1) A horizontal cross compound steam engine computes 300 kW at 90 rpm. The coefficient of fluctuation of energy as found from the turning moment diagram is to be 0.1 and the fluctuation of speed is to be kept within + 0.5% of the mean speed. Determine the weight of the flywheel required, if the radius of gyration is 2 m.
2) A single cylinder double acting steam engine designs the 150 kW at a mean speed of 80 r. p. m. The coefficient of fluctuation of energy is 0.1 and the fluctuation of speed is ± 2% of mean speed. If the mean diameter of the flywheel rim is 2 meter and the hub and spokes provide 5% of the rotational inertia of the flywheel, find the mass and cross-sectional area of the flywheel rim. Assume the density of the flywheel material (which is cast iron) as 7200 kg/m^{3}
3) A shaft carries the four masses in the parallel planes A, B, C and D in this order along its length. The masses at B and C are 18 kg and 12.5 kg respectively, and each has the eccentricity of 60 mm. The masses at A and D have the eccentricity of 80 mm. Angle between the masses at B and C is 100° and that between the masses at B and A is 190°, both being measured in same direction. The axial distance between the planes A and B is 100 mm and that between B and C is 200 mm. If the shaft is in complete dynamic balance, Find:
a) The magnitude of the masses at A and D;
b) The distance between planes A and D; and
c) The angular position of the mass at D.
4) The following data relate to a single cylinder reciprocating engine:-
Mass of reciprocating parts = 40kg
Mass of revolving parts = 30kg at 180 mm radius
Speed = 150 rpm,
Stroke = 350 mm.
If 60% of the reciprocating parts and all the revolving parts are to be balanced, Find
a) The balance mass required at a radius of 320mm.
b) The unbalanced force when the rank has turned 45° from the top dead centre.
5) A machine of mass 75 kg is mounted on springs and is fitted with a dashpot to damp out vibrations. There are three springs each of stiffness 10 N/mm and it is found that the amplitude of vibration diminishes from 38.4 mm to 6.4 mm in two complete oscillations. Suppose that the damping force varies as the velocity, Find:
a) Resistance of the dash-pot at unit velocity;
b) The ratio of the frequency of the damped vibration to the frequency of the undamped vibration; and
c) The periodic time of the damped vibration.