Mechanical Engineering Answers

QUESTION 3 Figure 2 depicts the schematic diagram of a phase shift oscillator . Figure 2 Phase shift oscillator for Question 3 The circuit will oscillate if it is designed to have poles on the jv-axis. 3.1Show that the transfer function for the passive network in the circuit is given by 𝑉2(𝑠) 𝑉1(𝑠) = −1 (1 + 1 𝑠𝑅𝐶) (2 + 1 𝑠𝑅𝐶) 2 − 3 − 2 𝑠𝑅𝐶 (10) 3.2Show that the oscillator’s characteristic equation is given by 1 − 𝐾 1 (1 + 1 𝑠𝑅𝐶) (2 + 1 𝑠𝑅𝐶) 2 − 3 − 2 𝑠𝑅𝐶 = 0 (10) [20]

3.1Apply Superposition theorem to calculate the following in figure 3; 3.1.1 the current 𝐼0 𝑣 with respect to the voltage source. (5) 3.1.2 the current 𝐼0 𝑖 with respect to the current source. (5) 3.1.3 the current 𝐼𝑜 with respect to the current source. (2) 4A R1 Io R3 4 R2 2 18V + - R4 1 R5 5 6Io 3 Figure 3. [12

In the circuit of Figure 2, switch has been closed for a long time, and opens at t = 0. Use the Laplace transform method to compute iL(t) for t>0 . For all t > 0, show the the t-domain and the s-domain circuits. Figure 2: [10] 

A boiler consumes 16,800 pounds of feul/hr when producing 210,000

lb of steam per hour at 620 psia and 800 deg F from feed water at

650 psia and 800F from feed water at 650 psia and 300F. The

heating value of fuel is 18,500 Btu/lb and the furnace volume is 1250

ft. Calculate: a) boiler capacity in mb/hr ; b) factor of evaporation ; c) equivalent evaporation ; d) furnace heat-release rate in Btu/hr-ft^3 ; e) boiler efficiency

Calculate the internal energy of 0.3 m3 of steam at 4 bar and 0.95 dryness. If this steam is superheated at constant pressure through 30°C, determine the heat added and change in internal energy

 Bolts holding a flanged joint in a steam piping are tightened to an initial stress of 400MN/m2. If the bolts are made from steel with a young's modulus of 200GN/m2, determine the relaxed a) stress after 10,000 hours of use. [The creep parameters for this material MN/m2] follows: n 3, A 4.8 x 103per hour per are as b) A series of creep test on an austenitic high temperature steel gave the following results Stress (MNm2) Eo(%) Steady state creep rate