Consider the lifting flow over a circular cylinder with a diameter of 0.8m. Calculate the lift per unit span, considering freestream sea level conditions.
Calculate the lift per unit span for a lifting flow over a circular cylinder with a diameter of 0.8 m, having a free stream velocity of 35 m/s and maximum velocity on the surface of the cylinder being 80 m/s , considering freestream sea level conditions.
At sea level, density of air = \(1.225\,kg/{m^3}\).The maximum velocity for a lifting flow over a circular cylinder occurs at top surface of the cylinder, where \(\theta \) equals to \({90^ \circ }\).\[{V_\theta } = – 2{V_\infty }\sin \theta – \frac{\tau }{{2\pi R}}\]\[ \Rightarrow \tau = – 2\pi R\left( {{V_\theta } + 2{V_\infty }} \right)\]\({V_\theta }\) is negative in clockwise direction and \(‘\tau ‘\) is positive, according to sign conventions.Therefore, \[\tau = – 2\pi R\left( {{V_\theta } + 2{V_\infty }} \right) = – 2\pi \left( {0.4} \right)\left[ { – 80 + 2\left( {35} \right)} \right]\]\[\tau = – 2\pi \left( {0.4} \right)\left[ { – 10} \right]\]\[\tau = 25.133\,{m^2}/s\]Therefore, lift per unit span is \[{L^\prime} = {\rho _\infty }{V_\infty }\tau \]\[{L^\prime} = 1.225 \times 35 \times 25.133\]\[ = 1077.577\,N/m\]