Problems and solutions in mechanical engineering singh and dwivedi

www.elsolucionario.net www.elsolucionario.net www.elsolucionario.net This page intentionally left blank www.elsolucionario.net www.elsolucionario.net Copyright © 2007, New Age International (P) Ltd., Publishers Published by New Age International (P) Ltd., Publishers All rights reserved No part of this ebook may be reproduced in any form, by photostat, microfilm, xerography, or any other means, or incorporated into any information retrieval system, electronic or mechanical, without the written permission of the publisher All inquiries should be emailed to rights@newagepublishers.com ISBN (13) : 978-81-224-2551-2 PUBLISHING FOR ONE WORLD NEW AGE INTERNATIONAL (P) LIMITED, PUBLISHERS 4835/24, Ansari Road, Daryaganj, New Delhi - 110002 Visit us at www.newagepublishers.com www.elsolucionario.net Preface Mechanical Engineering being core subject of engineering and Technology, is taught to almost all branches of engineering, throughout the world The subject covers various topics as evident from the course content, needs a compact and lucid book covering all the topics in one volume Keeping this in view the authors have written this book, basically covering the cent percent syllabi of Mechanical Engineering (TME102/TME-202) of U.P Technical University, Lucknow (U.P.), India From 2004–05 Session UPTU introduced the New Syllabus of Mechanical Engineering which covers Thermodynamics, Engineering Mechanics and Strength of Material Weightage of thermodynamics is 40%, Engineering Mechanics 40% and Strength of Material 20% Many topics of Thermodynamics and Strength of Material are deleted from the subject which were included in old syllabus but books available in the market give these useless topics, which may confuse the students Other books cover 100% syllabus of this subject but not covers many important topics which are important from examination point of view Keeping in mind this view this book covers 100% syllabus as well as 100% topics of respective chapters The examination contains both theoretical and numerical problems So in this book the reader gets matter in the form of questions and answers with concept of the chapter as well as concept for numerical solution in stepwise so they don’t refer any book for Concept and Theory This book is written in an objective and lucid manner, focusing to the prescribed syllabi This book will definitely help the students and practicising engineers to have the thorough understanding of the subject In the present book most of the problems cover the Tutorial Question bank as well as Examination Questions of U.P Technical University, AMIE, and other Universities have been included Therefore, it is believed that, it will serve nicely, our nervous students with end semester examination Critical suggestions and modifications by the students and professors will be appreciated and accorded Dr U.K Singh Manish Dwivedi Feature of book Cover 100% syllabus of TME 101/201 Cover all the examination theory problems as well as numerical problems of thermodynamics, mechanics and strength of materials Theory in the form of questions – Answers Included problems from Question bank provided by UPTU Provided chapter-wise Tutorials sheets Included Mechanical Engineering Lab manual No need of any other book for concept point of view www.elsolucionario.net This page intentionally left blank www.elsolucionario.net This page intentionally left blank www.elsolucionario.net IMPORTANT CONVERSION/FORMULA Sine Rule 80 – β R Q O γ 80 – α 80 – γ P P Q R = = sin (180 − α ) sin (180 − β) sin (180 − γ ) Important Conversion 1N = = g = H.P = Pascal(Pa) = 1KPa = 1MPa = 1GPa = bar = kg X m/sec2 1000 gm X 100 cm/sec2 9.81 m/sec2 735.5 KW 1N/m2 103 N/m2 106 N/m2 109 N/m2 105 N/m2 Important Trigonometrical Formulas sin (A + B) = sin A.cos B + cos A.sin B sin (A – B) = sin A.cos B - cos A.sin B cos (A + B) = cos A.cos B – sin A.sin B cos (A – B) = cos A.cos B + sin A.sin B tan (A + B) = (tan A + tan B)/(1 – tan A tan B) tan (A – B) = (tan A – tan B)/(1 + tan A tan B) sin2 A = 2sin A.cos A sin2A + cos2A = + tan2A = sec2A 10 + cot2A = cosec2A 11 + cosA = 2cos2A/2 α www.elsolucionario.net 502 / Problems and Solutions in Mechanical Engineering with Concept Diamond load Position of identor after applying major load Test specimen Principle of Rockwell Testing Fig A-13 Vicker’s Hardness Test: This test is similar to the Brinell test but uses a different indenter A square based pyramid of cone angle 136 degrees is used The applied load may be 5, 10, 30, 50 … etc kgf The same test procedure is adapted Obervation Table Sp.No Calculation: Result: BALL DIA LOAD APPLIED INDENTATION DIA (BY MICROSCOPE) DIAMETER OF INDENTATION IN MM www.elsolucionario.net Previous year Question Papers / 503 Previous Year Question Papers B Tech Second Semester Examination, 2004-2005 Mechanical Engineering Attempt any two parts of the following: (10 × = 20) (a) (i) What you understand by thermodynamic equilibrium? (ii) What you understand by flow work? Is it different from displacement work? How? (iii) A pump dischanges a liquid into a drum at the rate of 0.032 m3/s The drum, 1.50 m in diameter and 4.20 m in length, can hold 3500 kg of the liquid Find the denisty of the liquid and the mass flow rate of the liquid handled by the pump (b) Derive steady flow energy equation: The steam supply to an engine comprises two streams which mix before entering the engine One stream is supplied at the rate of 0.01 kg/s with an enthalpy of 2950 kj/kg and a velocity of 20 m/s The other stream is supplied at the rate of 0.1 kg/s with an enthalpy of 2565 kj/kg and a velocity of 120 m/s At the exit from the engine the fluid leaves as two streams, one of water at the rate of 0.001 kg/sec with an enthalpy of 421 kj/kg and the other of steam; the fluid velocities at the exit are negligible The engine develops a shaft power of 25 KW The heat transfer is negligible Evaluate the enthalpy of the second exit stream (c) Two identical bodies of constant heat capacity are at the same initial temperature T1 A refrigerator operates between these two bodies until one body is cooled to temperature T2 If the bodies remain at constant pressure and undergo no change of phase, find the minimum amount of work deeded to this, in terms of T4, T2 and heat capacity Attempt any two parts of the following: (10 × = 20) (a) Explain Rankine cycle with the help of p – v, T – s and h – s diagram (b) Steam at 10 bar, 250ºC flowing with negligible velocity at the rate of kg/min mixes adiabatically with steam at 10 bar, 0.7 quality, flowing also with negligible velocity at the rate of kg/min The combined stream of steam is throttled to bar and then expanded isentropically in a nozzle to bar Determine (a) the state of steam after mixing (b) the state of steam after throttling (c) the increase in entropy due to throttling (d) the exit area of the nozzle Neglect the kinetic energy of the steam at the inlet to the nozzle (c) (i) What is C engine? Why it has more compression ratio compared to S.I engines? (ii) A diesel engine operating on Air Standard Diesel cycle operates on kg of air with an initial pressure of 98 kPa and a temperature of 36ºC The pressure at the end of compression is 35 bar and cut off is 6% of the stroke Determine (i) Thermal efficiency (ii) Mean effective pressure www.elsolucionario.net 504 / Problems and Solutions in Mechanical Engineering with Concept Attempt any two of the following (10 × = 20) (a) Compute the simplest resultant force for the loads shown acting on the cantilever beam in Fig What force and moment is transmitted by this force to supporting wall at A? 6m w = 7N/m 500 N 3.5m A 21 N/m 5m 7m Fig (b) The pulley, in Fig 2, at D has a mass of 200 kg Neglecting the weights of the bars ACE and BCD, find the force transmitted from one bas to the other at C String E 0.6m B 2.5m A 0.3m (c) 5000 N 2m 2.5m 4m Fig Block C, shown in Fig has a mass of 100 kg and identical blcoks A and B have masses of 75 kg each are placed on the floor as shwon If coefficient of friction is µ = 0.2 for all mating surfaces, can the arrangement shown in the diagram remain in equilibrium? C A 45º 45º B Fig Attempt any two of the following: (10 × = 20) (a) Draw the shear force and bending moment diagram for the beam shown in Fig 40kN 3m 15kN/m 3m Fig 1.5m 50kN www.elsolucionario.net Previous year Question Papers / (b) 505 Find the force in members HF, FH, FE and FC of the truss shown in Fig I 3m 3m 3m 3m H 5kN G E F C D A 4m 5kN B Fig (c) (i) Derive the relation E = 2G (1 + v) where E = Young’s modulus, G = Modulus of rigidity v = Poisson’s ratio (ii) A m long steel rod of rectangular section 80 mm × 40 mm is subjected to an axial tensile load of 200 kN Find the strain energy and maximum stress produced in it for the following cases when load is applied gradually and when load falls through a height of 100 mm Take E = × 105 nm2 Attempt any two of the following: (10 × = 20) (a) A plane element is subjected to following stresses σx = 120 kN/m2 (tensile), σy = 40 kN/m2 (compressive) any Txy = 50 kN/m2 (counter clockwise on the plane perpendicular to x-axis) Find: (i) Principal stresses and their directions (ii) Maximum shearing stress and its direction (iii) Also, find the resultant stress on a plane inclined 40º with the x-axis (b) (i) If cross-sectional area of the beam shown in Fig is as shown in Fig 6, find the maximum bending stress 120mm 30mm 240mm 30 mm (ii) What are the assumptions taken in the theory of pure bending (c) (i) Draw stress-strain diagram for Aluminium and Cast iron (ii) A compound shaft is made up of a steel rod of 50 mm diameter surrounded by a closely fitted brass tube When a torque of kN-m is applied on this shaft, its 60% is shared by the steel rod for steel is 85 GPa and for brass it is 45 GPa Calculate (a) the outside diameter of brass tube (b) Maximum shear stress induced in steel and brass www.elsolucionario.net 506 / Problems and Solutions in Mechanical Engineering with Concept B.Tech Special Carry Over Examination, 2005-2006 MECHANICAL ENGINEERING Attempt any four parts of the following: (4 × = 20) (a) Explain microscopic and macroscopic point of view to study the subject of thermodynamics (b) A mass of 1.5 kg of air is compressed in a quasistatic process from 1.1 bar to 10 bar according to the law PV 1.25 = constant where v is specific volume The initial density of air is 1.2 kg/m3 Find the work involved in the compression process (c) State the first law of thermodynamics for a closed system undergoing a change of state Also show that the total energy is a property of the system (d) 0.8 kg/s of air flows through a compressor under steady state conditions The properties of air at entry are: pressure bar, velocity 10 m/s specific volume 0.95 m3/kg and internal energy 30 kj/kg The corresponding values at exit are bar, m/s 0.2 m3/kg and 124 kj/kg Neglecting the change in potential energy determine the power input and pipe diameter at entry and exit (e) Determine the sp work of compression when air flows steadily through a compressor from bar and 30° to 0.9 MPa according to (i) isothermal process (ii) adiabatic process (f) Show that entropy is a point function Calculate the entropy change, during the complete evaporation of water at bar to dry saturated steam at the same pressure and temperature Attempt any two parts of the following: (2 × 10 = 20) (a) Calculate the change in output and efficiency of a theoretical Rankine cycle when its condenser pressure is changed from 0.2 bar to 0.1 bar Inlet condition is 40 bar & 400°C (b) Air enters at a condition of bar and 30° C to an air standard Diesel cycle and compressed to 20 bar Cut-off takes place at 6% of stroke Calculate (i) Power output (ii) Heat input (iii) Air standard efficienc (iv) P-V and T-S diagram for cycle (c) With the help of neat sketches explain the working of 2-stroke CI engine Attempt any two parts of the following: (2 × 10 = 20) (a) State the transmissibility of forces Forces 2, 3, and kN respectively act at one of the angular points of a regular-hexagon towards five other angular points Determine the magnitude and direction of the resultant force (b) (i) State the necessary and sufficient conditions of equilibrium of a system of complanar nonconcurrent force system Define the following terms in connection with friction: (i) Coefficient of friction, (ii) Angle of friction, (iii) Angle of respose, (iv) Cone of friction and (v) Limiting friction (c) A uniform ladder of length 15 m rests ‘against a vertical wall making an angle of 60° with the horizontal Coefficient of friction between wall and ladder and the ground and ladder are 0.3 and 0.25 respectively A man weighing 65 kg ascends the ladder How high will he be able to go before the ladder slips? Find the magnitude of weight to be put at the bottom of the ladder so as to make it just sufficient to permit the man to go to the top Take ladder’s weight = 900 N www.elsolucionario.net Previous year Question Papers / 507 Attempt any two parts of the following: (2 × 10 = 20) (a) Define a beam What is a cantilever, a simply supported and a overhung beam? What is the point of contraflexure ? Draw the shear force and bending moment diagram for the beam as shown in Fig 4.1 200kN 100kN 3m 2m 50kN 4m 1m Fig 4.1 (b) (i) Derive the relationship between shear force, bending moment and intensity of loading at any section of a beam (ii) State the assumptions made while making an analysis of a framed structure (c) Determine the magnitude and nature of forces in the various members of the truss shown in Fig 4.2 100 kN 50 kN 50 kN 3m 3m 3m Fig 4.2 Attempt any four parts of the following: (4 × = 20) (a) Explain the stress-strain diagram for a ductile and brittle material under tension on common axes single diagram (b) A rectangular element is subjected to a plane stress system as shown in Fig Determine the principal planes, principal stresses and maximum shear stress by Mohr’s Circle method only 100 MPa 50 MPa 50 MPa 50 MPa (c) Explain: (i) Strain energy (ii) complementary shear stress 100 MPa www.elsolucionario.net 508 / Problems and Solutions in Mechanical Engineering with Concept (d) A steel bar is subjected to loads as shown in Fig 5.2 Determine the change in length of the bar ABCD of 18 cm diameter E = 180 kN/mm2 A 50 kN C B 30 kN D 40 kN 60 kN 300mm (e) 310mm 310mm Fig 5.2 Calculate the maximum tensile and maximum compressive stress developed in the cross-section of beam in Fig 5.3 subjected to a moment of 30 kNm 120mm 20mm 300mm 10mm 20mm 120mm (f) Fig 5.3 A propeller shaft 100 mm in diameter is 45 m long, transmits 10 MW at 80 rpm Determine the maximum shearing stress in shaft Also calculate the stress at 20 mm, 40 mm, 60 mm and 80 mm diameters Show the stress variation B Tech First Semester Examination, 2005-2006 TMT–101: Mechanical Engineering Attempt any four parts of the following: (5 × = 20) (a) Explain the following: (i) Thermodynamic Equilibrium (ii) Quasi-Static Process (b) An engine cylinder has a piston area of 0.12 m2 and contains gas at a pressure of 1.5 MPa The gas expands according to a process which is represented by a straight line on a pressure-volume diagram The final pressure is 0.15 MPa Calculate the workdone by the gas on the piston if the stroke is 0.3 m (c) A system undergoes a cyclic process through four states 1-2, 2-3, 3-4 and 4-1 Find the values of x1, x2, y1, y2 and y3, in the following table: www.elsolucionario.net Previous year Question Papers / Process 1-2 2-3 3-4 4-1 (d) Heat Transfer KJ/Min 800 400 –400 Work Transfer KW 5.0 x1 x2 3.0 509 Change of Internal Energy y1 600 y2 y3 A reversible heat engine operates between two reservoirs at temperature of 600°C and 40°C The engine drives a reversible refrigeration which operates between reserves at temperature of 40°C and – 20°C The heat transfer to the heat engine is 2000KJ and net work output of combined engine – refrigerator plant is 360KJ Evaluate the heat transfer to the refrigerator and the net heat transfer to the reservoir at 40°C (e) kg of ice at –10°C is kept in atmosphere which is at 30°C Calculate the change of entropy of universe when it melts and comes into thermal equilibrium with the atmosphere Take latent heat of fusion as 335 KJ/Kg and specific heat of ice is half of that of water (f) Explain: (i) Zeroth Law of thermodynamics and its application in temperature measurement (ii) Clausius inequality Attempt any two of the following questions: (10 × = 20) (a) (i) With the help of neat sketches explain working of two-stroke CI engine (ii) Define the following terms with reference to phase change for water: Saturation state, triple point, critical point, dryness fraction, compressed or subcooled liquid (b) Explain the Rankine cycle with the help of flow diagram or water/steam in various components Also draw the cycle on pay and T-s diagram Obtain the net output and thermal efficiency of a theoretical Rankine cycle in which boiler pressure is 40 bar and it is generating steam at 300°C Condenser pressure is 0.1 bar (c) Air enters at tiar and 230°C in an engine running on Diesel cycle whose compression ratio is 18, Maximum temperature of the cycle is limited to 1500°C Calculate (i) cut-off ratio, (ii) heat supplied per kg of air, (iii) cycle efficiency Attempt any two of the following questions: (10 × = 20) (a) Explain the following: (i) Principle of transmissibility of a force (ii) Necessary and sufficient conditions of equilibrium of a system of coplanar force system (iii) Laws of static friction (iv) Useful uses of friction (b) Two smooth sphare seach of weight W and each of radius ‘r’ are in equilibrium in a horizontal channel of width ‘b’ (b