Engineering Thermodynamics

Sixteen Marks Questions Bank

Unit – I- Basic Concept and First Law

1. In an isentropic flow through nozzle, air flows at the rate of 600 kg/hr. At inlet to the

nozzle, pressure is 2 MPa and temperature is 127°C. The exit pressure is 0.5 MPa.

Initial air velocity is 300 mig determine (i) Exit velocity of air (ii) Inlet and exit area

of nozzle. (16) (NOV/DEC 2006)

2. A centrifugal pump delivers 2750 kg of water per minute from initial pressure of 0.8

bar absolute to a final pressure of 2.8 bar absolute. The suction is 2 m below and the

delivery is 5 m above the centre of pump. If the suction and delivery pipes are of

15cm and 1.0 cm diameter respectively, make calculation for power required to run

the pump. (16) (NOV/DEC 2006)

3. A reciprocating air compressor takes in 2 m3/min air at 0.11 MPa, 293 K which it delivers at 1.5 MPa, 384 K to an after cooler where the air is cooled at constant pressure to 298 K. The power absorbed by the compressor is 4.15 kW. Determine the heat transfer in (i) the compressor (ii) the cooler. State your assumptions. (16)

4. In a turbo machine handling an incompressible fluid with a density of 1000 kg/m3 the

conditions of the fluid at the rotor entry and exit are as given below:

Pressure Inlet Exit 1 .15 MPa 0.05 MPa

Velocity 30 m/sec 15.5 m/sec

Height above datum 10 m 2 m

If the volume flow rate of the fluid is 40 m3 /s, estimate the net energy transfer

from the fluid as work. (16) Nov / Dec 2009

5. A rigid tank containing 0.4 m3 of air at 400 kPa and 30°C is connected by a valve to a piston cylinder device with zero clearance. The mass of the piston is such that a pressure of 200 kPa is required to raise the piston. The valve is opened slightly and air is allowed to flow into the cylinder until the pressure of the tank drops to 200 kPa. During this process, heat is exchanged with the surrounding such that the entire air

remains at 30°C at all times. Determine the heat transfer for this process. (16)

Nov / Dec 2010

6. The electric heating system used in many houses consists of simple duct with

resistance wire. Air is heated as it flows over resistance wires. Consider a 15 kW

electric heating system. Air enters the heating section at 100 kPa and 17°C with a

volume flow rate of 150 m3/min. If heat is lost from the air in the duct to the surroundings at a rate of 200 W, determine the exit temperature of air. (16)

Nov / Dec 2010

7. A gas contained in a cylinder is compressed from 1 MPa and 0.05 m3 to 2 MPa.

Compression is governed by 1.4 V P constant. Internal energy of gas is given by; U =

7.5 PV −425, kJ. where P is pressure in kPa and V is volume in m3. Determine heat,

work and change in internal energy assuming compression process to be quasi static

Also find out work interaction, if the 180 kJ of heat is transferred to system betwee n

same states. Also explain why it is different from above? (16) April / May 2011

8. In a gas turbine installation air is heated inside heat exchanger up to 750oC from ambient temperature of 27 0C. Hot air then enters into gas turbine with the velocity of 50 m/s and leaves at 600 0C. Air leaving turbine enters a nozzle at 60 m/s velocity and leaves nozzle at temperature of 500 oC For unit mass flow rate of air determine the following assuming adiabatic expansion in turbine and nozzle,

a. Heat transfer to air in heat exchanger

b. Power output from turbine c. Velocity at exit of nozzle.

Take up for air as 1.005 kJ / kg. K. (16)April / May 2011, May / June 2014

9. 25 people attended a farewell party in a small room of size 10 _ 8 m and have a 5 m

ceiling. Each person gives up 350 kJ of heat per hour. Assuming that the room is

completely sealed off and insulated, calculate the air temperature rise occurring in 10 minutes. Assume Cv of air 0.718 kJ/kg K and R = 0:287 kJ/kg K and each person occupies a volume of 0.05 m3. Take p = 101.325 kPa and T = 20oC. (10)

Nov / Dec 2011

10. Air flows at the rate of 0.5 kg/s through an air compressor, entering at 7 m/s, 100 kPa

and 0.95 m3/ kg and leaving at 5 m/s, 700 kPa, and 0.19 m3/kg. The internal energy

of air leaving is 90 kJ/kg greater than that of the air entering. Cooling water in the

compressor jackets absorbs heat from t he air at the rate of 58 kW. (1) Compute the rate of shaft work input to the air in kW (2) Find the ratio of the inlet pipe diameter to

outer pipe diameter. (8) Nov / Dec 2011

11. A gas of mass 1.5 kg undergoes a quasi-static expansion which follows a relationship p = a + bV, where a and b are constants. The initial and final pressures are 100 kpa and 200 kpa respectively and the corresponding volumes are 0.20 m3 and 1.20 m3. The specific internal energy of the gas is given by the relation U=1.5pv – 85 kJ / kg. Where p is in kpa and v is in m3/kg. Calculate the net heat transfer and the maximum internal energy of the gas attained during expansion. (10) Nov 2012, May 2009

12. A gas flows steadily through compressor. The gas enters the compressor at a temperature of 16oC, a pressure of 100 kpa, and an enthalpy of 391.2 kJ / kg. The gas leaves the compressor at a temperature of 245oC, a pressure of 0.6 MPa, and an enthalpy of 535.5 kJ /kg. There is no heat transfer to (or) from the gas as it flows through the compressor. Evaluate the external work done per unit mass of gas when the velocity at entry 80 m /s and that at exit is 160 m/s.

13. A nozzle is a device for increasing the velocity of a steady flowing steam. At the inlet

to a certain nozzle, the enthalpy of the fluid passing is 3000 kJ / kg and the velocity is

60 m / s. At the discharge end, the enthalpy is 2762 kJ / Kg. The nozzle is horizontal

and there is negligible heat loss from it. (i) Find the velocity at exit from the nozzle. (ii) If the inlet area is 0.1 m2 and the specific volume at inlet is 0.187 m3 / kg. Find the mass flow rate. (iii) If the specific volume at the nozzle exit is 0.498 m3 / kg. Find the

exit area of the nozzle. (8) April / May 2010

14. A room of four persons has two fans has two fans, each consuming 0.18 kW power,

and three 100 W lamps. Ventilation air at the rate of 80 kg / hr enters with an enthalpy

of 84 kJ / kg and leaves with an enthalpy of 59 kJ / kg. If each person puts out heat at

the rate of 630 kJ / hr. Determine the rate at which heat is to be removed by a room cooler, so that a steady state is maintained in the room. (7) (Nov / Dec 2007)

15. Three grams of nitrogen gas at 6 atm and 160oC is expanded adiabatically to double its

initial volume, then compressed at constant pressure to its initial volume and then compressed again at constant volume to its initial state. Calculate the net work done on the gas. Draw the p – V diagram for the process. Specific heat ratio of nitrogen is 1.4.

(12) (May / June 2007)

16. Air expands by isentropic process through a nozzle from 784 kPa and 220oC to an exit pressure of 98 kPa. Determine the exit velocity and the mass flow rate, if the exit area

is 0.0006 m2. (8) (May / June 2007) 17. A blower handles 1 kg / sec of air at 293 K and consumes a power of 15 kW. The inlet

and outlet velocities of air are 100 m / sec and 150 m / sec respectively. Find the exit air temperature, assuming adiabatic conditions. ake Cp of air as 1.005 kJ / kg.K.

(9) (Nov / Dec 2007)

18. One litre of hydrogen at 273 K is adiabatically compressed to one half of its initial

volume. Find the change in temperature of the gas, if the ratio of two specific heats for

hydrogen is 1.4. (Nov / Dec 2007)

19. The velocity and enthalpy of fluid at the inlet of a certain nozzle are 50 m / sec and

2800 kJ / kg respectively. The enthalpy at the exit of nozzle is 2600 kJ / kg. The nozzle is horizontal and insulated so that no heat transfer takes place from it. Find (i) Velocity of the fluid at exit of the nozzle (ii) Mass flow rate, if the area at inlet of nozzle is 0.09 m2. (iii)Exit area of the nozzle, if the specific volume at the exit of the nozzle is 0.495 m3 /

kg. (Nov / Dec 2007)

20. A three process cycle operating with nitrogen as the working substance has constant temperature compression at 34oC with initial pressure 100 kPa. Then the gas undergoes a constant volume heating and then polytrophic expansion with 1.35 as index of compression. The isothermal compression requires – 67 kJ / kg of work. Determine (i) P, v and T around the cycle. (ii) Heat in and out (iii) Net work.

For nitrogen gas, Cv = 0.7431 kJ / kg.K. May / June 2013

21. A fluid is confined in a cylinder by a spring loaded, frictionless piston so that the pressure in the fluid is a linear function of the volume (p = a + bV). The internal energy of the fluid is given by U= (34 + 3.15 pV) where U is in kJ, p in kPa and V in cubic meter. If the fluid changes from an initial state of 170 kPa, 0.03 m3 to final state of 400 kPa, 0.06 m 3, with no work other than that done on the piston, find the direction and magnitude of the work and heat transfer. Nov / Dec 2012 22. Determine the heat transfer and its direction for a system in which a perfect gas having

molecular weight of 6 is compressed from 101.3 kPa, 20oC to a pressure of 600 kPa following the law pV1.3 = constant. Take specific heat at constant pressure of gas as 1.7 kJ / kg. K. May / June 2014

23. Air at a temperature of 15oC passes through a heat exchanger at a velocity of 30 m/s

where its temperature is raised to 800oC. It then enters a turbine with the same velocity of 30 m/s and expands until the temperature falls to 650oC. On leaving the turbine, the air is taken at a velocity of 60 m/s to a nozzle where it expands until the temperature has fallen to 500oC. If the air flow rate is 2 kg /s, Calculate (a) the rate of heat transfer to the air in the heat exchanger (b) the power output from the turbine assuming no heat loss, and (c) the velocity at exit from the nozzle, assuming no heat loss. Take the enthalpy of air as h = Cp.t, where Cp is the specific heat equal to 1.005 kJ / kg.K and t is the temperature.

Theory questions

1. Considering a system which changes its state, prove that the internal energy is a point

function. (8) Nov / Dec 2011

2. Define the following terms (1) Thermodynamics (2) Macroscopic approach (3) Continuum. Nov / Dec 2012, Nov / Dec 2011 (6)

Deduce the expression for the displacement work in an isothermal process. (4)

4.

(May / June 2007)

Describe steady flow energy equation and deduce suitable expression for the expansion of gas in a gas turbine with suitable assumptions. (8)

5.

(May / June 2007)

(i)Derive the steady flow energy equation, stating the assumptions made. (6) (ii)Prove that energy is a property of a system. (5)

(iii)Enumerate and explain the limitations of first law of thermodynamics. (5)

6.

May / June 2013

Define enthalpy. How is it related to internal energy? (4)

7.

Nov / Dec 2012

Derive steady flow energy equation and reduce it for turbine, pump, nozzle and a heat exchanger. (16)

8.

Nov / Dec 2013

Briefly explain the following: (4) (i) Point function and path function.

(ii) Property, state, process and path (8)

(iii) Quasi- static process. (4)

Nov / Dec 2013

V.S.B. ENGINEERING COLLEGE, KARUR

Department of Mechanical Engineering

Question Bank

Sub Code/Name: CE6451-Fluid Mechanics & Machinery

Year/Sem: II / III

UNIT- I

PART-A

1. Define viscosity? 2. What is compressibility?

3. Define dynamic viscosity? 4. What is cause for viscosity?

5. Give some example of surface tension? 6. Define vapour pressure? 8. Give the Euler‘s equation of motion?

9. What is Bernoulli‘s equation for real fluid? 10. State momentum equation and Impulse momentum equation?

11. State moment of momentum equation? 12. State Bernoulli‘s theorem? 13. Differentiate steady and unsteady flow?

14. State the assumptions in Bernoulli‘s equation. PART-B

1. a) Derives Euler‘s Equation of Motion and proves the Bernoulli‘s equation. (12 Marks) b) Define the terms: i) Steady and unsteady flows ii) Specific weight (4 Marks)

2. a) Define the terms: i) Kinematics of flow ii) Uniform and non-uniform flows iii) Rotational and irrotational flows (6 Marks)

b) The Velocity Distribution for flow over a flat plate is given by u=(2/3)y-y2, Where u is the point velocity in metre per second at a distance y metre above the plate. Determine the shear stress aty=0 and y=15 cm. Assume dynamic viscosity as 8.63 poises (10Marks)

3. a) A pipe 200mm long has a slope of 1in100 and tapers from 1.2m diameter at thehigh end to

0.6m diameter at the low end and carries 100litres/sec of oil (Sp.gr.=0.8). If the pressure gauge at the high end reads 60kN/m², determine i)Velocities at the two ends and ii) pressure at the lower end. (12 Marks)

b) One litre of crude oil weighs 9.6 N. Calculate its Specific weight and density (4 Marks)

4. Two large plane surfaces are 150mm apart. The space between the surfaces is filled with oil of viscosity 0.972Ns/m². A flat thin plate of o.5m² area moves through the oil at velocity of 0.3m/sec. Calculate the drgg force i) When the plate is in the middle of the two plane

surfaces and ii)When the thinplate is at a distance of 30mm from one of the planes.(16 Marks)

5. a) Derive the three dimensional Continuity equation. (10 Marks)

b) Define the following i) Compressibility ii) Vapour pressureiii) Capillarity (6Marks)

6. a) Two plates are placed at a distance of 0.15mm apart. The lower plate is fixed while the upper plate having surface area 1.0 m2 is pulled at 0.3nm/s. Find the force and power

required to maintain this speed, if the fluid separating them is having viscosity 1.5 poise. (8 Marks)

b) An oil film of thickness 1.5 mm is used for lubrication between a square plate of size 0.9m ×0.9m and an inclined plane having an angle of inclination 200. . The weight of square

plate is 392.4 N and its slides down the plane with a uniform velocity of 0.2 m/s. find the dynamic viscosity of the oil. (8 Marks)

7. A pipe 300m long has a slope of 1 in100 and tapers from 1m diameter at the high end to 0.5m at the low end. The quantity of water flowing is 5400 m3/min. If the pressure at the high end is 49033 N/m², find the pressure at the low end. What is the change in pressure if the

head loss between the two sections is 0.45m of water? (16 Marks)

8. 250 liters/sec of water is flowing in a pipe having a diameter of 300mm. If the pipe is bent by

135° (that is change from initial to final direction is 135°), find the magnitude and direction of the resultant force on the bend. The pressure of water flowing is 39.24N/cm². (16 Marks)

9. The diameter of a pipe gradually reduces from 1m to 0.7m. The pressure intensity at

centerline of 1m section 7.848kN/m² and the rate of flow of water through the pipe is

600liters/sec. Find the intensity of pressure at the centerline of 0.7m section. Also determine the force exerted by flowing water on transition of the pipe. (16 Marks)

10.a) State the momentum equation. How will you apply momentum equation for determining

the force exerted by a flowing fluid on a pipe bend? (12 Marks)

b) Define Moment of Momentum equation. Where this equation is used? (4 Marks)

UNIT- II

PART-A

1. What do you mean by the term ‗Boundary Layer‘? 2. What is laminar sub- layer?

3. Define Momentum thickness in Boundary Layer concept. 4. Sketch the development of Boundary layer over a flat plate. 5. Define the term ‗Turbulence‘

6. Define: ‗Hydraulic Gradient Line‘ 7. Define: ‗Total gradient Line‘

8. What is the expression for head loss due to friction in Darcy formula ? 9. What are the factors to the determined when viscous fluid flows through the circular pipe ? 10. What do you understand by the terms a) major energy losses , b) minor energy losses?

11. Give an expression for loss of head due to sudden enlargement of the pipe :- 12. Give an expression for loss of head due to an obstruction in pipe

13. What are the basic educations to solve the problems in flow through branched pipes? 14. What is Dupuit‘s equation?

PART-B

1. a) Define Displacement thickness. Derive an expression for the Displacement thickness.(10 Marks) b) Define: i) Laminar Boundary layer ii) Laminar Sub- layer (6 Marks)

2. a) A thin plate is moving in still atmospheric air at a velocity of 5m/sec. The length of the plate is 0.6m and width 0.5m. Calculate i) the thickness of the boundary layer at the end of

the plate and ii) Drag force on one side of the plate. Take density of air as 1.24 kg/m3 and kinematic viscosity 0.15 strokes. (10 Marks)

b) What do you understand by the term Boundary layer and Boundary Layer theory? (6

Marks)

3. a) A plate of 600mm length and 400mm wide is immersed in a fluid of specific gravity 0.9 and kinematic viscosity 10-4 m²/sec. The fluid is moving with a velocity of 6 m/sec. Determine i) boundary layer thickness ii) shear stress at the end of the plate, and iii) drag force on one

side of the plate. (12 Marks) b) Differentiate Laminar & Turbulent Flow. (4 Marks)

4. a) What do you understand by the terms: Major energy losses and Minor energy losses (8

Marks)

b) Obtain expression for head loss in a sudden expansion in the pipe. List all the assumptions made in the derivation. (8 Marks)

5. a) Derive the darcy-Weisbach equation. (10 Marks)

b) Water is flowing through a pipe of diameter 250mm with a velocity of 3 m/sec. Find the

head loss due to friction for a length of 5.5m, if the coefficient of friction f is given by f = [0.03+(0.08/Re0.3)] where kinematic viscosity = 0.01strokes. (6 Marks)

6. The difference in water level between two tanks which are connected by three pipes in series

is 15m. Lengths and diameters of these pipe are 300m, 150m, 200m and 30cm, 20cm, and 30cm respectively. Find the discharge through the pipe line and tabulate all losses if friction

factor for three pipes are taken as 0.02, 0.025 and 0.03 (16 Marks) 7. a) A sudden enlargement of a water main from 230mm to 460mm diameter, the hydraulic

gradient rises by 10mm. Estimate the discharge. (10 Marks) b) Obtain expression for head loss in a sudden contraction in the pipe. (6 Marks)

8. Determine the length of an equivalent pipe of diameter 20cm and friction factor is 0.02 for a

given pipe system discharging 0.1 m3/sec. The pipe system consists of the following. i) 10m

line of 20cm diameter with friction factor 0.03, ii) three 90° bend with k=0.5 for each, iii) two sudden expansion of diameter 20cm to 30cm , iv) a 15cm line of 30cm diameter with

friction factor is 0.025 and v) a global valve fully open with k=10. (16 Marks) 9. Two reservoirs whose water surface elevations differ by 40m are connected by a pipe line

30cm in diameter and 3km long. In order to increase the discharge, an additional pipe line 20cm in diameter and 1.5km long is laid parallel from the midpoint of the first one upto the

lower reservoir. What is the increase in discharge due to newly laid pipe? Assume friction factor f = 0.02 (16 Marks)

UNIT- III

PART-A

1. Define Dimensional Analysis 2. Define dimensionally homogeneous equation.

3. What are the methods of dimensional analysis? 4. State Buckingham‘s Π theorem

5. What is dimensionless number? 6. What are the conditions for hydraulic similitude? 7. Explain the significance of Froude Model law

8. Explain the terms: Model and Prototype 9. List advantages of Dimensional Analysis.

10. Explain Model analysis.

PART-B

1. a) Explain with example, dimensional homogeneity of a physical equation. (6 Marks) b) Describe in detail the method of dimensional analysis using Buckingham‘s π theorem.

2. a) Define i) Geometric similarity ii) Dynamic similarity iii) Kinematic similarity. (6 Marks) b) The efficiency of a fan η depends upon following factors : 1) Density ρ 2) Dynamic

viscosity μ 3) Diameter D 4) Discharge Q and 5) Angular velocity ω, Show that η = Φ [μ/D²ωρ , Q/D3ω

]. 3. The pressure difference ΔP in a pipe of diameter D and length L due to turbulence flow

depends on the velocity V, viscosity μ, density ρ and roughness K. Using Buckingham‘s π theorem, obtain an expression for ΔP. (16 Marks)

4. The discharge Q through an oil ring depends on the diameter D of oil ring, speed N rpm, mass density ρ of oil, absolute viscosity μ of oil, surface tension σ and specific weight ע of oil.

Show that Q = ND3 f [ μ / ρND² , σ / ρN²D3 , ע / ρN²D ] (16 Marks)

5. Power P developed by a water turbine depends upon rotational speed N, operational head H, diameter D, breath B of runner, density ρ, viscosity μ and gravity g show that P = ρD5N5 Φ[H/D, B/D, ρD²N/μ, ND/(gH)1/2 ] (16 Marks)

6. Torque T of a propeller depends upon density of liquid ρ, viscosity μ, speed N, linear velocity

V, diameter of the propeller shaft D. Using Buckingham‘s π theorem show that T= ρN²D5 f[ ND/V, ρND²/μ ] (16 Marks)

7. a) A pipe of diameter 1.5m is required to transport an oil of specific gravity 0.9 and viscosity 3X10-2poise at the rate of 3000lit/sec. Tests were conducted on a 15cm diameter pipe using

water at 20°C. Find the velocity and rate of flow in the model. Viscosity of water at 20°C is 0.01poise. (8 Marks)

b) The ratio of length of a sub-marine and its model is 30:1. The speed of the sub-marine (prototype) is 10m/sec. The model is to be tested in a wind tunnel. Find the speed of air in wind

tunnel. Also determine the ratio of drag (resistance) between the model and prototype. Take the value of kinematic viscosity for sea water and air as 0.012strokes and 0.016strokes respectively. The density for sea water and air is given as 1030kg/m3 and 1.24kg/m3 respectively. (8 Marks)

8. a) The pressure drop in an aero-plane model of size 1:40 of its prototype is 80N/cm². The

model is tested in water. Find the corresponding pressure drop in the prototype. Take density of air 1.24 kg/m3. The viscosity of water is 0.01poise while the viscosity of air is 0.00018poise. (10 Marks)

b) Derive Euler, Froude and Weber numbers. (6 Marks)

UNIT- IV

PART-A

1. What is meant by Pump?

2. What is meant by Priming? 3. Differentiate between the single acting pump and double acting pump

4. What are the functions of air vessels? 5. Mention main components of Centrifugal pump 6. Define slip, percentage slip and negative slip of a reciprocating pump

7. Define Manometric efficiency 8. Define Mechanical efficiency.

9. Define overall efficiency. 10. Define speed ratio, flow ratio. 11. Mention main components of Reciprocating pump.

12. What is the use of air vessel? 13. What is meant by rotary pump?

14. What is indicator diagram? 15. What is meant by Cavitations?

PART-B

1. A radial flow impeller has a diameter 25cm and width 7.5cm at exit. It delivers 120litres of water per second against a head of 24m at 1440rpm. Assuming the vanes block the flow

area by 5% and hydraulic efficiency of 80%. Estimate the vane angle at exit. Also calculate the torque exerted on the driving shaft if the mechanical efficiency is 95%. (16 Marks)

2. Find the power required to drive a centrifugal pump which delivers 0.04m3/sec of water to a height of 20m through a 15cm diameter pipe and 100m long. The overall efficiency of the

pump is 70% and coefficient of friction is 0.15 in the formula Hf= 4flv2 / 2gd. (16 Marks)

3. A centrifugal pump having outer diameter equal to 2 times the inner diameter and running

at 1200rpm works against a total head of 75m. The velocity of the flow through the impeller

is constant and equal to 3m/sec. the vanes are set back at an angle of 30° at outlet. If the outer diameter of the impeller is 600mm and width at outlet is 50mm. Determine i) Vane angle at inlet (ii) Work done per sec by the impeller iii) Manometric efficiency. (16 Marks)

4. The impeller of a centrifugal pump has an external diameter of 450mm and internal

diameter of 200mm and it runs at 1440rpm. Assuming a constant radia l flow through the impeller at 2.5m/sec. and that the vanes at exit are set back at an angle of 25°. Determine i)Inlet vane angle

ii) The angle, absolute velocity of water at exit makes with the tangent and iii) The work done per N of water. (16 Marks)

5. The diameter and stroke of a single acting reciprocating pump are 200mm and 400mm

respectively, the pump runs at 60rpm and lifts 12litres of water per second through a height of 25m. The delivery pipe is 20m long and 150mm in diameter. Find i) Theoretical power

required to run the pump ii) Percentage of slip iii) Acceleration head at the beginning and middle of the delivery stroke. (16 Marks)

6. The cylinder of a single-acting reciprocating pump is 15 cm in diameter and 30 cm in

stroke. The pump is running at 30 r.p.m and discharge water to a height of 12 m. the diameter and length of the delivery pipe are 10 cm and 30 m respectively. If a large air vessel is fitted in the delivery pipe at a distance of 2 m from the centre of the pump, find the

pressure head in the cylinder. (i) at the beginning of the delivery stroke, and (ii) in the middle of the delivery stroke. Take f=0.01.

7. Explain the working principle of screw pump and gear pump with neat diagram in detail.

8. Explain the working principle of single and double acting reciprocating pumps with neat diagram in detail: Also explain the effects of inertia pressure and friction on the

performance of the pump using indicator diagrams with and without air vessel.

9. Show the workdone by a reciprocating pump is equal to the area of the indicator diagram.

10. Classify pumps. Explain the working of a double acting reciprocating pump with a neat

diagram.

11. Explain in detail about the performance curves for pumps

12. Write briefly on the following.

(i) Rotary pumps and their classifications. (8)

(ii) Indicator diagram for reciprocating pump. (8)

13. Calculate the work saved by fitting an air vessel for a double acting single cylinder reciprocating pump.

14. Explain in detail the working principle and construction of rotary pumps with neat sketch.

15. Discuss on the following: working of double acting pump, indicator diagram, acceleration head, and friction head.

16. With neat sketches, discuss about the rotary positive displacement pump.

UNIT- V

PART-A

1. What is a hydraulic turbine? 2. How will you classify the turbine? 3. Differentiate between the reaction and impulse turbine

4. Define specific speed of turbine 5. Give example for a low head, medium head and high head turbine.

6. What is Draft tube? 7. Define specific speed. 8. What is cavitation? How can it be avoided in reaction turbine?

9. Define the term ‗Governing of a turbine‘ 10. What are the functions of Surge tank?

11. Differentiate between an inward and an outward flow reaction turbines. 12. List out advantages of Francis turbine

PART-B

1. A jet of water having velocity of 20m/sec strikes a curved vane, which is moving with a

velocity of 10m/sec. The jet makes an angle of 20° with the direction of motion of vane at

inlet and leaves an angle of 130° to the direction of motion of vane at outlet. Calculate i)

Vane angles, so that the water enters and leaves the vane without shock. ii) work done per second per unit weight of water striking the vane per second. (16 Marks)

2. A jet of water having velocity of 15m/sec strikes a curved vane which is mo ving with a velocity of 5m/sec. The vane is symmetrical and it so shaped that the jet is deflected through

120°. Find the angle of the jet at inlet of vane so that there is no shock. What is the absolute velocity of jet at outlet in magnitude and direction and the work done per unit weight of

water? Assume the vane to be smooth. (16 Marks) 3. A jet of water having velocity of 30m/sec strikes a series of radial curved vanes mounted on

a wheel which is rotating at 200rpm. The jet makes an angle of 20° with the tangent to the wheel at inlet and leaves the wheel with a velocity of 5m/sec at an angle of 130° to the

tangent to the wheel at outlet. Water is flowing from outward in a radial direction. The outer and inner radii of the wheel are 0.5m and 0.25m respectively. Determine i) Vane angles at inlet and outlet ii) work done per unit weight of water iii) efficiency of wheel. (16 Marks)

4. The penstock supplies water from a reservoir to the pelton wheel with a gross head of 500m.

One third of the gross head is lost in friction in the penstock. The rate of flow of water through the nozzle fitted at the end of the penstock is 2m3/sec. The angle of deflection of the jet is 165°. Determine the power given by the water to the runner and hydraulic efficiency of

the pelton wheel. Take speed ratio=0.45 and Cv=1 (16 Marks)

5. A pelton wheel having a mean bucket diameter of 1m and is running at 1000rpm. The net head on the pelton wheel is 700m. If the side clearance angle is 15° and discharge through nozzle is 0.1m3/sec. Find i) Power available at the nozzle ii) Hydraulic efficiency of the

turbine. (16 Marks)

6. A reaction turbine works at 450rpm under a head of 120m. Its diameter at inlet is 120cm and the flow area is 0.4m². The angles made by absolute and relative velocities at inlet are 20° and 60° respectively with the tangential velocity. Determine i) The volume flow rate ii) The

power developed iii) Hydraulic efficiency (16 Marks)

7. As inward flow reaction turbine has external and internal diameters as 1m and 0.6m respectively. The hydraulic efficiency of the turbine is 90% when the head on the turbine is 36m.The velocity of flow at outlet is 2.5m/s and discharge at outlet is radial. If the vane angle

at outlet is 15° and width of the wheel is 100mm at inlet and outlet, Determine i) the guide blade angle ii) speed of the turbine iii) vane angle of the runner at inlet iv) volume flow rate

of turbine v) power developed. (16 Marks) 8. A Pelton turbine is required to develop 9000kW when working under a head of 300m the

impeller may rotate at 500rpm. Assuming a jet ratio of 10 and an overall efficiency of 85%. Calculate i) quantity of water required ii) diameter of wheel iii) Number of jets iv) Number

and size of bucket on the runner. (16 Marks) 9. The following data is given for a Francis turbine. Net head = 80m, Speed = 700rpm, Shaft

power = 300kW, Overall efficiency = 80%, Hydraulic efficiency = 90%, flow ratio =0.2, and breadth ratio = 1. The thickness of vane occupies 4% of circumferential area of the runner,

velocity of flow is constant at inlet and outlet and discharge is radial at outlet.Determine i) Diameters of runner at inlet and outlet, assume D2=D1/2. ii) Width of wheel at inlet iii) Guide blade angles iv) runner vane angles at inlet and outlet. (16 Marks)

10. i) Draw a neat sketch of Kaplan turbine, name the parts and briefly explain the working.(8

Marks)

11. ii) Define specific speed of the turbine? Derive an expression for the specific speed.(8

Marks)

12. Draw a neat sketch of Pelton wheel turbine, name the parts and briefly explain the working.

13. Draw a neat sketch of reaction turbine, name the parts and briefly explain the working.

14. Draw a neat sketch of Francis turbine, name the parts and briefly explain the working.

===================================================================== QUESTION BANK -MANUFACTURING TECHNOLOGY-I

UNIT-I METAL CASTING PROCESSES

1. Define casting. 2. What is foundry?

3. Name the properties of moulding sand 4. Name the materials used for making patterns

5. Name any five types of commonly used patterns. 6. What are the ingredients present in the moulding sands? 7. Name the different types of moulding sands.

8. Write the composition of good moulding sand? 9. Differentiate the terms 'mould' and 'core'.

10. When do you make core (or) what is function of core in moulding sand? 11. What are the processing steps involved in the core making process? 12. Define permeability number?

13. What are the advantages of shell moulding? 14. List the factors to be considered in the choice of metal melting furnace?

15. Name the different types of furnaces are most commonly used in foundries. 16. Name the different zones in cupola furnace? 17. What are chaplets?

18. What are the reasons for providing pattern allowances? 19. Mention the specific advantages of carbon di oxide (CO2) process?

20. Give any two merits and demerits of investment casting process? 21. List out the various defects. 22. Write short notes on inspection procedure for casting?

23. How casting defects are identified? 24. What is core venting?

25. Which processes is called ‗Lost wax processes? Why? PART-B

01. State the different type of mould. Write a short note on ‗Green sand mould‘ and shell

moulding. 02. Discuss the properties of moulding sand.

03. Explain the CO2 process of core making state its advantages and applications. 04. What are the pattern allowances? Explain briefly each 05. Explain the types of pressure die casting with suitable sketches?

06. Explain with the neat sketch of a cupola furnace? 07. Explain the working principle of sand slinger and jolt machine.

08. Discuss the casting defects and their inspection methods. 09. Explain in detail the working principles of the following

a) Investment casting

b) Centrifugal casting 10. Explain the various Non-destructive inspection methods of cast products.

UNIT-II

JOINING PROCESSES

PART-A 1. What are different methods of welding you know?

2. What is the purpose of flux? (April/May-2008) 3. List out any four arc welding equipment (May/June-2006) 4. Define resistance welding process. (May/June-2007)

5. Mention any two merits and Demerits of Laser beam welding.

6. Why flux is coated in filler rods? (Nov/Dec-2008)

7. What is the application of carburizing flame? (Nov/Dec-2009) 8. What are the diameter and length of the electrodes available in the market? (Dec-09)

9. Mention the various types of resistance welding. 10. Define friction welding process. 11. How does brazing differ from braze welding? (Nov/Dec-08)

12. List out the classification of brazing methods? 13. What are the types of adhesives used in permanent joint?

14. Define soldering and brazing? 15. List out the types of soldering methods? 16. State three merits and demerits of adhesive bonding?

17. Define welding process.

18. Define fusion welding .

19. What are different method of welding you know ?

20. Mention any two advantages of D .C and A. C welding.

21. What do you under stand by straight polarity?

22. When is the straight polarity used for arc welding?

23. What is the purpose of coating on an arc - welding electrode?

24. What are the two main different of consumable electrode and non -

consumable electrode?

25. How does MIG welding differ from TIG welding?

26. What is the main different between upset butt welding and flash butt welding ?

27. Define plasma arc welding?

PART-B

1) Explain the TIG and MIG system of welding. Give the application of each. (Nov/Dec-2009)

2) Illustrate the thermit welding process with neat sketch and also state its applications (2009)

3) (i) Explain the features of neutral, reducing and oxidizing flames. (April/May-2008) (ii)Explain gas metal arc welding (GMAW) process with neat sketch

4) With a neat sketch, explain the process of submerged arc welding.

5) Describe the various types of brazing methods

6) Explain various types of soldering methods?

7) Explain the method of laser beam welding and give their

applications

8) Explain the method of electron beam welding and given their

applications

9) Describe plasma Arc welding and given their applications

10) Describe and explain Ultrasonic welding and give their applications

11) Explain Thermit welding and given their applications

12) What is frication welding? give their advantage and limitations

13) Distinguish between brazing, soldering and welding .

14) Write briefly on testing and inspection .

UNIT-III

BULK DEFORMATION PROCESSES

PART-A

1. Define forging processes? 2. Write short notes on roll forging? 3. What are the disadvantages of forging processes?

4. What are the four major drawbacks of hot working? 5. List out the classification of cold working process?

6. List out the classification of cold working process? 7. What are the disadvantages of forging processes? (Nov/Dec-2009) 8. Distinguish between Press forging and Drop forging?

9. How are seamless tubes produced? (April/May 2008)

10. What is skew rolling? (Nov/Dec-2008)

11. What is Sejournet process? (Nov/Dec-2008 12. Define hot working and cold working of metals?

13. What is the difference between a bloom and a billet? (May/June-07) 14. Define forging processes? 15. Write short notes on roll forging?

16. Name the different types of forging machine? 17. Classify the types of extrusion? (May/June-06)

18. What is impact extrusion? (May/June-07) 19. Define cold working of metals 20. Define re crystallization temperature

21. Give some examples for mechanical working of metals 22. Define forging

23. Give some basic forging operations 24. Define extrusion ratio 25. Define tube drawing

26. Define degree of drawing 27. Name four different press-working operations

28. What are the defects in forging operations? PART-B

1. What is shape rolling? Mention the products of shape rolling and explain production of

any one of the product with sketches. (Nov/Dec-2008) 2. Explain briefly with neat sketch, the process of wire drawing? (April/May -08) 3. Differentiate between Open-die forging & Closed –die forging. (Nov/Dec-08)

4. Explain briefly with neat sketches direct and indirect extrusion process.(April/May-08 5. Describe the different kinds of rolling mills with neat sketches and also mention the

merits & limitations. (April/May -08) 6. Compare the difference between Hot and Cold extrusion process?(May/June-07) 7. Distinguish between wire drawing and tube drawing. (May/June-09)

8. Explain the hot working and cold working with suitable examples 9. Define rolling and discuss according to the classification

10. Discuss the various forging operations . 11. Give the advantage of press forging over drop forging 12. What are the defects in forgings? Explain it.

13. How the pipe and tubes are manufacturing? 14. Define drawing and discuss the classification with neat sketch

UNIT-IV

SHEET METAL PROCESSES

Part-A (2 Marks)

1.Define bending processes.

2. What is sheet metal work?

3. write down any four sheet metal characteristics

4. What is meant by clearance?

5. What is stretching?

6. Define the term ―spring back‖.

7. How force exerted on the form block is calculated

8. What are the formability test methods?

9. What is super plasticity of metals?

10.What is sheet metal work? 11. State the advantages of press working operations.

12. What do you mean by minimum bend radius?(Nov-Dec-2008) 13. Define limiting drawing ratio. (Nov-Dec-2008) 14. Define the term ―spring back‖.

15. List out the special forming process in sheet metal work. 16. How is hydro-forming similar to rubber forming? (April/May-2008)

17. What is super plastic forming operations? (May/June-2006) 18. Describe briefly power spinning process.

19. What is peen forming process?

Part-B (16 Marks)

1. Describe shearing operations in a sheet metal work with a neat sketch

2. Describe various types of bending operations with its neat sketches

3. Explain any one method of stretch forming operation with a neat sketch

4. Explain hydro forming process with its neat sketches. State their

advantage and applications

5. Explain the power spinning process with a neat sketch .give their

applications

6. How magnetic pulse forming process is carried out on sheet meta l?

7. Explain peen forming process with a neat sketch

8. What is super plastic of metal? how this process is carried out on sheet

metals?

9. Write short notes on following with neat sketches. (April/May-2008)

(i) Electro hydraulic forming process

(ii) Name and describe the common bending operations.

10 Explain the principle of magnetic pulse forming with neat sketches. (May/June-2006)

11.Describe the Stretch forming operations with neat sketches. (May/June-2006)

12.What is explosive forming? Explain with neat sketches? (Nov/Dec-2008)

UINT-V

MANUFACTURING OF PLASTIC COMPONENTS

PART-A (2 Marks)

1. How the plastic is defined?

2. Give some examples of additives

3. Give some examples for thermosetting plastics.

4. Give some example of thermo plastics.

5. Give some additives added to the manufacturing of rubber.

6. What are the processes of thermoplastics?

7. What are the two types of injection moulding?

8. What are the types of compression moulding?

9. define co polymerization

10. What are the foamed plastics?

11. What are the types of plastics? (AU-2008) 12. What are the characteristics of thermoplastics? (AU-2006)

13. What is film blowing? (AU-2007) 14. List out the materials for processing plastics

Part-B (16 Marks)

1. What are the characteristics of the forming and shaping processes?

2. What are the types of moulding and thermoplastics?

3. Explain the working principles and application of

a. injection moulding

b. blow moulding

c. rotational moulding

d. film blowing

4. Explain the thermoforming process

5. Explain induction and ultrasonic methods.

6. Explain working and principle of applications of

a. compression moulding

b. transfer moulding

7. Describe briefly the process of injection moulding as used for producing plastic

components.

8. What is film blowing? What are its relative merits and demerits?

QUESTION BANK

CE 6306 - STRENGTH OF MATERIALS

UNIT I

STRESS STRAIN DEFORMATION OF SOLIDS

PART- A (2 Marks)

1. What is Hooke‘s Law? 2. What are the Elastic Constants? 3. Define Poisson‘s Ratio. 4. Define: Resilience 5. Define proof resilience 6. Define modulus of resilience. 7. Define principal planes and principal stresses. 8. Define stress and strain. 9. Define Shear stress and Shear strain. 10. Define elastic limit. 11. Define volumetric strain. 12. Define tensile stress and compressive stress. 13. Define young‘s Modulus. 14. What is the use of Mohr‘s circle? 15. Define thermal stress. 16. Define Bulk modulus. 17. What is modulus of rigidity? 18. Define factor of safety. 19. State the relationship between young‘s modulus and modulus of rigidity.. 20. What is compound bar?

PART- B (16 Marks) 1. A Mild steel rod of 20 mm diameter and 300 mm long is enclosed centrally inside a hollow

copper tube of external diameter 30 mm and internal diameter 25 mm. The ends of the rod

and tube are brazed together, and the composite bar is subjected to an axial pull of 40 kN. If

E for steel and copper is 200 GN/m2 and 100 GN/m2 respectively, find the stresses

developed in the rod and the tube also find the extension of the rod.

2. A cast iron flat 300 mm long and 30 mm (thickness) × 60 mm (width) uniform cross section, is acted upon by the following forces : 30 kN tensile in the direction of the length 360 kN compression in the direction of the width 240 kN tensile in the direction of the thickness.

Calculate the direct strain, net strain in each direction and change in volume of the

flat.Assume the modulus of elasticity and Poisson‘s ratio for cast iron as 140 kN/mm2 and

0.25 respectively. 3. A bar of 30 mm diameter is subjected to a pull of 60 kN. The measured extension on gauge

length of 200 mm is 0.09 mm and the change in diameter is 0.0039 mm. calculate the Poisson‘s ratio and the values of the three modulus.

4. The bar shown in fig. is subjected to a tensile load of 160 KN. If the stress in the middle

portion is limited to 150 N/mm2, determine the diameter of the middle portion. Find also

the length of the middle portion if the total elongation of the bar is to be 0.2mm. young‘s

modulus is given as equal to 2.1 x 105 N/mm

2.

5. A member ABCD is subjected to point loads P1, P2, P3, P4 as shown in fig. calculate the

force P2 necessary for equilibrium, if P1 = 45 KN, P3 = 450 KN and P4 = 139 KN.

Determine the total elongation of the member, assuming the modulus of elasticity to be 2.1

x 105 N/mm

2.

6. A steel rod of 20mm diameter passes centrally through a copper tube of 50mm external

diameter and 40mm internal diameter. The tube is closed at each end by rigid plates of

negligible thickness. The nuts are tightened lightly home on the projecting parts of the rod. If

the temperature of the assembly is raised by 50˚C, calculate the stress developed in copper

and steel. Take E for steel and copper as 200 GN/m2 and 100 GN/m

2 and α for steel and

copper as 12 x 10-6

per ˚C and 18 x 10-6

per ˚C. 7. Two vertical rods one of steel and the other of copper are each rigidly fixed at the top and

50cm apart. Diameters and lengths of each rod are 2cm and 4m respectively. A cross bar

fixed to the rods at the lower ends carries a load of 5000 N such that the cross bar remains

horizontal even after loading. Find the stress in each rod and the position of the load on the

bar. Take E for steel = 2 x 105 N/mm

2 and E for copper = 1x 10

5 N/mm

2.

8. Drive the relationship between modulus of elasticity and modulus of rigidity. Calculate the

modulus of rigidity and bulk modulus of a cylindrical bar of diameter 30 mm and of length

1.5 m if the longitudinal strain in a bar during a tensile stress is four times the lateral strain.

Find the change in volume, when the bar is subjected to a hydrostatic pressure of 10 N/mm2. Take E = 1X 10

5 N/mm

2 A) what are the different types of machining operations that can be

performed on a lathe? And explain any six in detail.

9. (A). Find the young‘s modulus of a rod of diameter 30mm and of length 300mm which is

subjected to a tensile load of 60 KN and the extension of the rod is equal to 0.4 mm. (B). The ultimate stress for a hollow steel column which carries an axial load of 2MN is 500

N/mm2 .If the external diameter of the column is 250mm, determine the internal diameter

Take the factor of safety as 4.0 10. The extension in a rectangular steel bar of length 400mm and thickness 3mm is found be

0.21mm .The bar tapers uniformly in width from 20mm to 60mm E for the bar is 2x 105

N/mm2.Determine the axial load on the bar.

UNIT II

BEAMS – LOADS AND STRESSES PART- A (2 Marks)

1. State the different types of supports. 2. What is cantilever beam? 3. Write the equation for the simple bending theory. 4. What do you mean by the point of contraflexure? 5. What is mean by positive or sagging BM? 6. Define shear force and bending moment. 7. What is Shear stress diagram? 8. What is Bending moment diagram? 9. What are the different types of loading? 10. Write the assumption in the theory of simple bending. 11. What are the types of beams? 12. When will bending moment is maximum.

13. Write down relations for maximum shear force and bending moment in case of a

cantilever beam subjected to uniformly distributed load running over entire span. 14. Draw the shear force diagram for a cantilever beam of span 4 m and carrying

a point load of 50 KN at mid span. 15. Sketch (a) the bending stress distribution (b) shear stress distribution for a beam

of rectangular cross section. 16. A cantilever beam 3 m long carries a load of 20 KN at its free end. Calculate

the shear force and bending moment at a section 2 m from the free end. 17. Derive the relation between the intensity of load and shear force, in

bending theory. 18. A clockwise moment M is applied at the free end of a cantilever. Draw the SF

and BM diagrams for the cantilever.

19. What is maximum bending moment in a simply supported beam of span

‗L‘ subjected to UDL of ‗w‘ over entire span? 20. What is mean by negative or hogging BM?

PART- B (16 Marks)

1. Three blanks of each 50 x200 mm timber are built up to a symmetrical I section for a beam. The maximum shear force over the beam is 4KN. Propose an alternate rectangular section of the same material so that the maximum shear stress developed is same in both sections. Assume then width of the section to be 2/3 of the depth.

2. A beam of uniform section 10 m long carries a udl of 2KN/m for the entire length and a

concentrated load of 10 KN at right end. The beam is freely supported at the left end. Find the

position of the second support so that the maximum bending moment in the beam is as minimum

as possible. Also compute the maximum bending moment

3. A beam of size 150 mm wide, 250 mm deep carries a uniformly distributed load of w kN/m over entire span of 4 m. A concentrated load 1 kN is acting at a distance of 1.2 m from the left support. If the bending stress at a section 1.8 m from the left support is not to exceed

3.25 N/mm2 find the load w.

4. A cantilever of 2m length carries a point load of 20 KN at 0.8 m from the fixed end and

another point of 5 KN at the free end. In addition, a u.d.l. of 15 KN/m is spread over the entire

length of the cantilever. Draw the S.F.D, and B.M.D. 5. A Simply supported beam of effective span 6 m carries three point loads of 30 KN, 25 KN

and 40 KN at 1m, 3m and 4.5m respectively from the left support. Draw the SFD and BMD.

Indicating values at salient points. 6. A Simply supported beam of length 6 metres carries a udl of 20KN/m throughout its

length and a point of 30 KN at 2 metres from the right support. Draw the shear force and bending

moment diagram. Also find the position and magnitude of maximum Bending moment. 7. A Simply supported beam 6 metre span carries udl of 20 KN/m for left half of span and

two point loads of 25 KN end 35 KN at 4 m and 5 m from left support. Find maximum SF and

BM and their location drawing SF and BM diagrams. 8. A cantilever 1.5m long is loaded with a uniformly distribution load of 2 kN/m run over a

length of 1.25m from the free end it also carries a point load of 3kn at a distance of 0.25m from

the free end. Draw the shear force and bending moment diagram of the cantilever.

9. For the simply supported beam loaded as shown in Fig. , draw the shear force diagram and bending moment diagram. Also, obtain the maximum bending moment.

10. A cast iron beam is of T-section as shown in Fig. The beam is simply supported on a span of

6 m. The beam carries a uniformly distributed load of 2kN/m on the entire length (span).

Determine the maximum tensile and maximum compressive stress.

UNIT III TORSION

PART-A (2 Marks) 1. Define torsional rigidity of the solid circular shaft. 2. Distinguish between closed coil helical spring and open coil helical spring. 3. What is meant by composite shaft? 4. What is called Twisting moment? 5. What is Polar Modulus ? 6. Define: Torsional rigidity of a shaft. 7. What do mean by strength of a shaft?

8. Write down the equation for Wahl factor. 9. Define: Torsional stiffness. 10. What are springs? Name the two important types.

11. How will you find maximum shear stress induced in the wire of a close-coiled helical spring

carrying an axial load?

12. Write the expressions for stiffness of a close coiled helical spring.

13. Find the minimum diameter of shaft required to transmit a torque of 29820 Nm if the

maximum shear stress is not to exceed 45 N/mm2.

14. Find the torque which a shaft of 50 mm diameter can transmit safely, if the allowable shear

stress is 75 N/mm2.

15. Differentiate open coiled helical spring from the close coiled helical spring and state the type

of stress induced in each spring due to an axial load.

16. What is spring index (C)? 17. State any two functions of springs.

18. Write the polar modulus for solid shaft and circular shaft.

19. What are the assumptions made in Torsion equation

20. Write an expression for the angle of twist for a hollow circular shaft with external

diameter D, internal diameter d, length l and rigidity modulus G.

PART- B (16 Marks)

1. Determine the diameter of a solid shaft which will transmit 300 KN at 250 rpm. The maximum shear stress should not exceed 30 N/mm2 and twist should not be more than 10 in a

shaft length 2m. Take modulus of rigidity = 1 x 105 N/mm

2.

2. The stiffness of the closed coil helical spring at mean diameter 20 cm is made of 3 cm diameter rod and has 16 turns. A weight of 3 KN is dropped on this spring. Find the height by which the weight should be dropped before striking the spring so that the spring may be

compressed by 18 cm. Take C= 8x104 N/mm

2.

3. It is required to design a closed coiled helical spring which shall deflect 1mm under an axial load of 100 N at a shear stress of 90 Mpa. The spring is to be made of round wire having shear

modulus of 0.8 x 105 Mpa. The mean diameter of the coil is 10 times that of the coil wire. Find

the diameter and length of the wire.

4. A steel shaft ABCD having a total length of 2400 mm is contributed by three different sections as follows. The portion AB is hollow having outside and inside diameters 80 mm and 50 mm respectively, BC is solid and 80 mm diameter. CD is also solid and 70 mm diameter. If the angle of twist is same for each section, determine the length of each portion and the total angle of twist.

Maximum permissible shear stress is 50 Mpa and shear modulus 0.82 x 105 MPa .

5. The stiffness of close coiled helical spring is 1.5 N/mm of compression under a maximum load

of 60 N. The maximum shear stress in the wire of the spring is 125 N/mm2. The solid length of

the spring (when the coils are touching) is 50 mm. Find the diameter of coil, diameter of wire and number of coils. C = 4.5.

6. Calculate the power that can be transmitted at a 300 r.p.m. by a hollow steel shaft of 75 mm external diameter and 50 mm internal diameter when the permissible shear stress for the steel is 70 N/mm2 and the maximum torque is 1.3 times the mean. Compare the strength of this hollow shaft with that of an solid shaft. The same material, weight and length of both the shafts are the same.

7. A solid cylindrical shaft is to transmit 300 kN power at 100 rpm. If the shear stress is not to

exceed 60 N/mm2, find its diameter. What percent saving in weight would be obtained if this

shaft is replaced by a hollow one whose internal diameter equals to 0.6 of the external diameter, the length, the material and maximum shear stress being the same.

8. A helical spring of circular cross-section wire 18 mm in diameter is loaded by a force of 500 N. The mean coil diameter of the spring is 125mm. The modulus of rigidity is 80 kN/mm2.

Determine the maximum shear stress in the material of the spring. What number of coils must the spring have for its deflection to be 6 mm?

9. A close coiled helical spring is to have a stiffness of 1.5 N/mm of compression under a maximum load of 60 N. the maximum shearing stress producedinthewireofthespring.is125

N/mm2 .The solid length of the spring is 50mm. Find the diameter of coil, diameter of wire and

number of coils .C = 4.5 xl04N/mm2.

10. A closely coiled helical spring of round steel wire 10 mm in diameter having 10 complete turns with a mean diameter of 12 cm is subjected to an axial load of 250 N. Determine

I. the deflection of the spring II. maximum shear stress in the wire and

III. stiffness of the spring and

IV. frequency of vibration. Take C = 0.8 x 105 N/mm

2 .

UNIT IV

DEFLECTION OF BEAMS

PART-A (2 Marks) 1. State the condition for the use of Macaulay‘s method. 2. What is the maximum deflection in a simply supported beam subjected to uniformly

distributed load over the entire span? 3. What is crippling load? Give the effective length of columns when both ends hinged and

when both ends fixed. 4. Find the critical load of an Euler‘s column having 4 m length, 50 mm x 100 mm cross section

and hinged at both the ends E = 200 kn/mm2. 5. Calculate the maximum deflection of a simply supported beam carrying a point load of 100

KN at mid span. Span = 6 m, E= 20000 kn/m2. 6. A cantilever beam of spring 2 m is carrying a point load of 20 kn at its free end. Calculate the

slope at the free end. Assume EI = 12 x 103 KNm

2.

7. Calculate the effective length of a long column, whose actual length is 4 m when : a. Both ends are fixed b. One end fixed while the other end is free.

8. A cantilever is subjected to a point load W at the free end. What is the slope and deflection at

the free end?

9. What are the methods for finding out the slope and deflection at a section? 10. Why moment area method is more useful, when compared with double integration? 11. Explain the Theorem for conjugate beam method?

12. What are the points to be worth for conjugate beam method? 13. What are the different modes of failures of a column?

14. Write down the Rankine formula for columns. 15. What is effective or equivalent length of column? 16. Define Slenderness Ratio.

17. Define the terms column and strut. 18. What are the advantages of Macaulay method over the double integration method, for finding

the slope and deflections of beams? 19. State the limitations of Euler‘s formula 20. A cantilever beam of spring 4 m is carrying a point load of 2x10

3Nat its free end. Calculate

the slope at the free end. Assume EI = 2X105N/mm

2

PART-B (16 Marks)

1. A beam AB of length 8 m is simply supported at its ends and carries two point loads of 50 kN and 40 kN at a distance of 2 m and 5 m respectively from left support A. Determine, deflection under each load, maximum deflection and the position at which maximum deflection occurs.

Take E = 2 x 105 N/mm

2 and I = 8.5 X10

6 mm

4 .

2. A 1.2 m long column has a circular cross section of 45 mm diameter one of the ends of the

column is fixed in direction and position and other ends is free. Taking factor of safety as 3, calculate the safe load using

(i) Rankine's formula, take yield stress = 560 N/mm2 and a = 1/1600 for pinned ends.

(ii) Euler's formula, Young's modulus for cast iron = 1.2 x 105 N/mm2.

3. For the cantilever beam shown in Fig.3. Find the deflection and slope at the free end. EI =

10000 kN/m2.

Fig.3 4.A beam is simply supported at its ends over a span of 10 m and carries two concentrated loads of 100 kN and 60 kN at a distance of 2 m and 5 m respectively from the left support. Calculate (i) slope at the left support (ii)slope and deflection under the 100 kN load. Assume EI = 36 x 104

kN-m2.

5. Find the Euler critical load for a hollow cylindrical cast iron column 150 mm external diameter, 20 mm wall thickness if it is 6 m long with hinged at both ends. Assume Young's modulus of cast iron as 80 kN/mm2. Compare this load with that given by Rankine formula.

Using Rankine constants a =1/1600 and 567 N/mm2.

6.A 3 m long cantilever of uniform rectangular cross–section 150 mm wide and 300 mm deep is loaded with a point load of 3 kN at the free end and a udl of 2 kN/m over the entire length. Find the maximum deflection. E = 210 kN/mm2. Use Macaulay‘s method.

7. A simply supported beam of span 6 m is subjected to a udl of 2 kN/m over the entire span and a point load of 3 kN at 4 m from the left support. Find the deflection under the point load in terms of EI. Use strain energy method. 8.A simply supported beam of uniform flexural rigidity EI and span l, carries two symmetrically placed loads P at one–third of the span from each end. Find the slope at the supports and the deflection at mid–span. Use moment area theorems.

9. Derive double integration method for cantilever beam concentrated load at free end. 10. Determine the section of a hollow C.I. cylindrical column 5 m long with ends firmly built in. The column has to carry an axial compressive load of 588.6 KN. The internal diameter of the

column is 0.75 times the external diameter. Use Rankine‘s constants. a = 1 / 1600, σc = 57.58

KN/cm2 and F.O.S = 6.

UNIT V

THIN CYLINDERS, SPHERES AND THICK CYLINDERS PART-A (2 Marks)

1. A cylindrical pipe of diameter 1.5 m and thickness 1.5 cm is subjected to an internal fluid

pressure of 1.2 N/mm2. Determine the longitudinal stress developed in the pipe.

2. Find the thickness of the pipe due to an internal pressure of 10 N/mm2 if the permissible

stress is 120 N/mm2. The diameter of pipe is 750 mm.

3. The principal stress at a point are 100 N/mm2 (tensile) and 50 N/mm

2 (compressive)

respectively. Calculate the maximum shear stress at this point. 4. A spherical shell of 1 m diameter is subjected to an internal pressure 0.5N/mm

2. Find the

thickness if the thickness of the shell, if the allowable stress in the material of the shell is 75

N/mm2.

5. Normal stresses s x and s y and shear stress t act at a point. Find the principal stresses and the principal planes.

6. Derive an expression for the longitudinal stress in a thin cylinder subjected to an uniform

internal fluid pressure. 7. Distinguish between thick and thin cylinders.

8. What is mean by compressive and tensile force? 9. How will you determine the forces in a member by method of joints?

10. Define thin cylinder? 11. What are types of stress in a thin cylindrical vessel subjected to internal pressure? 12. What is mean by Circumferential stress (or hoop stress) and Longitudinal stress?

13. What are the formula for finding circumferential stress and longitudinal stress? 14. What are maximum shear stresses at any point in a cylinder

15. What are the formula for finding circumferential strain and longitudinal strain? 16. What are the formula for finding change in diameter, change in length and change volume of

a cylindrical shell subjected to internal fluid pressure p?

17. Distinguish between Circumferential stress (or hoop stress) and Longitudinal stress? 18. Find the thickness of the pipe due to an internal pressure of 10 N/mm

2 if the permissible

stress is 120 N/mm2. The diameter of pipe is 750 mm.

19. what do you mean by a thick compound cylinder? how will you determine the hoop stresses in a thick compound cylinder?

20. what are the different methods of reducing hoop stresses? PART –B ( 16 MARKS)

1.A thin cylinder 1.5 m internal diameter and 5 m long is subjected to an internal pressure of 2

N/mm2. If the maximum stress is limited to 160 N/mm

2, find the thickness of the cylinder. E =

200 kN/mm2 and Poisson‘s ratio = 0.3. Also find the changes in diameter, length and volume of

the cylinder.

2. At a point in a strained material the horizontal tensile stress is 80 N/mm2 and the vertical

compressive stress is 140 N/mm2. The shear stress is 40N/mm

2. Find the principal stresses and

the principal planes. Find also the maximum shear stress and its planes. 3. A thin cylindrical shell 3 m long has 1m internal diameter and 15 mm metal thickness. Calculate the circumferential and longitudinal stresses induced and also the change in the

dimensions of the shell, if it is subjected to an internal pressure of1.5 N/mm2 Take E = 2x10

5

N/mm2 and poison‘s ratio =0.3. Also calculate change in volume.

4. A closed cylindrical vessel made of steel plates 4 mm thick with plane ends, carries fluid under pressure of 3 N/mm2 The diameter of the cylinder is 25cm and length is75 cm. Calculate the longitudinal and hoop stresses in the cylinder wall and determine the change in diameter, length and Volume of the cylinder. Take E=2.1x105 N/mm2 and 1/m = 0.286. 5. A cylindrical shell 3 m long, 1 m internal diameter and 10 mm thick is subjected to an internal pressure of 1.5 N/mm2. Calculate the changes in length, diameter and volume of the cylinder. E

= 200 kN/mm2, Poisson‘s ratio = 0.3.

6. A steel cylindrical shell 3 m long which is closed at its ends, had an internal diameter of 1.5 m and a wall thickness of 20 mm. Calculate the circumferential and longitudinal stress induced and

also the change in dimensions of the shell if it is subjected to an internal pressure of 1.0N/mm2.

Assume the modulus of elasticity and Poisson's ratio for steel as 200kN/mm2 and 0.3

respectively. 7. A cylindrical shell 3 m long which is closed at the ends has an internal diameter 1m and wall thickness of 15 mm. Calculate the change in dimensions and change in

volume if the internal pressure is 1.5 N/mm2,E = 2 x 10

5 N/min2, μ= 0.3.

8. A cylindrical shell 3 m long which is closed at the ends, has an internal diameter of 1m and a wall thickness of 20 mm. Calculate the circumferential and longitudinal stresses induced and also changes in the dimensions of the shell, if it is subjected to an

internal pressure of 2.0 N/mm2 . Take E = 2 X 10

5 N/mm

2 and — 1= 0.3.m

9. A closed cylindrical vessel made of steel plates 5 mm thick with plane ends, carries fluid under pressure of 6 N/mm

2 The diameter of the cylinder is 35cm and length is 85 cm. Calculate

the longitudinal and hoop stresses in the cylinder wall and determine the change in diameter,

length and Volume of the cylinder. Take E=2.1x105 N/mm

2 and 1/m = 0.286

10. Determine the maximum hoop stress across the section of a pipe of external diameter 600mm and internal diameter 440mm. when the pipe is subjected to an internal fluid pressure of

50N/mm2