Thermo fluid

Problem 1

Water (density of 998.2 kg/m3 and a viscosity of 0.001002 Pa s) flows through a piping system into an open reservoir, as shown in the diagram. The internal diameter of the pipe is 5 cm. If the gauge pressure at point 1 is 75 kPa, calculate the elevation difference between the inlet and free surface in the reservoir for which a flow rate of 36 m3/h can be maintained. Neglect frictional losses. [3 Marks]

Problem 2

Cogeneration is often used when steam is needed to supply energy to an industrial process. Rather than generating process steam from a pump and boiler, the steam is generated at high pressure and then extracted from a turbine at an appropriate pressure to meet the process energy needs. The benefit of this process is that it generates both useful power and the necessary process steam. In this case, 20 kg/s of high-pressure steam at 10 MPa and 500oC enters a two- stage turbine. Following the high-pressure stage, 5 kg/s of steam at 0.5 MPa and 155oC is extracted to meet process needs. The remaining 15 kg/s of steam exits the low-pressure stage at 20 kPa, with

a quality of 0.9. Estimate the power generated by the turbine. [5 marks]

Problem 3

Two turbines with an inter-heater are used to power a refrigerator, as shown in the diagram below. The steam flow rate through the turbines is 0.2 kg/s and the turbines have isentropic efficiencies of 70%. Inlet and outlet temperatures and pressures are indicated on the diagram. The refrigerator operates with a coefficient of performance that is 70% of the maximum theoretical coefficient of performance. The refrigerator is being used to freeze a fluid at -20°C and rejects heat to the ambient surroundings. The temperature of the surroundings may be assumed to be 25°C. [26 Marks]

Determine:

a) The power output by the first turbine (kW).

b) The heat input to the inter-heater (kW).

c) The power output by the second turbine (kW).

d) The actual COP of the refrigerator.

e) The rate at which the fluid can be frozen (kg/s).

f) The rate at which heat is rejected to the ambient reservoir (kW).

g) The change in entropy of the hot reservoir (kW/K).

h) The change in entropy of the cold reservoir (kW/K).

i) The change in entropy of the ambient reservoir (kW/K).

j) The change in entropy of the steam from the inlet to the first turbine to the exit of the second turbine (kW/K).

k) The entropy generation rate for the entire system (kW/K).

l) The rate at which work is lost for the entire system (kW).

Problem 4

A simple steam power plant operating on a non-ideal Rankine cycle is used to drive an industrial refrigeration process. The net work output from the power cycle (i.e., turbine work minus pump work) is used to drive the refrigeration cycle. Important operating conditions for both the Rankine and vapour compression refrigeration cycle are provided in the diagram. Heat is supplied to the boiler using hot oil at 600°C, which exits the boiler at 450°C. The turbine and pump operate with isentropic efficiencies of 85% and 75%, respectively. The vapour compression refrigeration cycle operates using Refrigerant-22 (R-22) as the working fluid. The condenser operates at a temperature of 35°C and rejects heat to the ambient reservoir at 25°C. The refrigeration cycle is used to condense saturated isobutane vapour to saturated liquid at its normal boiling point of -12°C. To facilitate an adequate rate of heat transfer in the evaporator, the evaporator operates at -20°C. To solve this problem, assume that the oil has a constant

specific heat of 1.9 kJ kg-1 K-1 and that the latent heat of vaporization of isobutane is 366 kJ/kg.

[31 Marks]

a) Sketch a T-s diagram for both cycles and number the states to match the numbering system used in the block diagram.

b) The power input to the pump (kW).

c) The power output by the turbine (kW).

d) The mass flow rate of oil flowing through the boiler (kg/s).

e) The rate at which heat is rejected to the ambient environment from the condenser in the Rankine cycle (kW).

f) The thermal efficiency of the Rankine cycle.

g) The specific compressor work in the refrigeration cycle (kJ/kg).

h) The flow rate of R-22 in the refrigeration cycle (kg/s).

i) The rate at which heat is rejected to the ambient environment from the condenser in the refrigeration cycle (kW).

j) The rate of condensation of isobutane (kg/s).

k) The coefficient of performance (COP) of the refrigeration cycle.

l) The entropy changes of the oil stream (kW/K).

m) The entropy changes of the isobutane stream (kW/K).

n) The entropy changes in the ambient reservoir (kW/K).

o) The rate of lost work for the entire system (kW).