Conventional Paper I Determine time required in minutes for a 50mm diameter steel sphere

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Merilyn Morgan
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1 Conventional aper I-04. (a) Give reasons wy te Carnot cycle cannot be considered as te teoretical cycle for steam power plants even toug its efficiency is te igest for te given eat source and sink temperatures. A carnot cycle eat engine as an efficiency of 40%. If te ig temperature is raised by 0%, wat is te new efficiency keeping te same low temperature? (b) Wat do you understand by te lumped capacity? Wat are te pysical assumptions necessary for a lumped capacity unsteady state analysis apply? Determine time required in minutes for a 50mm diameter steel spere 7800 kg m,c 0.46 kj kg K, k 5W m K to cool from 600 O C temperature to 00 O C temperature if exposed to a cooling air at 0 O C. Te convection eat transfer coefficient is 0W/m-K. (i) From fundamental laws derive te randtl-mayer relation for a normal sock in compressible fluid flow in a constant area duct for a perfect gas. (ii) Sow tat te maximum efficiency for a jet striking at te centre of a single symmetrically, curved vane moving wit a velocity u is given by te curvature of te vane. 6 cos were is 7 (d) Define specific speed of a ydraulic turbine. Were is it used? Sow tat te specific speed (N S ) can be expressed as: N N S H N H N = speed, = power developed or saft power and H = ead under wic te turbine is woking Wat is te range of specific speed in r.p.m. for elton weel? (e) Calculate te volume rate of flow of water troug a pipe of 00mm dia. Wen measured by (a) An orifice plate of orifice size 50mm dia and (b) Venturi tube of troat size 50mm dia. Te recorded. D.. 50 pa. Te density of water is 00kg/m. Assume orifice C d equal to 0.6 and Venturi C d equal to 0.9. (f) A single acting reciprocating pump as a plunger 0cm diameter and a stroke of 00mm. Te centre of te pump is 4m above te water level in te sump and 4m below te level India s No. institute for GATE Training Lak+ Students trained till date 65+ Centers across India

2 of water in a tank to wic water is delivered by te pump. Te diameter and lengt of section pipe are 40mm and 6m respectively wile tose of delivery pipe are 0mm and 8m respectively. Determine te maximum speed at wic te pump may be run witout separation, if separation occurs at N/cm below te atmosperic pressure. Take atmosperic pressure ead = 0.m of water. (g) Use te following matematical relation for any tree properties x,y,z x y z y z x x y z to sow te following relations for te Joule-Tomson coefficient T T T p RT z j p Cp pcp T Z is compressibility factor. () Write down te cemical formula of R-4a. Wat does a signify in te nomenclature? Explain te effect of critical temperature and critical pressure of refrigerant on te CO of te cycle. A straigt-carged Termostatic Expansion Valve (TEV) is designed to operate at an evaporator temperature of 7 O C wit a degree of supereat of 5 O C. R-4a is te refrigerant used in te refrigeration system as well as te bulb. Find: (i) Te required spring pressure at te design condition, (ii) Assuming te spring pressure to remain constant, find te degree of supereat, if te same TEV operates at an evaporator temperature of - O C. Te saturation temperature and corresponding pressure of R-4a are given in te Table below: T, C O sat sat,k a India s No. institute for GATE Training Lak+ Students trained till date 65+ Centers across India

3 . (a) A cylinder aving a piston retrained by a linear spring (of spring constant 5 kn/m) contains 0.5 kg of saturated vapour water at 0 O C, as own in te above figure. Heat is transferred to te water, causing te piston to rise. If te piston cross-sectional area is 0.05m, and te pressure varies linearly wit volume until a final pressure of 500 ka is reaced. Find te final temperature in te cylinder and te eat transfer for te process. Te properties of water are given in te Table below: t, O C, ka V g,m kg u g,kj kg g,kj kg sat sat (b) In an oil cooler te oil enters 0mm diameter tubes of 60 O C and is cooled to 40 O C. Te mean velocity of oil in te tubes is.5 m/s. Calculate te mean eat transfer coefficient. For turbulent flow of liquid being cooled take Nu =0.065 Re 0.8 r 0. and for laminar flow Nu =.65. Take all properties at bulk mean temperature and te properties are listed below: t O C kg/m Vcenti stokes K W/m K C kj/kg K centi stoke = 0-6 m /s India s No. institute for GATE Training Lak+ Students trained till date 65+ Centers across India

4 Te cylinder bore diameter of a single acting reciprocating pump is 50mm and stroke is 00mm. Te pump runs at 50 rpm and lifts water troug a eigt if 5 m. Te delivery pipe is m long and 00 mm diameter. Find te teoretical discarge and power required to run te pump. If te actual discarge is 4. lit/s find te percentage slip. Also determine te acceleration ead at te beginning and middle of delivery stroke..(a) In an air standard Otto cycle te maximum and minimum temperatures are 400 O C and 5 O C.Te eat supplied per kg of air is 800kJ. Calculate te compression ratio and cycle efficiency. Also calculate te maximum to minimum pressure ratio in te cycle. (b) An R77 based vapour compression refrigerating macine works between 8 O C and -0 O C temperature. Te ammonia leaves te compressor dry and saturated. Liquid ammonia is undercooled to 0 O C temperature inside te condenser, before trottling. Find te teoretical CO of te macine. Te c p of saturated ammonia liquid is 4.9 kj/kg.k. If net refrigeration required is 5.0 TR, find te mass flow rate of ammonia in kg/, assuming relative CO Te saturation properties of R77 are given in te following Table: Liquid Vapour t, O C,kJ/kg S,kJ/kg-K, kj/kg (C) A smaller power plant produces steam at Ma, 600 O C in te boiler. It keep te condenser at 45 O C transfer of 0MW out as eat transfer. Te first turbine section expands to 500 ka and ten flow is reeated followed by te expansion in te low pressure turbine. Find te reeat temperature so te turbine output is saturated vapour. For tis reeat find te total turbine power output and te boiler eat transfer. roperties of water are given in te Table below: t C p,kpa v,kg m O l v g,m kg,kj kg v,kj kg s kj kg K p S,kJ kg K v sat 000 sat India s No. institute for GATE Training Lak+ Students trained till date 65+ Centers across India 4

5 4. A geotermal supply of ot water at 500 ka, 50 O C is fed to an insulated flas evaporator at te rate of.5 kg/s. A stream of saturated liquid at 00 ka is drained from te bottom of te camber and a stream of saturated vapour at 00 ka is drawn from te top and fed to turbine. Find te rate of entropy generation in te flas evaporator. roperties of water are given in te Table below: p,ka O t, C,kJ kg v,kj kg S,kJ kg K S v,kj kg K t sat t sat (b) In a cemical plant a solution of density 00kg/m and specific eat capacity 4.6 kj/kg-k is to be eated from 65 O C to 00 O C. Te required flow rate of te solution is.8 kg/s. A tubular eat excanger is used for tis wit te solution flowing about. m/s in 5 mm bore iron tubes and being eated by wet steam at 5 O C. Te lengt of te tubes is not to exceed.5m. Taking inside, and outside eat transfer coefficient as 5 and 0kW/m K and neglecting te termal resistance of te tube wall estimate te number of tubes and te number of tube passes required. A water storage tank 0m 0m 0m as a drainage opening on one of te vertical sides at te bottom wic is trapezoidal in sape wit a widt m at te bottom 4m at te top and m eigt. A gate of same dimension inged along te top edge is used to close it. Wat is te minimum orizontal force required to be applied at te bottom to keep te gate closed if te tank as full of water in it? Will tere by any cange in te force required if te tank is only alf full? If yes ow muc? India s No. institute for GATE Training Lak+ Students trained till date 65+ Centers across India 5

6 5. (a) A four cylinder 4 stroke diesel engine as a bore of mm and stroke 9 mm. At full load at 70 rpm te break mean effective pressure is 5.9 bar and specific fuel consumption is 0.6kg/kWH. Te air fuel ratio as determined by exaust gas analysis is 5:. Calculate te break termal efficiency and volumetric efficiency of te engine. Atmosperic conditions are.0 bar and 5 O C. Te calorific value of fuel may be taken as 4400 kj/kg. (b) One kg of air at 5 O C DBT and 60% RH is mixed wit kg of air at 0 O C DBT and O C dew point temperature. Calculate te specific umidity, temperature and entalpy of te mixture. Assume specific eat of steam as.88kj/kg K and te following properties may be used: Temperature O C Saturation pressure p S bar Entalpy saturated g kj/kg of steam Air at 7 O C temperature and 00 ka pressure flows over a flat plate at a speed of.5 m/s. Calculate te boundary layer tickness at distance of 5 and 50 cm from te leading edge of te plate. Calculate te mass flow tat enters te boundary layer between x = 5 cm and x = 50 cm from leading edge. Te viscosity of air at 7 O C is 0.8pa m. Assume unit dept in z-direction. 6. (a) A 00 cc petrol Engine wit a compression ratio of 6 compresses te air fuel mixture to 900 ka and 75 O C, At te end of compression te ignition is started and te pressure rises along a straigt line and attains te igest value of.0 Ma after te piston as travelled 4% of te working stroke. Te air fuel ratio is 5 : Take R for mixture as 0.75 kj/kg.k, calorific value of fuel = 44 MJ/kg and c V = 0.965kJ/kg-K. find te eat loss per kg of carge during explosion. Flue gases and air as same gas constant. (b) Te following data relates to an air-conditioned space: Outdoor condition Room condition Sensible eat load Laten eat load 8 O C DBT/50% RH 4 O C DBT/50% RH 4 kw 6 kw Bypass factor of te cooling coil 0.6 India s No. institute for GATE Training Lak+ Students trained till date 65+ Centers across India 6

7 If te ventilation requirement is suc tat on mass flow rate basis 0% fres air is introduced and 80% supply air is recirculated, determine (i) Supply air flow rate (ii) Outside air sensible eat (iii) Outside air latent eat (iv) Grand total eat (v) Effective room sensible eat factor. (i) m of air is eated at constant pressure from 5 O C to 00 O C and ten cooled at constant volume back to its initial temperature. If te initial pressure is.0 bar calculate te net eat flow and overall cange in entropy. Sow te process on a TS diagram. (ii) Wit simple scematic diagram explain te difference between fire tube and water tube boilers. Mention te merits and demerits of bot. 7. (a) A sample bituminous coal gave te following ultimate analysis by mass: Carbon 8.9% Hydrogen 4.9% Oxygen 6%, Nitrogen.% and As 4.9%. Calculate (i) te stocemetric air fuel ratio for complete combustion and (ii) te volumetric analysis of wet and dry products of combustion wen te air supplied is 5% in excess of te required for complete combustion. (b) Tree tin-walled, long, circular cylinders, and of diameter 50mm, 50 mm and 50mm respectively are arranged concentrically. Temperature of cylinder is 80K and tat of cylinder is 00K. Emissivity of cylinder, and is 0.05, 0. and 0. respectively. Assuming tat tere is vacuum inside te annular spaces, determine te steady state temperature attained by cylinder. Find an expression for te drag force on smoot spere of diameter. D, moving wit a uniform velocity V in a fluid of density and dynamic viscosity. India s No. institute for GATE Training Lak+ Students trained till date 65+ Centers across India 7

Optimized geothermal binary power cycles

Optimized geothermal binary power cycles Optimized geotermal binary power cycles Kontoleontos E., Mendrinos D., Karytsas C. Centre for Renewable Energy Sources, 9t km Maratonos ave., 9009 Pikermi Attikis, Greece ABSTRACT Tis study as been carried