UNIVERIY OF BOLON OCD5 WEERN INERNAIONAL COLLEGE FZE BENG (HON) MECHANICAL ENGINEERING EMEER ONE EXAMINAION 05/06 ADVANCED HERMOFLUID & CONROL YEM MODULE NO: AME 6005 Date: aturday 6 January 06 ime: :00 4:00 INRUCION O CANDIDAE: here are 6 questions. Answer 4 questions. All questions carry equal marks. Marks for parts of questions are shown in brackets. CANDIDAE REQUIRE : hermodynamic properties of fluids tables are provided ake density of water = 000 kg/m 3 Formula sheets provided
Page of 7 emester Examinations 05/6 Q. a ) For the laminar viscous flow through a circular pipe, derive an expression for the velocity distribution and shear stress distribution through it. Also prove the following: i) he velocity variation is parabolic ii) he shear stress variation across the section of the pipe is linear (0 marks) b) What power is required per kilometre of a line to overcome the viscous resistance to the flow of glycerine through a horizontal pipe of diameter 0mm at the rate of5 litres/s?ake µ =8 poise and kinematic viscosity(ν)= 6 stokes. (5 marks) c) An oil of viscosity 0.Ns/m and relative density 0.9 is flowing through a circular pipe of diameter 65mm and of length 400m.he rate of flow of fluid through the pipe is 4 litres/s. Determine the following: i) Pressure drop in a length of 400m ii) hear stress at the pipe wall. (0 marks) otal 5 marks Please turn the page
Page 3 of 7 emester Examinations 05/6 Q. a) Water at 5 o C flows at a rate of 45 litres/s in a cast iron pipe of 40cm diameter and 0m length. he system includes a sudden entrance (k e = 0.5) and a gate valve (k g =0.5).Determine the head loss of the pipe. Given the kinematic viscosity of water at 5 o C = x 0-6 m /s. he surface roughness value for cast iron = 0.6mm. (5 marks) b) he external and internal diameters of a collar bearing are 300mm and 50mm respectively.between the collar surface and the bearing, an oil film of thickness 0.5mm and of viscosity 0.9 poise,is maintained.if the shaft is running at 70 r.p.m,evaluate the following: i. orque generated (5 marks) ii. Power lost in overcoming the viscous resistance of the oil. (5marks) otal 5 marks Please turn the page
Page 4 of 7 emester Examinations 05/6 Q3. (a) team enters an engine at a pressure of MPa absolute and 550 o C. It is exhausted at bar. he steam at exhaust is 0.9 dry. Find the following: i) Drop in enthalpy (5 marks) ii) Change in entropy (5 marks) iii) ketch the process in - diagram ( marks) (b) A closed system contains air at pressure.5 bar, temperature 300K and volume 0.05 m 3. his system undergoes a thermodynamic cycle consisting of the following three processes in series: Process -: Constant volume heat addition till pressure becomes 4 bar. Process -3: Constant pressure cooling. Process 3-: Isothermal heating to initial state i. Evaluate the work done for each process (3 marks) ii. Evaluate the heat transfer for each process (3 marks) iii. Evaluate the change in entropy for each process (3 marks) iv. Represent the cycle on - and p-v plot. (4 marks) ake C v =0.78kJ/kgK and R= 87 J/kgK otal 5 marks
Page 5 of 7 emester Examinations 05/6 Q4. Please turn the page (a) An industrial control system shown in Figure Q4 uses a PID controller. Input(s) + - Gc(s) Gp(s) Output(s) Figure Q4 Where Ki 4 Gc( s) 0( skd), Gp( s) s s 6s i. If K i =0, determine the value of K d for critical damping. (4 marks) ii. With K d as determined in (i) determine the limiting value of K i such that stability is maintained. (6 marks) iii. Find the K i for a parabolic input (Ѳ i = steady state error is less than 5%. ) if G C (s) is a PI controller and the (3 marks) iv. Design a PID controller by determining K p and K d (using the K i obtained from (ii) above) to achieve maximum overshoot less than 0 % and settling time t s less than 4 seconds. (9 marks) (b) Analyse how system dynamics is affected by PID parameters K p, K i, K d. (3 marks)
Page 6 of 7 emester Examinations 05/6 otal 5 marks Please turn the page
Page 7 of 7 emester Examinations 05/6 Q5. (a) Obtain the state space model of a simplified industrial robotic system shown in Figure.5(a) y y B B M M u K K Figure.Q5.a (5 marks) (b) he state equations for a mechanical system are given below. Analyse controllability and observability of the system. (0 marks) otal 5 marks Please turn the page
Page 8 of 7 emester Examinations 05/6 Q6 (a) An industrial manufacturing system controlled by a digital controller is shown in Figure Q6. i/p A/D Digital Computer D/A Plant o/p ensor Figure Q6 (i) Discuss the roles of ADC, Digital Computer, and DAC. (3 marks) (ii) Illustrate stability criteria for sampled-data control systems. (3 marks) (iii) Analyze the stability of the sampled control system shown in Figure.6 (b), when the sampling time is (i) =0.5 sec, (ii) = sec. (9 marks) R(s) E(s) E * (s) C(s) +. s( ) - Figure Q6.iii otal 5 marks END OF QUEION
Page 9 of 7 emester Examinations 05/6 FORMULA HEE Please turn the page P = F/A ρ = m/v m. = ρav P = P g + P atm P = ρ gh = du/dy Q- W = ΔU + ΔPE + ΔKE W = PdV P V n = C P V - P V W = n - W = P (v v )
Page 0 of 7 emester Examinations 05/6 W = PV V ln V Q = C d A gh V g m C g h g F ΔM Δt. ΔM F = ρ QV τ = -( p/ x) r/ Re = V D ρ/ p = (3VL)/D U = /(4) -( p/ x) (R -r ) dq = du + dw du = Cv d dw = pdv pv = mr h = h f + xhf g
Page of 7 emester Examinations 05/6 s = s f + xsf g v = x Vg. Q -. w L F R L n R3 dq ds CpL Ln P mr L n P g C pl L n h 73. mh fg f C pl L n f hf 73 f g C pu L n f MC p L n MRL n P P
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Page 3 of 7 emester Examinations 05/6 F D CD u s F L C L u s p d ds ( P gz) D 4 p Q 8L 64 L v h f R D g h f 4fLv dg f 6 Re K h m g v k V V h m g L H η= (h h )/(h - h f ) gen ) Q
Page 4 of 7 emester Examinations 05/6 gen o U U W 0 ) ( ( ) V V P W W o u ) ( ) ( ) ( 0 0 V V P U U W rev ) ( ) ( ) ( 0 0 o V V Po U U o gen I F = τ πdl 000 60 4 4 gqh p R R t N R R L u L F t V r V n
Page 5 of 7 emester Examinations 05/6 ransfer Function for Blocks with feedback loop G(s) = Go( s) Go( s) H( s) (for a negative feedback) teady-tate Errors e ss lim[ s s0 G o i ( s)] (For the closed-loop system with a unity feedback) ( s) Performance measures for second-order systems Maximum Overshoot in % = exp ( ) 00% ( ) 4 ettling time t s = n Characteristic equation +GH=0 s + n s+ n =0 Observability est Matrix = [ C : A C ] Controllability est Matrix = [ B : AB]
Page 6 of 7 emester Examinations 05/6 Laplace ransforms Z ransforms A unit impulse function A unit step function s Exponential Function A unit ramp function s
Page 7 of 7 emester Examinations 05/6 able of Laplace, Z transform pairs