(Solved): Water flows over a flat surface at a velocity, \( u \). of \( 1.0 \mathrm{~m} / \mathrm{s} \) as sh ...

Water flows over a flat surface at a velocity, \( u \). of \( 1.0 \mathrm{~m} / \mathrm{s} \) as shown in the figure. A pump injects water through a narrow slit at a volumetric rate per unit slit length of \( q\left(\mathrm{~m}^{2} / \mathrm{s}\right) \) so that there is a stagnation point at A located a distance \( d \) upstream from the slit. Assume that the flow is incompressible and inviscid and can be represented by the combination of a uniform flow and a source. Determine the minimum injection rate \( q \) required for the stagnation point \( A \) to be \( 0.9 \mathrm{~m} \) away from the slit.