A distillation unit is to be used to generate pure water vapor. 5.0 lbm/s of liquid water at 100oF enters the system, and 1.0 lbm/s of saturated water vapor leaves through one port and 4.0 lbm/s of saturated liquid leaves through a second port (along with impurities in the water which can be neglected in the analysis). The pressure throughout the whole system is 20 psia. A stirring system is used, which is powered by a 0.4 hp motor – assume that all of the motor’s work enters the system. All other energy is added through heat transfer.

Question

(a) Determine the rate of heat transfer needed to produce this flow of saturated water vapor.
(b) Using your separation chamber model, plot the heat transfer rates needed to produce saturated water vapor flow rates between 0.5 lbm/s and 4.0 lbm/s (along with corresponding changes to the saturated liquid water exit flow rates).

State 1: Inlet stream; State 2: Saturated vapor exit stream; State 3: Saturated liquid exit.
Given: P1 = P2 = P3 = 20 psia; T1 = 100oF; x2 = 1.0; x3 = 0.0; m?1=5.0lbm/s; m?2=1.0lbm/a; m?3=4.0lbm/a; W?=?0.4 hp=?0.283 Btu/s
Assume: Given no other information regarding the mixing chamber, make the following common assumptions: ?KE=?PE=0. We are told there is heat transfer.
Also, assume the mixing chamber is a single-inlet, multiple-outlet, steady-state, steady-flow device.
What will be an ideal response?

Answer 1

Solution: The First Law for Open Systems reduces to Q??W?=(m?2h2+m?3h3)?m?1h1

For the entering liquid water, consider it to be a slightly compressed liquid (h1 = hf @T1)

For water: h1 = 68.04 Btu/lbm; h2 = 1156.19 Btu/lbm; h3 = 196.25 Btu/lbm

(a) Solving: ?????= 1,600 Btu/s (The power input is basically irrelevant.)

(b) Keeping in mind the conservation of mass: m?1=m?2+m?3

Plotting the heat transfer rate for the range of mass flow rates for the saturated vapor (m?2):



The large flow rates require rapid heating rates.