(W-ll)

Q. a) State Hooke's law and define the following terms : 5

i) Elasticity

ii) Elastic limit

iii) Young's Modulus

iv) Modulus of Rigidity

b) The following data refer to a mild steel specimen tested in a laboratory. 9

i) Diameter of the specimen = 25mm

ii) Length of the specimen = 300 mm

iii) Extension under a load of 15kN; = 0.045 mm

iv) Load at yield point - 127.65 kN

v) Maximum load 208.6 kN

vi) Length of specimen after failure - 375 mm

vii)Neck diameter 17.75 mm

Determine

i) Young's modulus

ii) Yield point stress.

iii) Ultimate stress.

iv) Percentage of elongation.

v) Percentage reduction in area

vi) Safe stress adopting a factor of safety of 2.

OR

Q. a) What is bulk modulus? Derive an expression for young's modulus in terms of bulk modulus and Poisson's

ratio.

b) A 12 mm diameter steel rod passes centrally through a copper tube 48 mm external and 36mm internal

diameter and 2.5 metres long. The tube is closed at each end by 24 mm thick steel plates which are secured by

nuts. The nuts are tightened until the copper tube is reduced in length by 0.508 mm. The whole assembly is then

raised in temperature by 60°C. Calculate the stresses in copper and steel before and after the rise of temperature,

assuming that the thickness of the plates remains unchanged.

Es = 2.1 105 N/mm2

Ec = 1.05 105 N/mm2

s = 1.2 l0-5 per°C

c = 1.75 l0-5 per°C 9

(S-12)

Distinguish between the following, giving due explanation.

i) force and stress.

ii) Tensile stress and compressive stress. 6

b) A tensile test was conducted on a mild steel bar. The following data was obtained from the test:

i) Diameter of steel bar = 3cm

ii) Gauge length of the bar = 20cm

iii) load at elastic limit = 250 kN

iv) Extension at a load of 150 kN=0.21 mm

v) Maximum load = 380kN

vi) Diameter of rod at the failure =2.25cm

Determine:

i) The Young's modulus.

ii) The stress at elastic limit.

iii) The percentage elongation and

iv) The percentage decrease in area. 8

OR

Q. a) Derive an expression for volumetric strain for a rectangular bar which is subjected to three mutually

perpendicular tensile stresses. 5

b) A copper bar 50 mm in diameter is placed within a steel tube 75 mm external diameter and 50 mm internal

diameter of exactly same length. The two pieces are rigidly fixed together by two pins 18 mm in diameter, one

at each end passing through the bar and tube. Caluclate the stress induced in the copper bar, steel tube if the

temperature of combined is raise by 50° C. Take

ES = 210GN/m2

Ec = 105 GN/m2

s = 1.2 l0-5 per°C

c = 1.75 l0-5 per°C 9

Unit-II(MOM)

(W-ll)

Q. a) Define and explain the following terms. 6

i) Shear force

ii) Bending moment

iii) Shear force diagram

iv) Bending moment diagram.

b) A cantilever beam 1.5 m long is loaded with UDL of 2kN/m run over a length of 1.25 m from the free end. It

also carries a point load end. Draw the shear force and bending moment diagram of the cantilever beam. 7

OR

Q. a) What do you mean by section modulus ? Find an express sion for section modulus for a rectangular,

circular and hollow circular section. 7

b) A steel plate of width 120mm and of thickness 20mm is bent into a circular arc of radius 1 Om. Determine

the maximum stress induced and the bending moment which will give maximum stress. Take E = 2 105

N/mm2 6

(S-12)

Q. a) What are the sign conventions for shear force and bending moment in general ? 4

b) Draw the shear force and bending moment diagrams for the over hanging beam carrying UDL of 2 kN/m

over the entire span as shown in fig 1. Also locate the point of contra flexure

OR

Q. a) Derive an expression for bending stress at a layer in a beam. 4 A timber beam of rectangular section is to

support a load of 20 kN uniformly distributed over a span 3.6m when beam is simply supported. If the depth of

section is to be twice the breadth, and the stress in the timber is not to exceed 7 N/mm2 find the dimensions of

the cross -section. How would you modify the cross section of the beam, if it carries a concentrated load of 20

kN placed at the centre with the same ratio of breadth of depth. 9

Unit-Ill (MOM)

(W-ll)

Q.a) Derive an expression for the shear stress produced in a circular shaft which is subjected to torsion. What

are the assumptions made in the derivation. 8

b) Find the maximum shear stress induced in a solid circular shaft of diameter 150mm when the shaft transmitts

150 kw power at 180 rpm. 5

OR

Q. a) Show that for a rectangular section of the beam maximum shear stress is 1.5 limes the average stress. 5

b) A closed coiled helical spring is ID carry a load of 50GN. Its mean coil diameter is to be 10 limes (hat of the

wire diameter. Calculate these diameter if the maximum shear stress in the material of the spring is to be 80

N/mm2. Also line! the number of coils in the closed coiled helical spring if the stiffness of the spring is 20N per

mm deflection and modulus of rigidity = 8.6 104 N/mm2 8

(S-12)

Q. a) When a circular shaft is subjected to torsion show that the shear stress varies linearly from the axis to the

surface. 4

b) A solid circular shaft and a hollow circular shaft whose inside diameter is ¾ of the outside diameter, are of

the same material of equal lengths and are required to transmit a given torque compare the weights of these two

shafts if the maximum shear stress developed in the two shafts are equal. 9

OR

Q. a) A timber beam of rectangular section is simply supported at the ends and carries a point load at the centre

of the beam. The maximum bending stress is 12 N/mm2 and maximum shear stress is 1 N/mm2. Find the ratio of

the span to the depth. 7

b) A closely coiled helical spring made of 10 mm diameter steel wire has 15 coils of 100 mm mean diameter.

The spring is subjected to an axial load of 100 N. Calculate: i) The maximum shear stress induced, ii) the

deflection, and iii) Stiffness of the spring Take modulus of rigidity G = 8.16 104 N/mm2

unit iv

(W-ll)

Q. a) Show that in thin cylindrical shells subjected to internal fluid pressure, the circumferential stress is

twice the longitudinal stress. 5

b) A copper cylinder, 90cm long, 40cm external diameter and wall thickness of 6mm has its both ends

closed by rigid blank flanges. It is initially full of oil at atmospheric pres sure. Calculate the additional

volume of oil which must be pumped into it in order to raise the oil pressure 5 MN/m 2 above atmospheric

pressure, for copper, E = 100 GN/m2, 1/m = 1/3 Bulk modulus of oil as 2.6 GN/m2. 9

OR

Q. a) Find the thickness of metal necessary for a cylindrical shell of internal diameter 150 mm to withstand

on internal pressure of 50N/ mm2. The maximum hoop stress in the section is not to exceed 150 N/ mm2. 7

b) A thin spherical shell 1.5m in diameter with its wall of 12.5 mm thickness is filled with the fluid at

atmospheric pressure. What intensity of pressure will be developed in it if 160 cm3 more of fluid is pumped

into it? Also calculate the hoop stress at that pressure and increase in diameter. 7

(S-12)

Q. a) Derive from the first principle the expression for circumferential and longitudianl stress in a thin

cylinder closed at both ends and subjected to internal fluid pressure. 5

Calculate:

i) the change in diameter. 9

ii) change in length and

iii) change in volume of a thin cylindrical shell 100 mm diameter, 1 cm thick and 5 m long when subjected

to internal pressure of 3 N/mm2. Take E = 2 105 N/mm2 Poission's ratio, = 0.3 9

OR

Q. a) Find the expression for the change in volume of the thin spherical shell subjected to internal fluid

pressure. 4

b) Determine the maximum and minimum hoop stress across the section of the pipe of 400 mm internal

diameter and 100 mm thick, when the pipe contains a fluid at a pressure of 8 N/mm2. Also sketch the radial

pressure and hoop stress distribution across the section. 10

Unit-V (MOM)

(W-ll)

Q. a) Define Resilience, proof Resilience and modulus of Resilience. 3

b) An unknown weight falls through a height of 10 mm on a collar rigidly attached to the low end of a vertical

bar 5 m long and 600 mm2 in section. If the maximum extension of the rod to be 2 mm, what is the

corresponding stress and magnitude of the unknown weight? Take E = 200 GN/m2. 10

OR

Q. a) i) Define the terms : Principal planes and principal stresses:

ii) Define the term 'Obliquity' how it is determined. 3

b) A rectangular block of material is subjected to a tensile stress of 110 N/ mm2 on one plane and a tensile stress

of 47 N/mm2 on the plane at right angles to the former. Each of above stresses are accompanied by a shear stress

of 63 N/mm2 and that associated with the former tensile stress tends to rotate the block anticlockwise. Find : i)

The direction and magnitude of each of the principal stress and ii) Magnitude of greatest shear stress. 8

(S-12)

Q. a) Explain the terms with example : Gradually applied load, suddenly applied load, and load applied with an

impact. 6 A rod 1 2.5 mm in diameter is stretched 3 .2 mm under a steady load of 1 0 kN. What stress would be

produced in the bar by a weight of 700 N, falling through 75 mm before commencing to stretch, the rod being

initially unstressed ? The value of E = 2.1 105 N/mm2 7

OR

Q. a) A rectangular bar is subjected to a direct stress () in one plane only. Derive the expression for the normal

and shear stress on an oblique plane which make angle '' with the normal cross section of the bar. 5

b) An elemental cube is subjected to tensile stresses of 60 N/mm 2 and 20 N/mm2 acting of two mutually

perpendicular planes and shear stress of 20 N/mm2 on these planes. Draw the Mohr 's circle of stresses and

hence or otherwise determine the magnitudes and directions of principle stresses and the magnitude of the

greatest shear stress. 8

Unit-VI (MOM)(W-ll)

Q. a) Find as expression for the slope at the supports and max deflection at centre of a simply supported

beam, carrying T point load W at the centre. 6

b) A beam 4 meter long, simply supported at its ends, carries a point load W at its centre. If the slope at the

end of the beam is not to exceed 1°. Find the deflection at the centre of the beam. 7

OR

A beam of length 6 m is simply supported at its ends and carries two point load 48 kN and 40kN at a

distance of 1 m and 3m respectively from the left support as shown in Fig. 1. Find : 13

i) Deflection under each load ii) Maximum deflection, and

iii) The point at which maximum deflection occurs.

Given: E = 2105N/mm2 I =85106mm4

S-12

Q. a) Prove the relation where

M - Bending Moment, E - Young's Modulus

I - Moment of Inertia. 7

b) A beam of uniform rectangular section 200 mm wide and 300 mm deep is simply supported at it ends. It

carries a uniformly distributed load of 9 kN/m run over the entire span of 5 m. If the value of E for the

beam material is 1 10 N/mm2 find

i) the slope at the supports and ii) maximum deflection. 6

OR

Q. A horizontal beam AB is simply supported at A and B, 6m apart. The beam is subjected to a clockwise

couple of 300 kNm at a distance of 4m from the left end as shown in fig. 2 If E = 2 105 N/mm2

I = 2 l08 mm4. Determine:

i) deflection at the point where couple is acting, and

ii) the maximum deflection. 13

(W-ll)

Q. a) What is Mach Number? Give its significance and application. 7

b) The resistance R experienced by a partially submerged body depends upon the velocity V length of the

body 'L' Viscosity of the fluid density of the fluid '' and gravitational acceleration 'g' using Buckingham

Theorem show that.

7

OR

Q. a) Explain the following :

i) Buckinghams Theorem

ii) Geometric similarity

iii) Kinematic similarity

iv) Dynamic similarity 3+2+1+1=7

OR

b) A 1:16 model of subrarine is to be tested in towing tank containing salt water. If the submarine moves at

5 m/sec, at what velocity should the model be towed for dynamic similarity? assume kinematic viscosity

and density for the model and prototype as same. 7 (S-12)

Q. a) State Buckingham's theorem why this theorem is considered superior over the Rayleigh's method

for Dimensional analysis? 6

b) The ratio of lengths of a sub-marine and its model is 30 :1. The speed of submarine (prototype) is 10

m/s . The model is to be tested in a wind tunnel. Find the speed of air in wind tunnel. Also determine the

ratio of drug (resistance) between the model & prototype. Take the value of kinematic viscosities for the

sea water & air as 0.012 stokes and 0.016 stokes resp. The density for sea water and air is given as 1030

kg/m3 and 1.24 kg/m3 resp. 7

OR

Q. a) Explain the term Dimensionally homogeneous equation. What are the methods of Dimensional

Analysis ? Describe what do you mean by repeating variables. 6

b) The frictional torque T of a disc of diam D rotating at a speed N in a fluid of viscosity and density in

a turbulent flow is given by Prove this by the method of Dimensions. 7

Unit-IV(FP-I)

(W-ll)

Q. a) What is Boundary layer separation ? State various methods of preventing the separation of boundary

layer? 6

b) A flat plate 2m x 2m moves at 50km/hr in stationary air of density 1.15 kg/m3. If the coefficient of drag

and lift are 0.75 resp. determine:-(1) The lift force (2) The Drag force (3) The resultant force. 7

OR

Q. a) Explain with neat sketch boundary Layer separation. 6

b) Determine the Drag; Lift and resultant force for a flat plate of size 2m long and 1m wide; on which

experiments were conducted so that the wind flowing at it is at 50 km/hr. The density of air is 1.15 kg/m 3

Coefficient of Drag and lift are 0.75 and 0.15 resp 7

(S-12)

Q. a) Define, explain & draw the figure of following. 6

i) Displacement thickness. ii) Momentum thickness iii) Energy thickness

b) A flat plate 1.5 m x 1.5 m moves at 50 km/hr in stationary air of density 1.15 kg/m 3 , if the coefficient of

drag and Lift are 0.15 and 0.75 resp; determine. i) The lift force, ii) The drag force. iii) The resultant force

iv) The power required to keep the plate in motion. 7

OR

Q. a) What do you mean by the foil terms. 6 i) Boundary layer. ii) Friction & pressure drag, iii) Coefficient

of drag & coefficient of lift.

b) Find the displacement, momentum & energy thickness of the velocity distribution in the boundary layer

given by

where = Boundary layer thickness. 7

Unit-V (FP-I)

(S-05) Q. (a) What is compound pipe ? How will you determine the equivalent size

of a compound pipe? 4 (b) When a sudden contraction is introduced in a horizontal pipe line from 50 cm

diameter to 25 cm diameter, the pressure changes from 105 KPa to 69 KPa. If coefficient of contraction is

assumed to be 0.65, calculate the water flow rate.

The contraction is subsequently followed by a sudden enlargemenr'from 25 cm diameter to 50 cm

diameter. If the pressure at the 25 cm section is 69 KPa, work out the pressure at 50 cm

enlarged section. 9

OR

126

M EC If III(b) Petrol (s = 0.716)'flows through a 200 mm dia. pipe at the rate of 600 lit/ see. at20°C. If the length

of pipe is 1 km, calculate the drop in pressure.: Assume kinematic viscosity as 4 x 10"3 cmVsec and f =0-013. 7

OR

Q. (a) Derive an expression for loss of head due to sudden expansion in pipe.

6

(b) The rate of flow of water pumped into a pipe line ABC, which is 200 m long is 20 lit/sec. The pipe is laid on

an upward slope of 1 in 40. The length of portion AB is 100 m and its diameter 100 mm, while the length of

portion BC is also 100 mm but its dia. is 200 mm. The change of dia. at B is sudden. The flow is taking place

from A to C, where the press at A is 19-62 N/cm2 and end C is connected to tank. Find the pressure at C and

draw hydraulic and total energy line. Take f = 0.008. 7

(W-10)

Q. (a) What are the various losses in pipe flow ? Explain in brief. 6

(b) Three pipes of same length L diameter D and friction factor f are connected in parallel. Determine the

diameter of the pipe of Length L and friction factor f which will carry same discharge for the same head loss.

hf =

fLV 2 2gD

Q. (a) Explain in brief hydraulic gradient line and the total energy line.

6

(b) For the distribution main of a city water supply a 0.30 m main is required. As pipes above 0.25 m are not

available, it is decided to lay two parallel mains of same diameter. Find the diameter of the parallel main. 7

Q. (a)

(b)

(s-ti) '-•--,•"

Explain and name all the losses taking place in pipe flow/Write formula related with each loss and explain all

notations used. Explain how these losses are minimised ? 7

In a 80 mm diameter pipeline an oil of specific gravity 0.8 is flowing at the rate of 6.012 m3/s, sudden expansion

takes place into a second pipeline of such diameter that maximum pressure rise is obtained. Find: (i) Loss of

energy in sudden expansion

(ii) Difference in mercury level of manometer connected between two pipes. 7 OR

132

Q, (a) Derive Darcy-Weisbach equation for flow through pipe. 7 (b) Three pipes of diameters 300 mm, 200 mm

and 400 mm and lengths 450 m, 255 m and 315m resp. are connected in series. The difference in water levels in

two tanks is 18m. Determine the rate of flow of water if coefficients of friction are 0.0075, 0.0078,0-0072 resp.

considering all minor losses. 7

(W-ll)

Q. a) Explain H.GLand T.E.L sketch. 6 b) Determine the rate of flow of water through a pipe of dia. 20cm and

length 50 cm. One end of the pipe is connected to a reservoir and other end is open to the atmosphere. The pipe

is horizontal and height of the water in the reservoir is 4m above the centre line of pipe. Take F = 0.09. 7

OR

Q. a) State the losses taking place in pipe flow. Write formula related with each loss and explain its notations.

How these losses are minimized ?

6

b) In a 80 mm dia. Pipe line an oil of specific gravity 0.8 is flowing at the rate of 6.012 mVsec, sudden

expansion takes place in to a second pipe line of such dia that maximum pressure rise is obtained, find, i) Loss

of energy in sudden expansion, ii) Difference in mercury level of manometer connected beftwo pipes.

7

(S-12)

Q. a) Derive Darcy Weisbach equation for pipe flow. 6

b) The rate of flow of water through a horizontal pipe is 0.25m 3/sec the diameter of the pipe which is 200m is

suddenly enlarged to 400 mm the pressure intensity in the smaller pipe is 11.77N/cm2 • Determine i) Loss of

head due to sudden enlargement, ii) Pressure intensity in the large pipe iii) Power lost due to enlargement. 7

OR Q. a) Explain Hydraulic Gradient Line & total energy lines with neat sketch.

6

b) Calculate the rate of flow of water through a pipe of diameter 300mm when the difference of pressure head

between the two ends of a pipe 400mm apart is 5m of water. Assume f=0.009. 7

\it,i ii in1Q. (a) Show that the force exerted by a Jet of water on an inclined fixed flail.,,!„<.„;,, *u_ J:~--.•.:- .>"•••

(b)

plate in the direction of Jet is given by Fx =pav2sin29.

Calculate the rate of flow of water for the following data:

i) Diameter of Jet = 50 mm

ii) Angle between plate and Jet = 30°.

iii) Force exerted in the direction of Jet = 1471.5 N. 7

(W-1I)

Q. a) Derive an expression for the force exerted by a jet of water on the fixed vertical plate in the direction

of jet. 7

b) A jet of water of diameter 50mm moving with a velo. of 20m/sec strikes a fixed plate in such a way that

the angle between the jet and the plate is 60°. Find the force exerted by the jet on the plate, i) In the

direction normal to plate, ii) In the direction of Jet. 7

Q. A Jet of water having a velo. of 15 m/sec strikes a curved vane which is moving with velo. of 5 m/sec

the vane is symmetrical and it is so shaped that the Jet is deflected through 120°. Find the angle of Jet at

inlet of vane so that there is no shock. What is the abs. velo.of the Jet at outlet in magnitude and direction

and the work done per unit wt. of water'/Assume vane to be smooth Draw velocity diagram. 14

(S-I2)

Q. a) Show that the force exerted by the jet of water on an inclined fixed

plate in the direction of jet is given by Fx-pav2sin26 7 b) A nozzle of 50rnm dia. delivers a stream of water

at 20m/sec perpendicular to a plate that moves away from the jet at 5m/sec find, i) The force on the plate.

ii) Tire work done & iii) The efficiency of jet. 7

OR

Q. a) A jet of water moving at ]2m/sec impings on vane shaped to deflect the jet through 120° when

stationary. If the vane is moving at 5 m/sec , find the angle of jet so that there is no shock at inlet. What is

the absolute velocity of the jet at exit in magnitue & direction and the work done per second per unit wt. of

water striking per second ? Assume that the vane is smooth. 14

ENGINEERING THERMODYNAMICS

Unit-I(ET)

(S-05)

Q. (a) Differentiate between the following: 4 (i) Homogeneous ari8 heterogeneous system, (ii) Heat and

Work.

(b) During the execution of reversible non-flow process work done is -155 kJ. If initial volume is 0.85 m 3

and pressure during process varies as P = (-3 V + 7) bar, where V is in m3, find the final volume. 4

(c) Define the following terms :

(i) State (ii)Path (iii) Process (iv) Cycle. 2

(d) What is relation between the system and its surrounding when system is : (i)Adiabatic (ii) Isolated (iii)

Closed. 3

OR

Q. (a) Define:

(i) Quasistatic process, (ii) Reversible process. 4

(b) A vessel of volume 0.2 m3 contains Nitrogen at 1.01325 bar and 15°C If 0.2 kg of Nitrogen is now

pumped into vessel, calculate the new pressure when vessel has returned to its initial temperature. Molar

mass of N2 is 28 kg/k-mol. - 4

(c) It is proposed to heat 2 liters of water initially at 15°C to a temperature of 80°C. What time will be

required to achieve this objective if 0.5 kW electric heater has been supplied for this purpose ? It is

presumed that system does not exchange any heat with the surroundings. Take sp.heatofwater = 4.2kJ/kg-

°K. 5

(W-05)

Q.(a) State the different between extensive nad intensive properties and state wherther following properties

are intensive or extensive: (i) Pressure (ii) Temperature (iii) Mass (iv) Density. (v) Volume (vi) Surface

area. 6

(b) Four Kmol of gas occupies 273.44m3 volume at a temperature of

130° C. If the density of the gas under these conditions is 0.644 kg/m',

determine:

__..'If

Q.(a)

(b)

Q-(a)

(b)

MECHANICS OF MATERIALS

(Unit-I)MOM

126

(W-12)

Q. a) Differentiate between the following, giving due explanation;

i) stress and strain.

ii) Lateral strain and longitudinal strain

iii) Tensile stress and compressive stress. 6

b) A steel rod of 20 mm diameter passes centrally through a copper tube 40 mm external diameter and

30mm internal diameter. The tube is closed at each end by rigid plates of negligible thickness. The

nuts are tightened lightly home on the projected parts of the rod. If the temperature of the assembly is

raised to 60°C, calculate the stresses developed in the copper and steel. Take E for steel as 2

105N/mm2 and E for copper as 1 205 N/mm2. Take a for steel as 12 10-6 per °C and = 18 10-6

per°C for copper. 8

OR

Q. a) Prove that the volumetric strain of a cylindrical rod which is subjected to an axial tensile load is

equal to strain in the length minus twice the strain of diameter. 6

b) A member ABCD is subjected to point loads P1 P2 P3 P4 as shown in figure and calculate the force

P3 necessary for equilibrium if P1 = 120kN, P2=220 kN and P4=160kN. Determine also the change in

the length of the member. Take E = 2 105 N/mm2.

(S-13)

Q. a) Define the following terms:

i) Modulus of Elasticity

ii) Bulk Modulus

iii) Modulus of Rigidity. .6

b) A compound bar consist of a circular rod of steel of diameter 25 mm rigidly fitted into a copper

tube of internal diameter 25 mm and thickness 5 mm. If the bar is subjected to a load of 120 kN. Find

the stresses developed in two materials. Take Es = 2 105 N/mm2 and Ec = 1.05 105 N/mm2. 8

OR

Q. a) A rod of steel is 20 m long at a temp, of 20 °C. Find the free expansion of the length when temp,

is raised to 85 °C. Find the temperature stress produced:

i) when the expansion of the rod is prevented,

ii) when the rod is permitted to expand by 6.0 mm

Take = 12 10-6/°C and E = 200 GN/m2 9

b) Explain the stress-strain curve for a mild steel bar. 5

(Unit-II)MOM

(W-12)

Q. a) Derive the relation between loading intensity, shear force and bending moment. 5

b) Draw shear force and bending moment diagrams for the cantilever beam shown in figure.

OR

b) A closely coiled helical spring of round steel wire 13 mm in diameter having 10 complete turns with

mean diameter of 140 mm is subjected to an axial load of 220 N. Determine:

i) The deflection of spring

ii) Maximum shear stress in the wire

iii) Stiffness of spring. (Take, C = 8 104 N/mm2). 6

(Unit-IV)MOM

(W-12)

Q. a) Derive the expressions for circumferential and longitudinal stresses in a thin cylinder closed at both

ends and subjected to internal fluid pressure. 6

b) A thin spherical shell of internal diameter 1.5 m and of thickness 8 mm is subjected to an internal

pressure of 2 N/mm2 Determine the increase in diameter and increase in volume. Take E = 2 105 N/mm2

and Poisson's ratio = 0.3. 8

OR

Q. a) Differentiate between a thin cylinder and a thick cylinder Name the stresses set up in a thick cylinder

subjected to internal fluid pressure. 5

b) A thin cylindrical shell 1000 mm long, 200mm internal diameter having thickness of metal as 10 mm is

filled with fluid at atmospheric pressure If an additional 20,000 mm3 of fluid is pumped into the cylinder,

find

i) The pressure exerted by the fluid on the cylinder.

ii) The hoop stress induced. Take E= 2 105 N/mm2and Poisson's ratio =0.3 9

(S-13)

Q. a) Derive expression from first principles for circumferential and longitudinal stresses in a thin cylinder

subjected to internal pressure. 7

b) A thick cylindrical shell with 300 mm outer diameter and 200 mm internal diameter is subjected to an

internal pressure of 10 N/mm2. Determine the minimum external pressure that can be applied so that tensile

stress in the metal does not exceed 15 N/mm2. 7

OR

Q. a) A cylindrical shell is 3 m long, 1 m in diameter, and the thickness of metal is 10 mm. It is subjected

to an internal pressure of 150 N/cm2. Calculate the change in dimensions of the shell and the maximum

intensity of shear stress induced. Take, E = 200 GPa and = 0.3. 7

b) A cylinder of 120 mm internal diameter to an internal fluid pressure of 80 N/mm2. If the maximum

stress developed in the cylinder is not to exceed 70 N/mm2. Find the thickness of thick cylinder. 7

(Unit-V)MOM

(W-12)

Q. a) Prove that the maximum stress induced in a body due to suddenly applied load is twice the stress

induced when the same load is applied gradually. 5

b) An unknown weight falls through a height of 20 mm on a collar rigidly attached to the lower end of a

vertical bar 5m long and 800 mm2 in section. If the maximum extension of the rod is to be 0.5mm, what is

the corresponding stress and magnitude of the unknown weight ? Take E = 2 105N/mm2 8

OR

Q. a) Define the following terms

i) Principal planes

ii) Principal stresses

iii) Obliquity

iv) Mohr's circle. 4

b) At a certain point in a strained material, the stresses on two planes, at right angles to each other are

20N/mm2 and 10 N/mm2 both tensile. They are accompanied by a shear stresses of magnitude 10 N/mm 2.

Find graphically or otherwise the location of principal planes and evaluate the principal stresses. 9

(S-13)

Q. a) Show that strain energy under uniaxial tension stored by a member per unit volume

b) A rectangular block of material is subjected to a tensile stress of 110 N/mm 2 on one plane and a tensile

stress of 47 N/mm2 on a plane at right angle, together with shear stress of 63 N/mm2 on the same planes,

find:

i) The direction of the principal planes

ii) The magnitude of the principal stress

iii) The magnitude of the greatest shear stress. 8

OR

Q. a) The principal stresses at a point in a bar are 200 N/mm 2 (tensile) and 100 N/mm2 (compressive).

Determine the resultant stress in magnitude and direction on a plane inclined at 60°to the axis of the major

principal stress. Also determine the maximum shear stress in the material at the point. 6

b) A weight of 1.5 kN is dropped on a collar attached at the lower end of a vertical bar 4 m long and 30

mm in dia. Calculate the height of drop if the maximum instantaneous stress is not to exceed 120 N/mm2

Also calculate the instantaneous elongation. Take E = 2 105 N/mm2. 7

(Unit-VI) MOM

(W-12)

Q. a) Prove that the deflection at the centre of a simply supported beam carrying a point load at the centre

is given by Yc = where W = point load, L= Length of beam. 6

b) A beam of uniform rectangular section 100 mm wide and 100 mm deep is simply supported at its ends.

It carries a uniformly distributed load of 10 kN/m run over the entire span of 4M. Find

i) Slope at the supports.

ii) Max. deflection. Take E = 1 104N/mm2 • 7

OR

Q. a) A simply supported beam of span 6 m is loaded as shown in Fig. Determine

i) Slope at the end A.

ii) Deflection at load point C.

iii) Deflection at point D.

iv) Maximum deflection. Take flexural rigidity EI = 15 109 KN-mm2 13

(S-13)

Q. a) Calculate Maximum deflection and slope, for a simply supported beam of span 'l' m having point

load at mid of the span. 5

b) A simply supported beam of 3m span carries a point loads of 120 kN and 80 kN at a distance of 0.6 m

and 2 m respectively from the left hand support. If I for the beam = 16 108mm4 and E = 210 GN/m2, find

the deflection under loads. Also calculate maximum deflection. 8

OR

Q. a) Calculate the deflection at point C and D. Also calculate the maximum deflection for a given Fig. by

Macaulay's method. Take, E = 200 GN/m2 and I = 20 107 mm4. 13

FLUID POWER-I

(Unit-I) FP-I

(W-12) Q.(a) Differentiate between :-

(i) Absolute and guage pressure.

(ii) Simple manometers and differential manometer.

Oil") Piezometer and pressure guages. 6

(b) Determine the total pressure on a circular plate of diameter 2m which is placed vertically in a water in

such a way that the centre of plate is 3 m below the free surface of water. Find position of centre of

pressure also. 7

OR

Q.(a) Explain the phenomenon of capillarity. Obtain an expression for capillary rise of a liquid. 4

(b) Explain the following Newtonian and NonNewtonian fluids,

vapour pressure and compressibility. 6

(c) The capillm y rim- in a ^lass tube is not to exceed 0.2 mm of water. Determine llN minimum si/c, ^iven

that surface tension for water in conlncl with nil ~ (1,07; 1 N/m. 3

232

MECH III

MECII III

233, principal stress. Also determine the maximum shear stress in the material at the point. 6

(b) A weight of 1.5 kN is dropped on a collar attached at the lower end of a vertical bar 4 m long and

30 mm in dia. Calculate the height of drop if the maximum instantaneous stress is not to exceed 120

N/mm2 Also calculate the instantaneous elongation. TakeE=2xl05N/mm2. 7

(Unit-VI) MOM

Q. (a)

(b)

Q.

Q-(a)

(b)

Q.

(W-12)

Prove that the deflection at the centre of a simply supported beam

carrying a point load at the centre is given by Yc =

WL 3 48 El

13

where W = point load, L= Length of beam. 6

A beam of uniform rectangular section 100 mm wide and 100 mm deep is simply supported at its

ends. It carries a uniformly distributed load of 10 kN/m run over the entire span of 4M. Find-(i) Slope

at the supports. (ii) Max. deflection. TakeE=lxl04N/mm2 7

OR

A simply supported beam of span 6 m is loaded as shown in [Fig.Q.12] Determine

(i) Slope at the end A. (ii) Deflection at load point C. (iii) Deflection at point D. (iv) Maximum

deflection. Take flexural rigidity EI= 15xl09KN-mm2

(S-13)

Calculate Maximum deflection and slope, for a simply supported beam of span '/' m having point load

at mid of the span. 5

A simply supported beam of 3m span carries a point loads of 120 kN and 80 kN at a distance of 0.6 m

and 2 m respectively from the left hand support. If I for the beam =16xl0 8mm4andE = 210 GN/m2,

find the deflection under loads. Also calculate maximum deflection.

8

OR

Calculate the deflection at point C and D. Also calculate the maximum deflection for a given Fig. Q.

12 by Macaulay's method. Take, E = 200GN/m2 and I = 20xl07mm4. 13

5 KN/m

2KN.m

B

3m

2.5m

1.5m

Fig Q 12

FLUID POWER-I

(Unit-I)FP-I

(W-12) Q. (a) Differentiate between:-

(i) Absolute and guage pressure.

(ii) Simple manometers and differential manometer.

(iii) Piezometer and pressure guages. 6

(b) Determine the total pressure on a circular plate of diameter 2m which is placed vertically in a

water in such a way that the centre of plate is 3 m below the free surface of water. Find position of

centre of pressure also. 7

OR

Q.(a) Explain the phenomenon of capillarity. Obtain an expression for capillary rise of a liquid. 4

(b) Explain the following Newtonian andNonNewtonian fluids,

vapour pressure and compressibility. 6

(c) The capillary rise in a glass tube is not to exceed 0.2 mm of water. Determine its minimum size,

given that surface tension for water in contact with air = 0.0725 N/m. 3

232

MECH III

MECH HI

233(S-13)

Q. (a) Explain with neat sketch the following :-(i) U tube differential manometer

(ii) Total pressure on a vertical plane surface submerged in liquid. 6

(b) The dynamic viscosity of an oil, used for lubrication between a shaft and sleeve is 6 poise. The shaft is

of diameter 0.4 m and rotates at 190 rpm. Calculate the power lost in the bearing for a sleeve length of 90

mm. The thickness of oil film is 1.5 mm. 7

OR

Q. (a) Differentiate between: (i) Liquid and gases (ii) Real fluid and ideal fluid (iii) Specific weight and

specific volume of fluid. 6

(b) Derive an expression for the depth of centre of pressure from free surface of liquid of an inclined plane

surface submerged in the liquid. 7

(Umt-II)FP-I

(W-12)

Q. (a) What is "Metacentre" and "Metacentric height". Derive an

expression for the metacentric height of a floating body. 7

(b) A jet of water from a 25 mm diameter nozzle is directed vertically upwards. Assuming that the jet

remains circular and neglecting any loss of energy, that will be the diameter at a point 4.5 m above the

nozzle, if the velocity with which the jet leaves the nozzle is 12m/s. 6

OR

Q. (a) Define velocity potential function and stream function. 4

(b) What is venturimeter? Derive an expression for the discharge through a venturimeter. 6

(c) A fluid field is given by: V = x2 yi +y2zj - (2xyz+yz2) k

Prove that it is a case of possible steady incompressible fluid flows. Calculate the velocity and acceleration

at the point (2, 1,3)

3

(S-13)

Q. (a) State different types of flow lines with sketches. 6

(b) A pipeline carrying oil of specific gravity 0. 87, changes in diameter from 200 mm. diameter at a

position A to 500 mm diameter at a position B which is 4m at a higher level. If the pressure at A& B are

9.81 N / cm2 and 5.886 N/cm2 respectively and the discharge is 200 liters/s. Determine the loss of head and

direction of flow, 7

OR Q. (a) What is Euler's equation of motion? Also derive Bernoulli's

equation from Euler's equation. 6

(b) A horizontal venturimeter with inlet diameter 20 cm and throat diameter 10 cm is used to measure the

flow of water. The pressure at inlet is 17. 658 N/cm2 and the vacuum pressure at the throat is 30 cm of

mercury. Find the discharge of water through venturimeter. Take Cd = 0.98. 7

(Unit-Ill) FP-I

Q. (a)

. (W-12)

Define the following non-diamensional numbers Reynold's number, Froude's number and mach number.

What are their sign ificances for fluid flow problems ? 7 (b) Using Buckingham's n -theorem, show that the

velocity through a circular arifice is given by

234

MECH HI

where, Ft is the head causing flow,

D is diameter of the orifice,

^ is coefficient of viscosity

i is the mass density and

g is acceleration due to gravity. . 7

OR Q. (a) State various methods of diamentional analysis. Describe

Reyleigh's method for diamensional analysis. 7 (b) Find an expression for the drag force on smooth sphere

of

diameter D, moving with a uniform velocity V in a fluid flow of

density g and dynamic viscosity |^. 7 I MECH in 23JQ.(a)

(b)

Q. (a)

(b)

Q. (a)

(b)

Q.(a)

(S-13)

Define the following dimensionless numbers :-(i) Reynold's number (ii) Mach's number (iii) Froude's

number (iv) Weber's number.

8

Find an expression for the drag force on smooth sphere of diameter D, moving with a uniform velocity V

in a fluid of density p and dynamic viscosity JJ,. 6

OR

What are different similarities that can exist between model and prototype ? 6

A ship 300 m long moves in sea water, whose density is 1030 kg/m3. Al : 100 model of this ship is to be

tested in a wind tunnel. The velocity of air in the wind tunnel around the model is 30 m/s and the resistance

of the model is 60 N. Determine the velocity of ship in sea water and also the resistance of the ship in sea

water. The density of air is given as 1.24 kg/m3. Take the kinematic viscosity of sea water and air as 0.012

stokes and 0.018 stokes respectively. 8

(Unit-IV)FP-I

(W-12)

Define displacement thickness. Derive an expression for the displacement thickness.

Air is flowing over a flat plate 500 mm long and 600 mm wide

with a velocity of 4 m/s. The kinematic viscosity of air is

giyenas 0.15xl04m2/S. Find

(i) The boundry layer thickness at the end of the plate.

(ii) Shear stress at 200 mm from the leading edge and

(iii) Drag force on one side of the plate.

Take the velocity profile over the plate as -

U

5;

and density air 1.24 kg/m3 OR

What do you mean by separation of boundry layer ? What is the effect of pressure gradient on boundry

layer separation?

(b) For the velocity profile for turbulent boundry layer.

~ = (y /§) • obtain an expression for boundry layer thickness, shear stress, drag force on one side of the

plate and coefficient of drag in terms of Reynold number. Given the shear stress (TO) for

the turbulent boundry layer as *o - 0.0225 £U

(S-13)

Q. (a) For a real fluid flow over a flat plate, explain momentum thickness and deduce a relation for

momentum thickness. 6

(b)

Air is flowing over a smooth plate with a velocity of 10 m/s. The length of plate is 1.2m and width 0.8m. If

laminar boundary layer exists up to a value of Re = 2 x 105 , find the maximum distance from the leading

edge upto which laminar boundary layer exists. Find the maximum thickness of laminar boundary layer if

the velocity profile is given by

u .Take kinematic viscosity for air = 0. 15 stokes. 7

OR

Q. (a) What is drag and lift? Also explain with neat sketch coeffi cient of drag and lift.

(b) The velocity distribution in the boundary layer is given by

—

U 5

where u is the velocity at distance y from plate and u = U at y = 8, 6 being boundary layer thickness.

Find:

(i) The displacement, momentum and energy thickness.

5**•!

(ii) Value of

9

236

MECH III(Unit-V)FP-I

(Unit-VI)FP-I

(W-12)

Q. (a) Show that loss of head due to sudden expansion in pipeline is a function of velocity head. 6

(b) At a sudden enlargement of a water main from 240 mm to 480rrm diameter, the hydraulic gradient rises

by 10 mm. Estimate the rate of flow. 7

OR Q.. (a) Explain the phenomenon of water Hammer. Obtain an expression

for the rise of pressure when the flowing water in pipe is brought to rest by closing the valve gradually. 6

(b) A pipe line 300 mm in diameter and 3200 m long is used to pump up 50 kg per second of an oil whose

density is 950 kg/m3 and whose kinematic viscosity is 2.1 stokes. The centre of the pipeline at the upper

end is 40 m above than that at the lower end. The discharge at the upper end is atmospheric. Find the

pressure at the lower end and draw the hydraulic gradient and the total energy line. 6*»

(S-13)

Q. (a) Derive an expression for loss of head due to sudden contrac tionin pipe. 7

(b) A pipeline 60 cm diameter bifurcates at a Y junction into two branches 40cm and 3 Ocm in diameter. If

the rate of flow in the main pipe is 1.5m'/s and mean velocity of flow in 30cm diameter pipe is 7.5 m/s,

determine the rate of flow in the 40 cm diameter pipe. 7

OR

Q. (a) What do you mean by water hammer? Explain factors affecting water hammer. Also discuss various

cases of water hammer. 6

(b) A horizontal pipeline 50 m long is connected to a water tank at one end and discharged freely into the

atmosphere at the other end. For the first 30 m of its length from the tank, the pipe is 200 mm diameter and

its diameter is suddenly enlarged to 400 mm. The height of water level in the tank is 10m above the centre

of the pipe. Considering all minor losses, determine the rate of flow. Take f = 0.01 for both sections of

pipe. Also draw HGL and TEL.

8

(W-12)

Show that the force exerted by a jet of water on moving inclined plate in the direction of jet is given by Fx

= /a(v-u)2sin2# where, a = area of jet

(b)

Q-(a)

(b)

Q.(a)

(b)

0= Inclination of the plate with the jet

v= Velocity of jet 7

A jet of water of diameter 50 mm moving with a velocity of 40 m/s strikes a curved fixed symmetrical

plate at the centre Find the force exerted by the jet of water in the direction of the jet, if the jet is deflected

through an angle of 120° at the outlet of the curved plate. 7

OR

Show that the efficiency of free jet striking normally on a series of flat plates mounted on the periphery of

a wheel can never exceed 50%. 7

A jet of water having a velocity of 3 5 m/s impinges on a series of vanes moving with a velocity of 20 m/s.

The jet makes an angle of 30° to the direction of motion of vanes when entering and leaves at an angle of

120°. Draw the triangles of velocities at inlet and outlet and find (i) The angle of vanes tips so that water

enters and leaves

without shock.

(ii) The work done per unit weight of water entering the vane and (iii) The efficiency. 7

Define:- (i) (u) (iii)

(S-13)

Hydraulic efficiency Mechanical efficiency Volumetric efficiency.

6

A jet of water of diameter 50 mm moving with a velocity of 20 m/sec strikes a fixed plate in such a way

that the angle between the jet and the plate is 60°. Find the force exerted by the jet on one plate-(i) in the

direction normal to the plate

(ii) in the direction of jet. 7

238

MECH HI

239OR

Q. A jet of water moving at 18 m/s impinges on vane shaped to deflect the jet through 120° when

stationary. If the vane is moving at 8 m/s, find the angle of jet so that there is no shock at inlet. What is the

absolute velocity of the jet at exit in magnitude and direction and the work done per second per unit wt.of

water striking per second? Assume the vane is smooth.Draw velocity diagram . 13

ENGINEERING THERMODYNAMICS

(Unit-I)ET

(W-12)

Q. (a) Define the terms State, Property, Process and Cycle of a

thermodynamic system. 4

(b) A car has a mass of 1600 kg. It has an engine which develops 35 kW when travelling at a speed of 70

km/h. Neglecting losses; determine the resistance to the motion in N/kg* 5

(c) Define the characteristic gas constant. How does it differ from

universal gas constant? Write the ideal gas equation associated with these constant and units of these

constant. 4

OR

Q. (a) An oxygen cylinder has a capacity of 300 liters and contains oxygen at a pressure of 3.1 MN/m 2and

temperature 18°C The stop valve is opened and some gas is used. If the pressure and temperature of the

oxygen left in the cylinder fall to 1.7 MN/m2 and 15°C, respectively, determine the mass of oxygen used.

The density of oxygen at 0°Cand 1.01325 bar may be taken as 1.429kg/m3. 5

(b) How does classical thermodynamics differ from statistical thermodynamics? 4

(c) State the difference between extensive, intensive and specific properties of a thermodynamic system.

Give three examples of each. 4

"240 ^______________________:_______MECHIH

(S-13) Q. (a) What do you understand by macroscopic and microscopic

viewpoint? 4 (b) An automobile vehicle of 1500 kg mass is running at a speed of 60 km/hr. The brakes are

applied and the vehicle is brought to rest. Calculate the rise in temperature of the brakes if their mass is 15

kg. Take specific heat of the brake material = 0 .46 kJ/kg. K

4

(c) Define the law that forms the basis for temperature measure ment. Establish the correlation between

Centigrade and Fahrenheit temperature scale. 2 + 3 = 5

OR

Q. (a) Two spheres, each of capacity 2 m3, are connected by pipe with valve inserted in between. When the

valve lies in a closed position one sphere contains oxygen at 50 KPa and 320 K and other contains oxygen

at 45 KPa and 290 K. Subse quently the valve is opened and the entire system is allowed to attain the

equilibrium. At this state the final temp, is noted to be 27°C. Presuming that the volume of connecting pipe

is negligible, determine final pressure of the complete system. (M for02=32). 5

(b) State the concept of temperature and equality of temperature . 3

(c) State giving brief justification, whether the following proper ties of system are intensive or extensive :

Viscosity , I'lilltnlpv. Pressure, specific volume, density, surface nrcn. vHoi ily Differentiate between

intensive and extensive pmpeilit-M

1 i }-••

(Unit-II)ET

(W-12)

Q. (a) A gas is compressed hyperbolically from a pressure and volume of 100 KN/m2and 0.056 m3,

respectively, to a volume of 0.007m3.' Determine the final pressure and the work done on the gas. 3

(b) Prove that heat transferred in polytropic process for a closed system is given by Q = mcn (T,-T2) Joules,

where cn is polytropic

heat capacity given byCv. (y-n)/(n-l). 5

(c) A gas has a density of 1.875 kg/m3 at a pressure of 1 bar and with a temperature of 15°C. Amass of 0.9

kg of gas requires a heat transfer of 175 kJ to raise its temperature from 15°C to 250°C while

MECH IN

241