Repeat Prob. 7–49, but with an additional independent parameter included, namely, the speed of sound c in the fluid. Use the method of repeating variables to generate a dimensionless relationship for Kármán vortex shedding frequency f_k as a function of free-stream speed V, fluid density ρ, fluid viscosity μ, cylinder diameter D, and speed of sound c. Show all your work.

Data from Problem 49

A periodic Kármán vortex street is formed when a uniform stream flows over a circular cylinder (Fig. P7–49). Use the method of repeating variables to generate a dimensionless relationship for Kármán vortex shedding frequency f_k as a function of free-stream speed V, fluid density ρ, fluid viscosity μ, and cylinder diameter D. Show all your work.

FIGURE P7–49

Transcribed Image Text:

V P. M D fk