Cork Institute of Technology Bachelor of Engineering (Honours) in Chemical & Process Engineering – Stage 1 (NFQ – Level 8)
Summer 2006 CE1.5 Process Principles
(Time: 3 Hours) Instructions Answer FOUR questions. All questions carry equal marks.
Q1
(a)
Examiners: Mr. I. O Sullivan Prof. L. Kershenbaum Mr. D. O Connor
3
In an article on measuring flow from pipes, the author calculated Q = 41 m /s using the formula
Q = CA1
2gV( p1 − p 2 ) A 1 − 1 A 2
2
Where Q = volumetric volumetric flowrate, m3/s C = dimensionless coefficient, 0.6 A1 = area (2 m 2) A2`= area (5 m 2) -3
3
V = specific volume, 10 m /kg P = pressure; (p1 – p2) is 50 kPa g = acceleration due to gravity gravity (9.81 (9.81 m/s 2) Was the calculation correct? Answer yes or no and briefly explain your answer. (5 Marks) (b)
A cylindrical rod of Silica (SiO2) is heated to its melting point and a cylindrical thread of silica 0.125 mm is drawn from the melt. By careful control of the temperature and the tension on the string being drawn, long cylindrical threads of uniform diameter can be obtained to make optical fibres. (i)
Calculate how much fibre (in km) can be drawn from one cylindrical rod of silica 1.0m in length and 2.5 cm in diameter. Also estimate the mass if the specific gravity of silica is 2.25.
(5 Marks)
(ii) Before optical fibre is used, it is typically covered with a thin protective coating of a polymer with density 1,740 kg/m 3. How much polymer (kg) is needed to coat the entire fibre? (c)
(5 Marks)
Calculate all temperatures from the one given for scenario i to iv (i)
°F °R K
(ii)
(iii)
(iv)
140 500 298
°C
-40 (5 Marks)
(d)
Pressure in a gas cell PG is measured with an inverted manometer as shown in figure Q1(d). The scale on the right hand side shows the distances in mm (not to scale) of the liquid interfaces within the manometer. What is the pressure in the cell P G (mmHg) if the pressure in tank 1 (P 1) is 12.5 psia? NOTE: The temperature in the system is 300K.
Figure Q1(d) (5 Marks)
2
Q2
(a)
Calculate the volume (ft3) occupied by 88 lb of CO 2 gas at 15 °C and a pressure of 32.2 ft (abs) of water.
(b)
(5 marks)
3000 m3/d of a gas mixture containing methane and n-butane at 21 °C enters a separation tower (stream F). The partial pressures at the inlet conditions are 103 kPa for methane and 586 kPa for n-butane. In the separator 80% of the butane is removed via stream L. The remaining butane leaves the tower at 38 °C along with all of the methane (stream V). The total pressure of exit stream V is 550 kPa. How many moles per day of n-butane are removed from the feed gas in this process? What is the volumetric flowrate of the gas at the exit? Assume a basis of 1 day.
V
L
(20 Marks)
Q3
(a)
A sample of natural gas taken at 3500 kPa absolute and 120 °C is separated by chromatography at standard conditions. It was found by calculation that the grams of each component in the gas were Component
(g)
Methane (CH4)
100
Ethane (C2H6)
240
Propane
150 (C3 H8)
Nitrogen (N2)
50
Total
540
What was the density of the original gas sample?
3
Figure Q3(a)
Figure Q3(b) (13 Marks)
4
(b)
The pressure gauge on an O 2 cylinder stored outside at 0 °F in the winter reads 1375 3
psia. By weighing the cylinder (whose volume is 6.7 ft you find that the net mass, that is, the mass of the O 2 is 63.9 lb. Using the Redlich-Kwong equation of state determine whether the pressure reading is correct.
p =
RT
V^ − b
^
R 2TC2.5
b = 0.08664
^
T 0.5 V V + b
a = 0.42748
RT = p +
a
−
p c RTc p c
^ V− b ^ 2 V a
27 R 2 TC2 a = 64 pc 1 RTc b = 8 pc (12 marks) Q4
(a)
For each of the conditions of temperature and pressure listed below for water, state whether the water is in the solid phase, the liquid phase, the saturated state or in the superheated state. Use the steam tables attached to this paper to assist in your determinations. 3
State
P (kPa)
T (K)
v (m /kg)
1
2000
475
-
2
1000
500
0.2206
3
101.3
200
-
4
245.6
400
0.7308
5
1000
453.06
0.001127
6
200
393.38
0.8857 (6 marks)
5
(b)
A vessel that has a volume of 0.35 m3 contains 2 kg of a mixture of liquid water and water vapour at equilibrium with a pressure of 450 kPa. What is the quality of the water vapour? ^
Hint:
^
^
V liquid & vapour = (1 − x ) V f + x V g (8 marks)
(c)
1000 m3 of air saturated with water vapour at 30 °C and 99.0 kPa is cooled to 14 °C and compressed to 133 kPa. How many kg of water will condense out? (11 marks)
Q5
(a)
In the final stages of the industrial production of penicillin, air enters a dryer having a dry bulb temperature of 34 °C and a wet bulb temperature of 17 °C. This moist air 3
flows over the penicillin at a pressure of 1 atm and a flowrate of 4500 m /hr. 68.2 kg of the penicillin/water feed is placed in the dryer at 34 °C with a moisture content of 80% (of total mass) and leaves the dryer with a moisture content of 71.4%. Calculate the outlet dry bulb temperature of the air assuming that adiabatic drying occurs. (15 marks) (b)
Air is being compressed from 100 kPa and 255K (where it has an enthalpy of 489 kJ/kg) to 1000 kPa and 278 K (where it has an enthalpy of 509 kJ/kg). The exit velocity of the air from the compressor is 60 m/s. What is the power required (in kW) for the compressor if the load is 100 kg/hr? Hint: Assume that the inlet air flowrate is negligible.
6
(10 marks)
Figure Q5(a)
7
Q6
(a)
Calculate the heat of vaporization of water at 3.5 °C using the Clausius-Clayperon equation. Compare the value calculated to an appropriate value from the steam tables.
ρmercury = 13590 kg/m3. g = 9.81 m/s
log10
p1* p*2
2
^
1 1 ∆ H v − = 2.303R T2 T1 (10 marks)
(b)
Determine the enthalpy change when 1 gmol of SO 2 gas is cooled from 538 °C to –101
°C at a pressure of 1 atm. Data: Boiling point:
-5 °C
Melting point:
-75.5 °C
Latent heat of vaporization:
24940 J/gmol
Latent heat of fusion:
7401 J/gmol
Average liquid Cp:
1.28 J/gmol °C
Average solid Cp:
0.958 J/gmol °C (8 marks)
(c)
In a fluidised bed gasification system you are asked to find out the heat of formation of a solid sludge of composition C 5H2 from the following data. H kJ/gmol
