Consider the two-dimensional flow field in which u=Ax2 and υ=Bxy, where A= 1=2 ft−1 s−1, B= −1 ft−1 s−1, and the coordinates are measured in feet. Show that the velocity field represents a possible incompressible flow. Determine the rotation at point ðx, yÞ=ð1, 1Þ. Evaluate the circulation about the "curve" bounded by y= 0, x= 1, y= 1, and x= 0.

Awall of 0.5m thickness is to be constructed from a material which has average thermal conductivity of 1.4 w/mk. the wall is to be insulated with a material having an average thermal conductivity of 0.35 w/mk so that heat loss per square meter shall not exceed 1450 w. assume inner wall surface temperature of 1200°c and outer surface temperature of the insulation to be 15°c. calculate the thickness of insulation required.