Liquid propane leaving the reflux pump of a distillation column flows through a 3.5 in ID pipe at a flowrate of 90 lbm/s. There is a flowrate control valve in this line, and it is set such that the pressure drop across the valve (delta)P=15 lbf/in^2. Upstream of the valve , the pressure P1=18 bar and the temperature T1=310 K. Assume there is negligible heat transfer with the surroundings and that the density of the liquid does not change significantly.a) What is the kinetic energy change across the valve?b) What is the enthalpy change across the valve?c) What is the temperature change across the valve?d) What is the entropy change across the valve?
If there is NO change in the density of liquid propane as it passes through the valve, and if the size (area) of the pipe upstream and downstream of the valve is the same, then a) there will be no change in the velocity of propane, hence there will be no kinetic energy change. b) this is a process of throttling, with no change in kinetic energy, hence there is no change in the enthalpy. c) temperature change can be determined using the detailed property table of propane, but if it is an almost-incompressible liquid, then this too, will be negligible. d) dh = T ds + v dp. Since there is no change in h, integrate this along a constant h line from inlet to exit (upstream to downstream) and you will get ds = -(v/T) dp. Since p reduces from inlet to exit, the change in entropy will be positive. This is as expected. If we assume density (=1/v) and temperature (T) to remain constant, then the change in entropy will be s_downstream - s_upstream = (p_upstream - p_downstream) v /T.
