Modern Engineering Thermodynamics

Problems 445
57.* Cooling towers are large evaporative cooling systems that can be
used to transfer heat from warm water to the atmosphere by
evaporation of the water to be cooled. Prepare a preliminary
design for a cooling tower that will cool 30,000 kg/s of water
from 40.0°C to 30.0°C. Atmospheric air enters at 20 ± 10°C with
a relative humidity of 45 ± 15%. Establish the overall physical
dimensions of the cooling tower, air flow rate, water pumping
power, fan power (if forced convection is used), makeup water
requirements, air exit conditions, and so forth (Figure 12.15).
Cooled
water
Makeup
water
Warm
water
FIGURE 12.15
Problem 57.
Warm moist air out
Computer Problems
Water
spray
Fan
Cool dry
air in
The following open-ended computer problems are designed to be
done on a personal computer using a spreadsheet or equation solver.
58. Develop a computer program that returns all four ideal gas
mixture composition fractions when any one composition
fraction is input for an arbitrary mixture of ideal gases. Have the
user input the values of the gas constant, molecular masses,
number of gases in the mixture, and anything else you need to
make the appropriate calculations. Make sure the user enters the
input variables in the proper units, and make sure that correct
units appear with the output values.
59.* Develop a simple computer version of the gas tables (Table C.16
in Thermodynamic Tables to accompany Modern Engineering
Thermodynamics) for an arbitrary mixture of ideal gases with
constant specific heats. Input the composition (on a mass, molar,
or volume basis), specific heats (in proper units), and temperature
from the keyboard. Output, in a properly formatted manner, the
values of u, h, ϕ, p r ,andv r with correct units. Use reference levels of
h 0 = ϕ 0 =0atT 0 =300.Kandp 0 =1.00atm.
60.* Modify Problem 59 by adding the mixture pressure to the list of
keyboard input variables and output the specific entropy s instead
of ϕ. Uses 0 = ϕ 0 =0atT 0 = 300. K and p 0 =1.00atm.
61.* Create an accurate expanded version of the gas tables (Table C.16)
for an arbitrary mixture of ideal gases with temperaturedependent
specific heats. Allow the user to choose the gases in
the mixture from those you list in a screen menu. Have the user
input the composition (on a mass, molar, or volume basis), the
pressure, and the temperature from the keyboard in response to
screen prompts. Output the values of u, h, s,p r ,andv r with
correct units. Use reference levels of h 0 =s 0 =0atT 0 =300.K
and p 0 = 1.00 atm.
62. The saturation pressure curve for ammonia (NH 3 ) can be
approximated with
p sat = exp A − B/T DB − CðlnT DB Þ− DT ð DB Þ+ EðTDB 2 Þ
, where psat is
in psia, T DB is in R, and A = 58.88706, B = 8.58730 × 10 3 ,
C = 6.40125, D = 9.55176 × 10 −4 , and E = 3.39860 × 10 −6 .
Equation (12.28) can be modified to give the humidity ratio ω
of an air-ammonia mixture as follows:
ω = ðM NH3 /M a Þ½p NH3 /ðp m − p NH3 ÞŠ = 0:588½p NH3 / ðp m − p NH3 ÞŠ
Using these equations and Eq. (12.24), develop an interactive
computer program in English units that returns properly
formatted values for p m , T DB , ϕ, and ω for an air-ammonia
mixture, when
a. p m , T DB , and ϕ are input from the keyboard.
b. p m , T DB , and ω are input from the keyboard.
Make sure the user is prompted for the input variables in the
proper units, and that correct units appear with the output values.
63. Modify the program of Problem 62 to allow the user to
separately choose either English or Metric (SI) units for the
input and the output values.
64.* Using Eqs. (12.24) and (12.26a) and the four equations that
follow, 10 develop an interactive computer program in metric
(SI) units that replaces the psychrometric chart of Chart D.6.
Prompt the user for keyboard input of atmospheric pressure p m ,
atmospheric temperature T DB , and either the relative humidity ϕ
or the humidity ratio ω. Return to the screen properly formatted
values (with units) for p m , T DB , T DP , ω, ϕ, h # , and v a .
a. p sat = 0.1 exp[14.4351 − 5333.3/(T DB + 273.15)], for
0 ≤ T DB ≤ 38°C
b. T DP = 5333.3/[14.4351 − ln(p w /0.1)] − 273.15, for 0 ≤ T DP
≤ 38°C
c. h # = 1.005(T DB )+ω[2501.7 + 1.82(T DB )]
d. v a = ð0:286×10 −3 ÞðT DB + 273:15Þ/ ðp m − p w Þ
where p sat , p m , and p w are in MPa; T DB and T DP are in °C; h # is in
kJ/(kg dry air); and v a is in m 3 /(kg dry air).
65.* Modify the program of Problem 64 to allow the user to
separately choose either metric (SI) or English units for the
input and the output values.
66.* Expand Problem 65 by adding Eq. (12.31) to your program.
In Eq. (12.31), let ω 1 = ω, T 1 ω = T DB ,T 2 = T WB , and use
c pa = 1.005 kJ/(kg · K). Also, use 11
e. h g1 = 2501.7 + 1.82(T DB )
f. h f2 = 4.194(T WB )
g. h fg2 = 2501.7 − 2.374(T WB )
h. ω 3 = 0.622p sat /(p m − p sat )
where h g1 ,h f2 , and h fg2 are in kJ/kg, T is in °C, and p sat is
evaluated at T WB and obtained from Eq. (a) in Problem 64 by
10 These equations are from Liley, P. E., 1980. Approximations for the thermodynamic properties of air and steam useful in psychrometric calculations.
Mech. Eng. News 17 (4), 19–20.
11 These equations also are from Liley, P. E. Approximations for the thermodynamic properties of air and steam useful in psychrometric calculations.