In an oscillating incompressible flow field the force per unit mass acting on a fluid particle is obtained from Newton’s second law in intensive form

Suppose the characteristic speed and characteristic length for a given flow field are V_∞ and L, respectively. Also suppose that ω is a characteristic angular frequency (rad/s) of the oscillation (Fig. P7–32). Define the following nondimensionalized variables,

Since there is no given characteristic scale for the force per unit mass acting on a fluid particle, we assign one, noting that {F(vector)/m} = {L/t²}. Namely, we let

Nondimensionalize the equation of motion and identify any established (named) dimensionless parameters that may appear.

FIGURE P7–32

151 F m av at + (VVV