Question #2

Dodecane is pumped into a well-insulated 2 m diameter cylindrical tank where it is heated to a temperature of

150 °C. The tank is 10 m tall, and the steady state liquid height is 6.5 m. The inlet temperature of the dodecane

is 10 °C.

In answering this question you can assume that the density and specific heat capacity of dodecane are constant,

and that they have values of 750 kg m³ and 2200 J kg-¹ K¹, respectively.

a. Draw a clear diagram of the system, and referring to this diagram derive suitable mass and energy

balances for the system. Clearly state any assumptions that you have made.

[5 marks]

b. The outlet flow rate (Four) is proportional to the liquid height and the resistance of the outlet valve (R):

h

Fout R

The inlet flow rate to the system is 120 L min¹¹. What is the value of R?

[2 marks]

c. If the inlet flow rate is 120 L min¹ how much energy needs to be supplied by the heater such that the

outlet temperature is 150 °C? Here you can assume that the system is at steady state.

[2 marks]

d. The inlet flow-rate is increased stepwise from 120 to 180 L min-¹ and at the same time the energy

supplied to the system is increased from the value calculated in part (c) to 550 kW. Plot the response

of the system to these changes. Determine:

• The steady-state value of the liquid height.

• The steady-state value of the liquid temperature.

• The values of the gain and time constant for the liquid height.

16 marksl