MECHANICAL ENGINEERING – 2003,PAPER – II ,Section A

                              Time Allowed: Three Horus      Maximum marks: 200

Candidates should attempt Questions 1 and 5 which are compulsory and any THREE of the remaining questions selecting at least ONE question from each Section.

If any data is considered insufficient, assume suitable valur.

Newton may be converted to kg using the equality 1 kolonewton (1 kN) = 100 kg, if found necessary.

All answers should be in SI units.

Take: 1 kcal = 4. 187 kJ and 1 kg /cm³ = 0.98 bar

1 bar = 10⁵ Pascals

Universal gas constant = 8314.6 J/ k mol – k

Section A

1.       Answer any four parts:

(a)    (i) Two cannot engines work in series between the source and sink temperatures of 600 K and 300 K, if both engines develop equal power, determine the intermediate temperature.

               (ii) Show that the compression ratio for the maximum work to be done per kg of air in an Otto cycle between upper and lower limits of absolute temperatures T₃ and T₁ is given by the expression

R= (T₃ / T₁)    1 / 2(γ-1) 

(b)   (i) An ideal gas is heated at constant volume until its temperature is 3 times the original temperature, then it is expanded isothermally till is reaches its original pressure, the gas is then restored to its original state. Determine the expression of net work done.

               (ii) 300 kj / sec of heat is supplied at a constant fixed temperature of 290˚C to a heat engine. The heat rejection takes place at 8.5˚C. The following results were obtained:

                              (I)                 215 kJ/ s of heat is rejected

                             (II)               150 kJ/ s of heat is rejected

                            (III)             75 kJ/ s of heat is rejected

Using Clausius inequality which of the results report a reversible cycle of irreversible cycle, or impossible result? 

(c)    (i) What is petrol injection? What are its advantages and disadvantages?

                  (ii) What is petrol injection? What are its advantages and disadvantages?

(d)   Make a detailed comparison of SI and CI engines with respect to basic cycle, fuel, introduction of fuel in the cylinder, ignition, compression ratio and weight.

(e)   Two parallel flat plates of equal area 0.5 m² each face each other. These are at 1000 K and 500 k respectively. Shape factor between them F₁₂ = F ₂₁ = 0.285. These are placed in room whose walls are at 300 k. Find radiation heat transfer rate between the plates and between the plates and wall. Assume that outer part of both the plates is insulated.

Stefan- Boltzmann constant = 5.67 x 10 ⁻⁸ W/ K ⁴ - m³.

2.       (a) What is detonation? Factors leading to increase detonation in SI engines tend to reduce knock states above in the light of differences in their nature. Indicate the methods to reduce knock in CI engines.

(b) Determine the diameter of a fuel orifice for a 4-stroke engine working on diesel cycle developing 18 kg/ kw-hr fuel of 30˚ API. The duration of the crank injection is 30˚ of crank travel the fuel injection pressure is 125 bars and the combustion chamber pressure is 35 bars. Take velocity coefficient as 0.9 and

Ƿ = 141.5 / 131.5 + ˚API

3.       (a) (i) What is stoichiometric air requirement and excess air factor?

                                   (ii) What do you understand by higher calorific value and lower calorific value?   Explain the methods to measure them

                            (b) Determine the air-fuel ratio at 6000 m altitude in a carburetor adjusted to give an air-fuel ratio of 15: 1 at sea level where the air temperature is 300 k and pressure of 1.013bar.

The temperature of air decreases with altitude and is given by the expression

t =ts – 0.0065 h.

Where h is altitude in meters and ts is the temperature at sea level in ˚C.

The air pressure decreases with altitude as per the relation

 H= 19220log 10 (1.013 /P)

Where, p is in bar.

What remedies would you suggest to compensate for the decrease in air fuel ratio at high altitudes? Discuss them giving justification

4.       (a) show that the governing equation for temperature distribution in a fin of uniform cross –section is given by

d² Ѳ/ dx² - m² Ѳ = 0

Where, Ѳ = T – T, and m² = hP/ kA.

Further, show that the solution for boundary conditions Ѳ = Ѳₒ at X = 0 and Ѳ = Ѳ ₁at x = L is

Ѳ = [Ѳ₁ sin h mx + Ѳₒ sin h m (L – X)] / sin h mL.

                           (b) Water flows in the tube and brine flows in the annulus of a double –tube heat exchanger. Water at the rate of 0.015 kg/s is cooled from 30˚ C to 20˚C and temperature of brine increases from - 15˚C to - 5˚C. The inner and outer diameters of water of water-carrying tube are 25mm and 30 mm respectively, and thermal conductivity of metal is 45 W/ m –K. The convective heat transfer coefficients on the brine and water, side are 2700 and 2100 W/ m² - K respectively. Find 

 Overall heat transfer coefficient and then the length of the heat exchanger for parallel flow and counter flow and counter flow. Specific heat of water = 4.18kJ / kg –k.