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4.1 A 600 MVA, 50 Hz turbine-generator has a regulation constant R=0.06 per
unit based on its own rating. If the generator frequency increases by 0.02 Hz
in steady-state, what is the decrease in mechanical power output. Assume
a fixed reference power setting. (5)
4.2 A three-phase, 50 Hz, 100 MVA, 4-pole synchronous generator has an
inertia constant H of 3.5 s and is supplying 0.16 pu real power on a system
base of 500 MVA. The input to the generator is increased to 0.18 pu. Determine:
4.2.1 The kinetic energy stored in the moving parts of the generator (2)
4.2.2 The acceleration of the generator
The diameters of the plunger and ram are 50 mm and 0.5 m respectively.
The ram is 1.75 m below the plunger and the mass density of the liquid
in the hydraulic press is 820 kg/m3. The mass of the plunger and the ram
are 6 kg and 400 kg respectively. The plunger is forced vertically down
by a lever with a mechanical advantage of 6 to 1 onto which a force of
800 N is applied. The ram moves upwards when the plunger moves
downwards. Determine the maximum lifting force exerted by the ram.
One thousand kilograms per hour of a mixture of benzene (B) and Toluene (T) containing 60% benzene by mass is separated by distillation into two fractions. The mass flowrate of the benzene (B) in the top stream is 500 kg (B) /h and that of toluene in the bottom stream is 485 kg (T) / h. The unit operates at steady state.
3.1.1. Draw a schematic diagram showing all the relevant streams in the distillation unit. (8)
3.1.2. Write the basis for calculation.
Evaluate∫∫R r²drdθ over the region R between the circles r = asinθ and r = 2asinθ
Solve ∫y=0 ^ 1 ∫x=y^ 2 ^ 1∫z=0 ^ 1-x x dzdxdy
Solve (2y³xe^y+ y² + y)dx + (y³x²e^y-xy- 2x)dy = 0.
Solve dy/dx= 4x² (y-x)² + if y /x is a particular solution.
Solve the initial value problem y²y'-y^3 tanx = sin x cos² x, y(0)=1
Solve (x²D² + 4xD + 2)y= (logx/x)^2,x> 0, where D =d/dx.
Solve d²y/dx²-6 dy/dx +13y= 20e^3x cos(2x+5)
#340153 on Dec 2023