An irrotational region of two-dimensional flow is formed by superimposing a source of strength m₁= 2.00 m²/s at (x,y) = (0, –1), a sink of strength m₂= –1.00 m²/s at (x,y) = (1, –1), and a vortex of strength Γ = 1.50 m²/s at (x,y) = (1,1), where all spatial coordinates are in meters. Calculate the fluid velocity at the point (x,y) = (1,0).  In the figure below, m is represented as (V& / L), which can be used to approximate three dimensional line source of length L  (perpendicular to the figure plane) and volume flow rate V . (picture is attached)

A long circular cylinder of diameter 2a meters is set horizontally in a steady stream (perpendicular to the cylinder axis) of velocity U m/s. The cylinder is caused to rotate at ω rad/s around its axis. Obtain an expression in terms of ω and U for the ratio of the pressure difference between the top and bottom of the cylinder divided by the dynamic pressure of the stream (i.e., the pressure coefficient difference).