Calculate velocity over the airfoil.

Pressure coefficient at a certain point on an airfoil is -4.2.Calculate velocity at this point assuming the flow over the airfoil to be inviscid and incompressible is (a) 50 ft/s and (b) 200 ft/s.

Asked on 1st January 2019 in Aerodynamics.
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    (a) For inviscid and incompressible flow coefficient of pressure is given as \[{C_p} = 1 – {\left( {\frac{v}{{{v_\infty }}}} \right)^2}\]\[v = \sqrt {v_\infty ^2\left( {1 – {C_p}} \right)} \]\[ = \sqrt {{{\left( {50} \right)}^2}\left( {1 – \left( { – 3.84} \right)} \right)} \]\[ = \sqrt {2500\left( {1 + 3.84} \right)} \]\[ = 110\,{\rm{ft/sec}}\]also (b) for \({{v_\infty }}\) = 200 ft/sec \[{C_p} = 1 – {\left( {\frac{v}{{{v_\infty }}}} \right)^2}\]\[v = \sqrt {v_\infty ^2\left( {1 – {C_p}} \right)} \]\[ = \sqrt {{{\left( {200} \right)}^2}\left( {1 – \left( { – 3.84} \right)} \right)} \]\[ = \sqrt {40000\left( {1 + 3.84} \right)} \]\[ = 440\,{\rm{ft/sec}}\]

    Answered on 1st January 2019.
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