TOTAL POINTS: 100 points
1. (16 points) Choose the correct answers. Write down (a), (b), (c), (d), (e), (f), (g), and (h) on the answer sheet, and give each item a proper corresponding number.
(1) two phase region (2) q line
(3) mole fraction of the bottom product (4) mole fraction of the overhead product (5) mole fraction of the feed
(6) tie line (7) feed tray (8) one phase region
x = mole fraction of lighter component in liquid phase
Figure 1 McCabe-Thiele diagram for distillation
Figure 2 Phase diagram
2. (18 points) What pressure gradient (in Palm) is required to cause a liquid to Aow in a horizontal, smooth, circular tube of inside diameter D=3cm a t a mass flow rate of 1028 g/s a t 20 O C ? At this temperature the density of the liquid is p=0.935g/cm3 and its viscosity is p=1.95cp.
Figure 3 Ftiction factor for tube flow
3. (16 points) The following equation of energy change is for a Newtonian fluid
with constant thermal conductivity and without heat generation.
Please write down the equation of energy change for the following special cases, respectively. Simply write down the equations and don't have to derive them.
(1) Fluid a t constant pressure (2) Fluid a t constant density (3) Solid
(4) Solid with heat generation, q(J/s)
4. (16 points) A straight fin is shown in the following figure. The fin has a constant rectangular cross section, A;and its dimension is L x W x t . The base temper- ature is To. The temperature of the surrounding air is T,, and the convection between the overall surface of the fin and air cannot be ignored.
Figure 4 Schematic illustration of a rectangular fin
(1) Perform a shell balance to derive the governing equation of the temperature profile along the fin and list the boundary conditions. Be sure to follow the indicated coordinates.
(2) Show the t.he temperature profile can be obtained in t,he following form.
h .
0 T - T, cosh[m(L - x)] + - sinh[m(L - x)]
- - - mk
0, To - T, h .
cosh mL + - sinh m L
mk where m2 = -, hP and P = ( 2 W + 2t)
k A
5. (16 points) An incompressible fluid is confined between two parallel, vertical plates as shown in the following figure. One of the plate is moving upward a t a constant velocity v,. One can assume that no pressure gradient exists except the gravity along the vertical direction. Use the shell balance to derive the velocity profile and locate the position of zero shear stress by following the indicated coordinates.
Figure 5 Flow between two vertical parallel plates
I a
I ' 1
i Fluid :
I
I 1
I I
--
I---I
A " '
L
6. (18 points) Cold air a t 55 O F , and 50% relative humidity is conditioned by being passed through a bank of heating coils, then through a water spray, and finally through a second set of heating coils. In passing through the first coil bank, the air is heated to 80°F. The temperature of the water supplied t o the spray chamber is adjusted to the wet-bulb temperature of the air admitted t o the chamber, so th& the humidifying unit may be assumed to operate adiabatically.
It is required that air emerging from the conditioning unit be a t 85 "F and 30%
relative humidity.
7
.
(1) Calculate the temperature of the water supplied to the spray chamber and the relative humidity and dry-bulb temperature of the air leaving the spray chamber. .
(2) Calculate the mass of water evaporated (lb,) per cubic foot of air fed to the whole conditioning unit.
(3) Roughly sketch the path. Show and label the path followed by the air in each of the three steps. (DO NOT attach the psychrometric chart.)
Figure G Psychrometric chart
