Given an incompressible 2d flow with x and z velocity given by u= alpha*x and w= beta* z
a) how are alpha and beta related?
b) if the initial positions (t=0) are given by x and z what are the fluid positions x, z in terms of x, z,t?
c) sketch the x, z fluid element trajectory d) express the velocity field in lagrangian coordinates.

4r-134a enters the condenser of a residential heat pump at 800 kpa and 50°c at a rate of 0.022 kg/s and leaves at 750 kpa subcooled by 3°c. the refrigerant enters the compressor at 200 kpa superheated by 4°c determine (a) the isentropic efficiency of the compressor, (b) the rate of heat supplied to the heated room, and (c) the cop of the heat pump. also, determine (d) the cop and rate of heat supplied to the heated room if this heat pump operated on the ideal vapor-compression cycle between the pressure limits of 200 and 800 kpa. (0.757, 4.37 kw, 5.12, 6.18, 3.91 kw)