UNIVERSITY OF BOLTON TW30 SCHOOL OF ENGINEERING BENG (HONS) IN MECHANICAL ENGINEERING SEMESTER EXAMINATION 06/07 ADVANCED THERMOFLUIDS & CONTROL SYSTEMS MODULE NO: AME6005 Date: Thursday Jauary 07 Time: 0.00.00 INSTRUCTIONS TO CANDIDATES: There are SIX questios. Aswer ANY FOUR questios. All questios carry equal marks. Marks for parts of questios are show i brackets. This examiatio paper carries a total of 00 marks. All workig must be show. A umerical solutio of a questio obtaied by programmig a electroic calculator will ot be accepted. CANDIDATES REQUIRE : Thermodyamic properties of fluids provided Formula Sheet provided Take desity of water as 000 kg/m 3
Page of 5 Q (a) show that the torque for the collar bearig show i figure Qa is Use T = τ = μv t π μn 60 t ad V= r ω (Ro 4 -Ri 4 ) Figure Qa (5 mark b) A shaft of diameter 74.90 mm rotates i oiled bearig of diameter 75.03mm ad legth 75 mm. The aular space betwee the shaft ad the bearig is filled with oil havig a dyamic viscosity of 0.096 s/m.determie the power used i overcomig viscous resistace i this bearig at 400 rev/mi. (0 mark Total 5 marks Please tur the page
Page 3 of 5 Q (a) Show from first priciples that the chage of etropy for a gas is S - S = p L V V + V L p p Use dq = du + dw du = V d T ad dw = pdv PV T = PV T ( mark (b) A Frictioless pisto cylider device cotais saturated liquid water at 00kpa pressure. Now 450KJ of heat is trasferred to water from a source at 500 o C, ad part of the liquid vaporiser at costat pressure. Determie the total etropy chage for this process. Is this process reversible, irreversible or impossible? (3 mark Total 5 marks Q3 a) The pressure rise across a pump ca be expressed as ΔP = f (D, p,, Q) Where D is the impeller diameter, p the fluid desity, the rotatioal speed ad Q the flow rate. Determie a suitable set of dimesioless parameters. (0 mark b) Water flows through a 5 cm diameter pipe at the rate of 0. m 3 /s. The head loss i a 00 m legth of this pipe was foud to be 50 cm. What is the frictio factor? (8 mark c) Steam power plat workig to the Carot operatio betwee pressure of bar ad 0 bar. Determie its efficiecy ad work output per kg of steam. (7 mark Total 5 marks Please tur the page
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Page 5 of 5 Q4 A simplified model of a aircraft flight cotrol system is show i Figure Q4 ad the aircraft dyamics are give by: G P ( 0 s(3s 6.5) Iput R( + - Aircraft Flight Cotroller Aircraft Dyamics Gp( Output X( Measuremet = Figure Q4 A aircraft cotrol system The system resposes for a uit ramp iput are required as: The maximum overshoot is less tha 5% The rise time is less tha 0. secods The steady-state error is 0. a) Evaluate the performaces of closed loop system (ξ, ω, Percet Overshoot, tr, ts ad steady-state error) without the PID cotroller to determie how much improvemet is required. (0 mark b) Follow the PID cotroller desig procedure to determie the PID parameters KP, Ki, ad Kd. (5 mark Total 5 marks Please tur the page
Page 6 of 5 Q5 (a) Usig block diagrams, briefly explai a aalogue closed loop cotrol system ad a digital closed loop cotrol system. Assume that iput, output ad sesor sigals for both cotrol systems are all aalogue sigals. (6 mark (b) Explai what is meat by a zero-order hold (ZOH) system. (5 mark (c) A cotroller has a 0 bit Aalogue to Digital Coverter with the sigal rage betwee - Volt to + Volt: (i) What is the resolutio of the AD coverter? ( mark (ii) What iteger umber represeted a value of +0 Volts? ( mark (iii) What voltage does the iteger 500 represet? ( mark (iv) What voltage does 000 represet? ( mark (d) If the cotroller cosists of a Digital to Aalogue Coverter with zero order elemet i series with the processig cetre which has a trasfer fuctio G ( ) s p s ( s 4) fid the sampled-data trasfer fuctio, G(z) for the digital cotrol system. The samplig time, T, is 0. secods. (6 mark Total 5 marks Please tur the page
Page 7 of 5 Q6 Figure Q6 shows a simplified idustrial robotic system. The iput to the system is the Force F ad the outputs are displacemets x ad x. a) Derive the differetial equatios describig the behaviour of the system. (8 mark b) Determie the state variables x, x ad dx/dt. (3 mark c) Determie the state space equatios ad system matrices A, B, C ad D, where A, B, C, ad D have their usual meaig ad M = 00 Kg, K = 40 N/m, C = 3 Ns/m, K = 80 N/m X K X K M F C Figure Q6 A Simplified Idustrial Robotic System (4 mark Total 5 marks END OF QUESTIONS
Page 8 of 5 FORMULA SHEETS P V - P V W = - W = P (v v) W = PV V l V Q = Cd A gh V g m C g h g F F = ρ QV ΔM Δt Re = V L ρ/ dq = du + dw du = cu dt dw = pdv pv = mrt h = hf + xhfg. ΔM
Page 9 of 5 s = sf + xsfg v = x Vg. Q -. w. mh F L R L R3 dq ds T S T S CpL L T S g C pl L T h 73 T fg f S C pl L Tf hf 73 T f g C pu L T T f S S MC p L T T MRL P P F D CD u s F L C L u s S p d ds ( P gz) D 4 p Q 8L
Page 0 of 5 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 T T L H S ge S S ) Q T U UTo ( S S) T Sge W 0 W u W P ( V ) V o W rev ( U U) T0 ( S S) P0 ( V V ) ( U U0) T( S S0) Po( V Vo ) I ToS ge
Page of 5 V r V t Lu F R L R T p N 60t gqh 000 R 4 R 4 G( = G( = Go( Go( H( Go( Go( H( (for a egative feedback) (for a positive feedback) Steady-State Errors e lim[ s( G ( ) ( ] (for a ope-loop system) ss s0 O i e e e ss ss ss lim[ s s0 G o i ( ] (for the closed-loop system with a uity feedback) ( lim[ s i ( ] (if the feedback H( ) s0 G ( G ( [ H( ] G ( lim[ s d ] (if the system subjects to a disturbace iput) s 0 G ( G ( ) Laplace Trasforms A uit impulse fuctio
Page of 5 A uit step fuctio s A uit ramp fuctio s First order Systems O O G ss ( e t / ) (for a uit step iput) t / AG ( e ) (for a step iput with size A) ss ( t) G o ss ( ) e ( t / ) (for a impulse iput) Secod-order systems d dt o do o b o dt o( G( ( s i bo s i dtr = / dtp = P.O. = exp ( ) 00% ( ) ts = 4 d = (- )
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