In an oscillating incompressible flow field the force per

Chapter 7, Problem 31P

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Problem 31P

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 (see Prob. 7-22),

 

Suppose the characteristic speed and characteristic length for a given flow field are V͚ and L, respectively. Also suppose that ω is a characteristic angular frequency (rad/s) of the oscillation (Fig. P7-33). 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. Namely, we let

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