# Find the circulation around a spinning circular cylinder in free stream flow of velocity $$40\,m/s$$ at a standard sea level conditions, if the lift produced by the cylinder is $$8\,N/m$$ of span.

Find the circulation around a spinning circular cylinder in free stream flow of velocity $$40\,m/s$$ at a standard sea level conditions, if the lift produced by the cylinder is $$8\,N/m$$ of span.

Asked on 16th June 2021 in
Lift per unit span produced by a circular cylinder with circulation, $$\tau$$,  is  $L^\prime=\rho _{\infty} v_{\infty }\tau$ This is also called the Kutta-Joukowski theorem. A spinning cylinder has a higher velocity at the top surface and a lower velocity at the bottom surface. Therefore, pressure at the top surface of the cylinder is lower than the bottom. This pressure difference creates a net upward force, which is called lift.
Since,$L^{\prime}=\rho _{\infty} v_{\infty }\tau$$\Rightarrow 8=1.225\times 40\times \tau$$\Rightarrow \tau = 0.1633$Therefore, circulation around the spinning circular cylinder is $$0.1633\, m^{2}/s$$ .