A Correlating Modulus for Fluid Resistance in Accelerated Motion

The resistance to accelerating movement of objects in a fluid is normally evaluated with a mass term in the equation of motion that is greater than the actual mass of the object by an added mass described as a constant times the displaced mass of fluid. This added mass has been evaluated by numerous investigators for different body shapes from potential flow considerations. Published experimental results, mostly with oscillating systems with small amplitudes of motion, show an added mass constant that is higher than that derived from potential flow with values that are dependent upon the fluid and the object size. A few previous experiments on resistance in unidirectional accelerated motion indicate that the added mass is variable and depends upon the state of motion. The present investigation includes a development from model law considerations that results in a resistance equation of the form $$\mathrm{F=C}\frac{1}{2}{\mathrm{\rho V}}^{2}S$$ . This is identical with the normal resistance equation for steady state except for the coefficient C which, in addition to being a function of Reynolds' modulus, Froude's modulus, and the geometry, is also a function of a modulus, AL/V², where A is the acceleration, L is a characteristic length, and V is the velocity. Experiments with circular disks moving perpendicular to the plane of the disk under the action of approximate constant driving forces show this resistance coefficient to be correlated by the modulus AL/V².