EP204 Introduction to Material and Energy Balances Questions Answers

Question 1

Mass flow through a sonic nozzle is a function of gas pressure and temperature. For a given pressure p and temperature T, mass flow rate through the nozzle is given by the equation:

where m is in lb_m/min, p is in atm, and T is in °R.

(a) Identify the unit for the constant ‘0.0853’.

(2 marks)

(b) Determine the new expression of the equation, if m, p and T are expressed in g/hr, mmHg and K, respectively.

(8 marks)

Question 2

Formic acid, CH₂O₂ (MW=46.025) is a colorless, clear, corrosive liquid with a pungent odor. It is widely used in used textiles and leather processing industries. For a given 75 wt % formic acid solution of specific gravity 1.86:

(a) Identify the mole fraction composition of this solution with a basis of 385 g solution.

(4 marks) (b) Estimate the volume (in gallons) of 3 mol CH₂O ₂ solution.

(6 marks)

Question 3

The heat capacity of liquid pentane is represented by the following correlation:

Express the correlation for C_p with the unit Btu/(lb-mol.°R) in terms of T in °R. [Hint: 1 lb-mole = 454 gmol]

(9 marks)

Question 4

A differential manometer filled with manometer fluid X is used to measure the pressure drop between two points in a process line containing liquid glycerol, C₃H₈O₃ (SG=1.260). The pressure drop is found to be 13.5 mm Hg with the reading of the differential manometer is shown in Figure 4(a). In another occasion, a sealed end manometer (Figure 4(b)) containing manometer fluid X is used to measure the atmospheric pressure. Estimate h in cm, if the atmospheric pressure is 745 mm Hg.

(6 marks)

Question 5

Evaporation and recycling systems are adopted in the calcium chloride (CaCl ₂) crystallization process. The simplified process flow diagram is depicted in Figure Q1.

The recycled stream (R) is maintained at the composition of 0.7 kg CaCl ₂/kg H₂O.

Figure Q1

(a) Sketch a completely labelled process flow diagram (with compositions) for the process.

(8 marks) (b) Compute the mass flow rate (kg/hr) of stream W, R and D, respectively.

(8 marks) (c) In the case of evaporator failure, it is found that the evaporator can only cope with the water evaporation rate (W) of 1.5 lb_m/s. Estimate the new feed flow rate (F) required (lb _m/s) and the formation rate (lb_m/s) of crystal product (P), if the composition of all streams is to be remained unchanged.

(4 marks)

Question 6

A proposed process to remove H₂S is by the reaction with SO ₂ through the following equation:

2𝐻₂𝑆(𝑔)+𝑆𝑂₂(𝑔)→3𝑆(𝑠)+2𝐻₂𝑂(𝑔)

In a test of the process, a gas stream containing 20 mole % H₂S and 80 mole % CH₄ is combined with a stream of pure SO ₂. The process produces 3500 g of S (s) in an hour. In the product gas, the ratio of SO₂ to H₂S equals to 2 and the ratio of H₂O to H₂S is 5.

(a) Calculate the extent of reaction (mol/hr) of the process.

(3 marks)

(b) Determine the molar flow rates (mol/hr) for both feed gas streams and all components in the product gas stream by using extent of reaction method.

(12 marks) (c) Identify the limiting reactant.

(3 marks)

Question 7

A stream of 100 kg/min superheated steam enters a turbine at 20 bar and 450°C at a linear velocity of 80 m/s and leaves at a point 2 m below the turbine inlet at 5 bar and a velocity of 350 m/s. The heat loss from the turbine is estimated to be negligible, while the turbine develops 1800 kW of work. Determine the specific enthalpy, 𝐻̂ (kJ/kg) of the turbine outlet stream, if the 𝐻̂_in of the inlet stream is 3358 kJ/kg.

(12 marks)

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