Consider a circular cylinder with a diameter of 4 cm being held stationary in a

Question

Consider a circular cylinder with a diameter of 4 cm being held stationary in a water channel, with the flow oriented as in the figure below. The free stream speed of the water is 50 cm/s. What is the Reynolds number for this cylinder flow? Assume the cylinder has a span (into the page) of 300 cm and neglect end-effects, i. e. assume the flow is two-dimensional and that the cylinder spans the water channel test section. What is the average drag force on the cylinder in Newton's? The cylinder is a bluff body, and here it will shed alternating vortices of opposite sign from its top and bottom surface and in to a wake. What is the vortex shedding frequency in Hz? (The shedding frequency is taken as that of the vortices shedding from the top or the bottom, the value is the same.)

Explanation / Answer

1)   Re   = rho * v * d / mu    = 10^6 * 0.5 * 0.04   = 20000    (kinematic viscoity = 10^-6 m^2/s

2)   For Re of the order of 10^4   Cd = 0.96   approx

     Fd   =    Cd * 0.5 * rho * v^2 * A

             = 0.96 * 0.5 * 1000 * 0.5^2 * 0.04 * 3    = 14.4 N

3)    frequency   = St * V / d       (St is the Strouhal number   = 0.2 for a cylinder at   Re = 2*10^4

       frequncy = 0.2 * 0.5 / 0.04   = 2.5 Hz

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