This experimental study investigates the effects of acceleration on the instantaneous fluid force on a body moving through the fluid. An empirical and somewhat arbitrary technique is developed to emphasize the effect of the history of the motion.

The technique consists of separating the total force, FT' on the body into three parts: the virtual mass force, FV' based on the instantaneous acceleration; a conventional pseudo-steady-state drag force, FD, based on the instantaneous velocity; and a history force, FH, which accounts for any remaining force on the body.

As an example of the technique, a series of 28 experiments were performed-on an instrumented cylinder section towed through water. The results indicate that the history force is significant. It can be as great as the added mass force during acceleration, and over half the steady state drag force during deceleration.


In contrast to the highly sophisticated analyses used to determine the structural response of offshore platforms to wave forces, the estimation of these forces is only approximate. Various analyses of Wave Project I and II data (Dean and Aagaard, 1970), (Evan s, 1970), (Wheeler, 1970) using the standard Morison equation show standard deviations of from 33% to 74% in the inertial and drag coefficients. It?s proposed that the introduction of a history force term may account for an important feature of the fluid dynamics and reduce the variability between measured and calculated forces. Total forces on a circular cylinder submerged in water were measured for four dynamical conditions:

  • acceleration from rest to constant velocity,

  • deceleration to rest from constant velocity,

  • acceleration from a low velocity to a higher constant velocity, and

  • reversal of motion from a constant forward velocity to a constant reverse velocity.

Experiments were conducted for two different constant velocity conditions in Cases A and B. Cases C and D were run at single sets of conditions only.

The objective of this study is to reduce the measured forces into three components (the inertial force, a pseudo-steady drag force and a history force) and to investigate the possibility of applying the results obtained from simple step changes to general motions.

By isolating the various components of the fluid forces and studying them individually, these components, once quantitized, could be recombined to make better predictions about the forces resulting from wave trains of varying heights and periods. Presently, predictions are based either on laboratory studies of simple steady wave trains of single height and period; or on statistical distributions obtained from open ocean studies of a few monitored offshore pile installations, which must be correlated to the conditions expected at a proposed site.

The most direct area of application for this study is envisioned as that of wave forces on submerged structural members, namely offshore oil platforms. Other applications include fluid forces on accelerating ships and submarines, and that of the forces on vibrating heat exchanger tubes (e.g., those in nuclear reactors subjected to earthquakes.

This content is only available via PDF.
You can access this article if you purchase or spend a download.