Q$2$: Design a two$-$dimensional contraction with an area ratio of $3$: $1.$ The inlet section is rectangular with $60cm40cm,$ while the exit section is $20cm40cm.$ Assume the contraction's longitudinal length to be $100cm.$

A$.$ Calculate the shape of the contraction.

B$.$ Draw a neat sketch of the contraction showing its main features.

C$.$ Derive a formula for the pressure coefficient distribution along the contraction.

D$.$ Comment on the effect of boundary layer development on the contraction's inner walls on the pressure coefficient distribution.