Name: Nguyen Huu Cong
ID: Cttt 10210113
ECH158B: Processes Design
Homework Assignment #2
Problem 3:
In centrifugal compressor we need to estimate the polytropic head each stage. First thing to correlation is polytropic efficiency.

𝜂
𝑝=
n
n−1
γ
γ−1
or
n
n−1=
γ
𝜂
𝑝
γ−1=
1.67∙0.75
1.67−1= 1.87
So,
n−1
n= 0.535 and
γ
γ−1= 2.49
Then, we calculate the compression ratio:

P
2
P
1= 100psia/25psia = 4
We have 5 stages, the polytropic head can be determined by
Hpoly=
n
n−1
Nsz1
𝑅
𝑔
T1
𝑃
2
𝑃
1
𝑛−1
𝑛
𝑁
𝑠−1=
n
n−1
Nsz1
𝑅
𝑔
𝑐
𝑔
𝑀
𝑤
T1
𝑃
2
𝑃
1
𝑛−1
𝑛
𝑁
𝑠−1

Assuming the compressibility (z1) is 1 :

Therefore Hpoly =

= 5777 ft
And the adjust speed is:
N= Nnom
𝐻
𝑟𝑒𝑞
𝐻
0.5= 8100
5777
12000
0.5 = 5620 rpm
The outlet temperature is:
T2 = T1
𝑃
2
𝑃
1
𝑛−1
𝑛
𝑁
𝑠= 500∙40.107= 580°𝑅 = 120℉
Problem 4:
The flow rate will be given as:
Q= Cvf(z
𝑃
𝑐𝑣
𝑠𝑔
and equal-percentage valve (=%) valve: f(z) = Rz-1
So flow rate is: Q = 5030)0.55-1
17.5
1= 45.27 QPM
Problem 2:
We have the specific gravity of toluene is 0.877. To find the pressure drop across the valve, we need to estimate the pressure at points around the valve.
h =
𝑃
𝜌𝑔=
𝑃
𝑆𝐺
𝜌
𝑤𝑎𝑡𝑒𝑟∙𝑔

Pressure have to be shown in psi (lbf/in2) so h =
𝑃
𝜌𝑔=
𝑃(144
𝑆𝐺∙62.4∙(𝑔
𝑔
𝑐=
2.31𝑃
𝑆𝐺

Then, pressure at point 2:
P2 = 152psia – 9.5psi -
ℎ∙𝑆𝐺
2.31= 152psia – 9.5psi -
120𝑓𝑡∙0.877
2.31= 96.94 psia
Pressure at point 3:
P3 = (68psig + 14.7psi) + 3psi +
20𝑓𝑡∙0.877
2.31= 93.29 psia
So the pressure drop at valve is: ∆= P3 – P2 = 96.94 – 93.29 psia = 3.65psia
Using the design equation at maximum flow rate: Q= Cvf(z
𝑃
𝑐𝑣
𝑠𝑔

equal-percentage valve (=%) valve: f(z) = Rz-1, at 100% f(z) = 1
Therefore, Cv = Q
𝑠𝑔
𝑃
𝑐𝑣= 500
0.877
3.65= 245
At minimum flow rate: Cv = Q
𝑠𝑔
𝑃
𝑐𝑣= 60
0.877
3.65= 29.4
Using Masonelian 21000 Series control valves, we can select a 5 inch contoured trim linear valve with a Cv at 100% opening 400 and the maximum flow corresponding to about 70% open.
/



Problem 1:
We convert standard cubic feet per day to actual cubic feet per day
ACFD = SCFD
𝑃
𝑠
𝑅𝐻
𝑠
𝑃𝑉
𝑠
𝑃
𝑏
𝑅𝐻
𝑎
𝑃𝑉
𝑎
𝑇
𝑎
𝑇
𝑠
𝑃
𝑏
𝑃
𝑎

where:
Ps = Standard pressure (PSIA)
Pb = Atmospheric pressure - barometer (PSIA)
Pa = Actual pressure (PSIA)
RHs = Standard relative humidity
RHa = Actual relative humidity
PVs = Saturated vapor pressure of water at standard temperature (PSI)1
PVa = Saturated vapor pressure of water at actual temperature (PSI)1
Ts = Standard temperature (°R) NOTE: °R =°F+460
Ta = Actual temperature (°R)1.
At standard temperature is 70oF, standard pressure is 1atm=14.7 psia
Humidity at standard is 0.36…
So we calculate ACFD = 1.2∙13.106 = 15.6.106 (ft3/day)
Assume pipelines are commercial steel so 𝜀 = 0.000046,