Only one step is left to do: introduce w = f ( z ) , the complex potential of the flow. This is related to the velocity components as w ′ = v x − − i v y = v ¯ ¯ , where the apostrophe denotes differentiation with respect to the complex variable z. The velocity is tangent to the borderline C, so this means that v = ± ± | v | e i ϕ ϕ . Therefore, v 2 d z ¯ ¯ = | v | 2 d z , and the desired expression for the force is obtained: