or Feynman sprinkler), the putt-putt boat, and the aspirating cantilever. We then briefly mention some applications of Machian propulsion, ranging from microengineering to astrophysics.