Newton on objects moving in a fluid - the penetration length Academic Article uri icon

abstract

  • We solve for the motion of an object with initial velocity v0 and subject only to the combined drag of forces linear and quadratic in the velocity. This problem was treated briefly by Newton, after he developed a theoretical argument for the quadratic term, which we now know is characteristic of turbulent flow. Linear drag introduces a time , and the two drag forces are equal at a critical velocity vc; this defines a characteristic distance R = vc; details are discussed for spheres and for cylinders moving along their axis. For v0/vc 1 the role of quadratic drag is largely to reduce the velocity to vc, below which linear drag dominates. The penetration length is given by LN = Rln(1 + v0/vc). As noted by Gamow, LN is relevant to the range of non-self-propelled projectiles, such as artillery shells, bullets, ground penetration bombs and spears shot from spearguns; it is also relevant to windmills and fans. 2008 IOP Publishing Ltd.

published proceedings

  • EUROPEAN JOURNAL OF PHYSICS

author list (cited authors)

  • Saslow, W. M., & Lu, H.

citation count

  • 9

complete list of authors

  • Saslow, Wayne M||Lu, Hong

publication date

  • July 2008