Assignment Sheet-4

Subject: Process Modelling and Simulation

Max. Marks:2

1)A tank has a cross-sectional area of 1m

2 and normal discharge of 20m

3/hr . How does the

depth change with time if the flow to the tank is suddenly increased to 25 m3/hr. F2 is

related to h by F2= 10*h0.5

. Derive the dynamic model of the system.

2) A dilute solution at 20oC is added to a well stirred tank at a rate of 180kg/hr. A heating

coil having an area 0.9m2 is located in the tank and contains steam condensing at 150

oC.

The heated liquid leaves at 120 kg/hr and at a temperature of the solution in the tank.

There is 500kg of solution at 40oC in the tank at the start of the operation. The overall heat

transfer coefficient is 342 kg/hr.m2.oC and heat capacity of water is 1Kcal/kg

oC . Derive a

relation between the outlet temperature and time

3)Water flows from a conical tank at a rate of Kh0.5

m3/min. The entering flow rate is

given by Fo m3/min . The radius and height of the conical tank is R and H respectively.

Derive model equation relating time and height at any time t. Given the initial height of

water in the tank is ho at time t=0.

4)Consider a set of reversible reaction:

K1 K3

A B and B C

K2 K4

Where NA,NB, NC be the moles of A, B,C respectively present at any time t. Since the

reaction is constant volume, NA,NB, NC are proportional to concentration. Derive

+ ( )

+(( ) ( ) ( )) ( )

5) A batch distillation unit is charged with 100 moles of 60 mole % benzene and 40 mole %

toluene. Given mixture at any instant and the vapor leaving the still may be considered to

be at equilibrium with the remaining liquid. The benzene in vapor and liquid are related

by y= 2.6x / (1+1.6x) . Derive the equation relating the amount of liquid remaining in the

still to mole fraction of benzene.

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