ENGR217 Fluid Mechanics & Thermodynamics 2018 EXAMINATIONS
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2018 EXAMINATIONS
PART II (Second Year)
ENGINEERING
Paper 5 (3 hours)
Fluid Mechanics & Thermodynamics (ENGR217)
A1 Answer ALL parts (a) and (b)
Property tables including the steam tables are provided in the Appendix
(a) Draw a property diagram for the phase-change process of water at a constant pressure of 1 atm. Show change in the specific volume with temperature. (4 marks)
Give a phase description, and label the processes or states such as ice,
melting, subcooled water, saturated water, evaporation, saturated steam and superheated steam. (3 marks)
How will increase in pressure to 1 MPa affect the boiling temperature of
water, the specific volume of the saturated water and the specific volume of the saturated steam? (2 marks)
(b) Dry saturated steam at a pressure of 20 bar is expanded isentropically to a final pressure of 1 bar. Determine the dryness fraction at 1 bar. (10 marks)
Find the specific work done by the steam if the expansion is
(i) in a cylinder (consider as closed system), (3 marks)
(i) through a turbine (consider as open system). (3 marks)
A2 Answer ALL parts(a)-(c).
(a) Air enters a nozzle at a pressure of 5 bar, 200° ℃ and a velocity of 30 m s¹, it exits at 1 bar and 180 m s¹ . The nozzle inlet area is 100 cm² . The gas constant is R=0.287 kJkg¹K¹,and the specific heat is cp=1.005kJ kg¹K¹ .
Determine for steady adiabatic flow:
(i) the mass flow rate of air; (4 marks)
(ii) the air exit temperature; (4 marks)
(iii) the nozzle exit area. (4 marks)
(b) A gas turbines operating on the ideal Brayton cycle, draw and label:
(i) pressure against volume (P-V) diagram, (2 marks)
(i) temperature against entropy (T-s) diagram. (2 marks)
Show on the T-s diagram and explain in terms of the work input and output, how the actual gas-turbine cycle differs from the ideal Brayton cycle. (4 marks)
(c) List three main components of a gas turbine system operating in an ideal cycle. (3 marks)
How can the cycle efficiency and the work output be improved with addition of new components to the system? (2 marks)
A3 Answer ALL parts(a)-(e)
A petrol engine operates on an air-standard Otto cycle, with a compression ratio of 11.At the start of compression, the pressure and the temperature of the air are 1 bar and 303 K respectively.
The compression and expansion of this engine can be assumed as adiabatic. The adiabatic law is given as
PV =constant
Tvy-l =constant
P¹-T=constant,where the variables carry their usual meanings.
(a) Find the pressure and the temperature of the air at the end of the compression stroke for the isentropic compression with y=1.4. (3 marks)
(b) Determine the maximum pressure and the temperature of the cycle, when the
heat supplied at constant volume is 1350 kJ kg, and the heat capacity (or the specific heat) is cy=0.88 kJ kg¹ K¹while heat is added. (4 marks)
(c) Consider the isentropic expansion with y= 1.33, and the heat capacity cy equal to 0.74 kJ kg¹ K¹ while heat is rejected. Find the heat rejected and the efficiency. (4 marks)
(d) Assume the compression process to be isothermal rather than isentropic, for the same heat addition as above, r=1.33 for expansion, cv=0.88 kJ kg¹K¹for heat addition and cy=0.74 kJ kg¹K¹ for heat rejection, determine the new thermal efficiency. (5 marks)
(e) Draw the indicator pressure versus volume (P-V) diagrams of:
(i) a real cycle,
(ii) the Otto cycle.
List the main losses neglected in an air-standard Otto cycle, analysing the P-V diagrams. (9 marks)
B1 Answer ALL parts(a)-(c).
(a) A pipeline 1200 mm in diameter carries a flow of methane gas at 15 ℃ and gauge
pressure 3.5 bar. The density of the gas is 2.70 kg/m³ and its viscosity is 1. 15x10⁵
Ns/m² . The mean velocity of flow of the gas is 0.90 m/s.
Is the flow laminar or turbulent? (5 marks)
(b) Find the friction factor for the condition given above, and estimate the pressure drop in a 250 m length of the pipeline. The roughness value of the inner surface of the pipeline is k =0.35 mm. (10 marks)
(c) Diesel fuel flows along a pipe 6 m long, whose bore (internal diameter) is 5 mm.The density and viscosity of the fuel are 850 kg/m³and 1.8x10³Ns/m² respectively. If the pressure drop over the length of the pipe is 1.3 kN/m²,estimate the volume flow rate of fuel along the pipe.(Hint: Poiseuille's equation: Q=( △PπR⁴)/(8μL).) (10 marks)
B2 Answer ALL parts(a)-(c).
(a) To find the metacentric height in roll of his 9.9 tonne vessel, a yachtsman
uses a heavy container of mass 150 kg. When placed at one side of the deck, the container causes the yacht to heel by 4.2° . The container is then moved across the deck to the opposite side, and produces a heel of 4.2° the other
way. The overall width of the deck is 9.5 m.
What is the metacentric height in roll? (8 marks)
(b) A block in the form of a cube of side 12.0 m floats with half its height submerged as shown in Figure B2(b).
Figure B2 (b): Semi submerged block.
The mass of the block is not uniformly distributed: the centre of gravity G is below the geometrical centre by a distance y.
(i) What is the height of the centre of buoyancy B above the
bottom of the block? (2 marks)
(ii) Find the value of the metacentric radius, BM, and so find the
height of the metacentre M above the bottom of the block. (5 marks)
(iii) If the block is to float stably as shown, what is the minimum
distance y by which the centre of gravity G is below the geometric centre of the block? (2 marks)
(c) A ship of displacement 7000 tonne carries oil fuel in four tanks 10.0 m long
and 5.0 m broad, the tanks arranged with their length in the fore- and-aft
direction (lengthwise of the ship). The specific gravity of the oil is 0.84, and
the density of sea-water in which the ship is floating is 1,020 kg/m³ .By how much is the metacentric height of the ship reduced by the oil contained in the tanks? (8 marks)
B3 Answer ALL parts(a)-(e).
(a) A road haulage truck has an approximate rectangular frontal area 2.5 m wide by 3.8 m high. To investigate the drag on the truck, a one-fifth scale model is to be tested in a wind tunnel. We can assume that the density and viscosity of the air are the same for the model as for the full size truck. If the truck travels at 120 km/h, what is the appropriate air speed for the model in the wind tunnel? (7 marks)
(b) Suppose the wind tunnel available is only capable of generating an air speed of 75 m/s. Can we obtain an appropriate estimate of the drag coefficient? (2 marks)
(c) For the one fifth scale model tested at an air speed of 75 m/s the drag force is
700 N.In these conditions, what is the drag coefficient? (5 marks)
(d) So if we assume that the drag coefficient for the full size truck has
approximately the same value as (c) above, what drag force will it experience when traveling at 120 km/h? (5 marks)
(e) If the vehicle speed is reduced to 100 km/h, calculate the associated
reduction in power required to overcome the drag force, commenting on the result. (6 marks)
2023-08-05