Consider the flow field represented by the velocity potentialφ=Ax+Bx2−By2, whereA= 1 m/s, B= 1 s−1, and the coordinates are measured in meters. Obtain expressions forthe velocity field and the stream function. Using water as the working fluid, calculate thepressure difference between the origin and the point (x, y) = (1,2). What is the volume flowrate (per unit depth) between streamlines passing through these two points?

Air is to be cooled in the evaporator section of a refrigerator by passing it over a bank of 0.8-cm-outer-diameter and 0.4-m-long tubes inside which the refrigerant is evaporating at -20°c. air approaches the tube bank in the normal direction at 0°c and 1 atm with a mean velocity of 4 m/s. the tubes are arranged in-line with longitudinal and transverse pitches of sl- st 1.5 cm. there are 30 rows in the flow direction with 15 tubes in each row. determine (a) the refrigeration capacity of this system and (b) pressure drop across the tube bank. evaluate the air properties at an assumed mean temperature of -5°c and 1 atm. is this a good assumption?