STRENGTH OF MATERIALS -I Civil Engineering

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Set No. 1Code No: W0101/R05

I I B.Tech I Semester Supplementary Examinations, April/May 2011

STRENGTH OF MATERIALS -I (Civil Engineering)

Time: 3 hours Max Marks: 80Answer any FIVE Questions

All Questions carry equal marks

1. A steel bolt of 650 sq.mm C.S.A passes centrally through a copper tube of C.S.A.1200 sq. mm. the tube is 500 mm long and is closed by rigid washers which are

fastened by the threads on the steel bolt. The pitch of the thread is 3 mm. If the

nut is tightened through 90 , find the stresses in the bolt and the tube. [16]0

2. A weight of 210 kN is supported by three short pillars each of sectional area 500

mm . The central pillar is of steel and the outer ones are of copper. The pillars are2

so adjusted that at a temperature of 15 C each carries equal load. The temperature0

is then raised to 950C. Find the stress in each pillar at 15 C and 95 C. Take E =0 0s

200 GPa and E = 80 GPa a = 12 × 10 / C and a = 18 × 10 / C. [16]-6 0 -6 0C s c

3. (a) What are the di erent types of beams possible - describe the behavior of eachof them.

(b) Draw the S. F. and B.M. diagrams for a cantilever with a point load at thefree end and u.d.l & throughout. [6+10]

4. (a) State the assumptions made in the theory of simple bending.

(b) Derive the simple bending equation. [6+10]

5. An I-section shown in Figure 5 is subjected to the S.F. = 120KN . Sketch the shear stress distribution. Obtain maximum and mean shear stress. [16]

Figure 5

6. A horizontal beam of uniform section is pinned at its ends which are at the same

level and is loaded at the left hand pin with an anticlockwise moment M and at the right hand pin with a clockwise moment 2m both in the same vertical plane.

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The length between the pins is L. Find the angles of slope at each end and the

de ection of the midpoint of the span in terms of M, L, E and I. [16]

7. A shell 3.25m. long, 1m in diameter is subjected to an internal pressure of 1N/mm .2

If the thickness of the shell is 10mm, find the circumferential and longitudinal

stresses. Also find out the maximum shear stress and the changes in the dimensionsof the shell.

Take E = 2 × 10 N/mm , µ = 0.3. [16]5 2

8. A compound cylinder is formed by shrinking a hollow cylinder of 150 mm external dia. over another hollow cylinder of 130 mm internal dia. The common dia after

shrinking on its 140 mm. If the radial pressure at the junction is 1200N /mm and 2

E = 200KN/mm , Find the original di erence in dia. of the two cylinders before2

shrinking. [16]

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1. A rectangular block of size 50 mm × 100 mm × 80 mm is subjected to the following

axial loads.

500 kN (tensile) on 100 mm × 80 mm faces

900 kN (tensile) on 500 mm × 80 mm faces

1000kN (Compressive) on 500 mm × 100 mm faces.

Taking the poisson’s ratio as 0.3, find the change in volume of the block. If

E = 200GPa, find the modulus of rigidity and the bulk modulus. [16]

2. A thin tyre is shrunk on a wheel of 1 m dia. Find the internal dia. of the tyre, if the

circumferential stress is limited to 90 N/ mm . Find also the least temperature to2

which the tyre must be heated above that of the wheel, before it could be slipped

on. For the tyre material take E = 200 GPa and a = 12 × 10 / C. [16]-6 0

3. Construct the S. F. D and B. M. D for the cantilever beam shown in Figure 3.[16]

Figure 3

4. For a channel section shown in Figure 4 determine the section modulus. Hencecalculate the maximum bending stresses. Sketch the distribution of bending stress

if the section is subjected to a B. M = 40 KNm. [16]

Figure 4

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5. Obtain the shear stress distribution for a rectangular cross section 230 × 400 mm

subjected to a shear force of 40 KN. Calculate maximum and average shear stress.[16]

6. (a) Explain Macaulay’s method.

(b) Derive the expression for the slope and de ection of a cantilever beam of lengthL, carrying a point load W at the free end by double integration method. [8+8]

7. (a) Define the terms

i. Longitudinal stress

ii. Volumetric strain

(b) A boiler shell of 2m. diameter is made up of mildsteel plates of 20mm thick.The e ciency of the longitudinal and circumferential Joints is 70% and 60%

respectively. Determine the safe pressure in the boiler, if the permissible tensilestress in the plate section through the rivets is 100 N/mm . Also determine the2

circumferential stress in the solid plate section and longitudinal stress throughthe rivets. [4+12]

8. (a) Find the ratio of thickness to internal dia. Of a tube subjected to internal

pressure when the pressure is 3/8 of the max permissible hoop stress.

(b) Find the increase in internal dia of such a tube 100 mm in internal dia. Sub-

jected to an internal pressure of 90N/mm . Neglect longitudinal strain and2

take E = 200GN/m and = 0.3. [8+8]2 1

m

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1. Two vertical wires are suspended from a rigid support at top at a horizontal distance

of 60cm apart. Both wires are initially 4.5 m long. At their lower ends there is

a rigid horizontal bar carrying a load P. The left steel wire is of 1 mm dia. while

the right copper wire is of 1.5 mm dia. Find the position of load P, if both wiresextend by the same amount. Find the slope of rigid bar if a load of 300 N is hung

at the center of bar. Neglect the weight of the bar. Take E = 130 GN/m . [16]2 S

2. A uniform metal bar of 1.5 m length, area of section 600 mm has an elastic limit2

of 160 N / mm . Find its proof resilience, if E = 200 Gpa . Find also the max.2

applied load which can be suddenly applied without exceeding the elastic limit.

Calculate the magnitude of the gradually applied load which will produce the sameextension. [16]

3. (a) What are the di erent types of beams possible - describe the behavior of each

of them.

(b) Draw the S. F. and B.M. diagrams for a cantilever with a point load at the

free end and u.d.l & throughout. [6+10]

4. Define Neutral axis. Sketch the bending stress distribution across the cross section

of a rectangular beam section 230 × 400 m subjected to 60 KNm moment. [16]

5. Derive an expression for the distribution of shear stress across the cross section.

How is average shear stress defined. Relate maximum shear stress to the average

shear stress in a rectangular section. [16]

6. Determine the mid-span de ection and slopes at the supports in the beam as shown

in Figure 6. [16]

Figure 6

7. (a) A water main 600mm diameter contains water at a pressure head of 100m. Find the thickness of the metal required if the permissible stress is 30 N/mm .2

(b) A vessel in the shape of a spherical shell 800mm in diameter, 10mm shellthickness is completely filled with a uid at atmospheric pressure. Additional

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uid is then pumped in, till the pressure increases by 5N/mm . Find the2

volume of this additional uid.

Take E = 2 X 10 N/mm , µ = 0.25. [6+10]5 2

8. A steel cylinder of outside diameter 240 mm and inside diameter 200 mm is shrunk

on to one having diameters 200 and 160 mm, the interference fit being such that under an internal pressure p, the inner tensile stress in both cylinders = 85.4N/mm .2

Find the initial di erence in the nominal 200 mm diameters and the value of p ifE = 2.1 × 10 N/mm . [16]5 2

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1. Explain the Following: -

(a) Elasticity and Plasticity

(b) Ductility and Malleability

(c) Stress and Strain

(d) Limit of proportionality and Elastic Limit [4+4+4+4]

2. (a) A bar of length L is fixed at its ends. If there is a rise in temperature of t C,0

what will be the stress induced if E is the elastic modulus and a, coe cient of

linear expansion of the rod material. What will be the change in stress if thesupport yields of d?

(b) A steel rod 2m long is fixed at its ends. It is subjected to an initial tensilestress of 48 MPa. Find the change in temperature required to make the rod

stress free. Find also the stress in the rod if its temperature is further increased

by 15 C. Take E = 200 GPa and a = 12 × 10 / C. [6+10]0 -6 0

3. Obtain the location & magnitude of the maximum S.F. and B. M and draw the B.

M. D for a simply supported beam subjected to uniformly varying load (figure3).

[16]

Figure 3

4. For a T-section shown in Figure 4. Obtain section modulus and hence obtain the

maximum bending stress if it is subjected to a B. M of 20 KNm. [16]

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Figure 4

5. Design the cross section for a beam acted upon by a bending moment = 50 KNm.If width of beam is 200 mm calculate, depth. f = 9 N/mm . [16]2

6. (a) Explain the application of moment area method and Macaulay’s method for

slope and de ection for cantilever beams.

(b) A Cantilever of uniform cross-section of length L carries two point loads, W

at the free end, 3W at a distance “a” from the free end. Find the maximum

de ection due to this loading. [8+8]

7. An air vessel of a torpedo is 500mm diameter, 10mm thick and length 2m. Deter-

mine

(a) Hoop stress

(b) Longitudinal stress

(c) Change in diameter

(d) Change in length

(e) change in volume if it is subjected to an internal pressure of 10 N/mm . 2

Take E = 2 X 10 N/mm , µ = 0.3. [16]5 2

8. A C.I pipe of 200mm internal dia. And thickness of metal 50mm carries water under a pressure of 7N/mm . Find the max. and minimum intensities of hoop2

stress, sketch the Variation of hoop stress and radial pressure across the section.[16]

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Set No. 1Code No: X0202/R05


PULSE AND DIGITAL CIRCUITS( Common to Electrical & Electronic Engineering, Electronics &

Communication Engineering, Electronics & Instrumentation Engineeringand Electronics & Telematics)

Time: 3 hours Max Marks: 80

Answer any FIVE Questions


1. (a) Prove that an RC circuit behaves as a reasonably good integrator if RC > 15T,

Where T is the period of an input ‘E sin t’.m

(b) What is the ratio of the rise time of the three sections in cascade to the rise

time of Single section of low pass RC circuit. [8+8]

2. (a) Design a clipping circuit with ideal components, which can give the waveform

shown in figure 2a for a sinusoidal input.

Figure 2a

(b) State and prove clamping circuit theorem. [8+8]

3. Explain the following:

(a) Storage and transition times of the diode as a switch.

(b) The behaviour of the transistor switch in saturation. [8+8]

4. (a) Design a collector coupled transistor monostable multivibrator to produce a

time delay of 100 µsec. Use transistors have h of 250. Use ±12v sources,FE

V = 0.3v, V = 0.7v and V = 0vCE(sat) BE(sat) BEcutoff

(b) Show that the astable multivibrator works as voltage controlled oscillator.

[10+6]

5. (a) Draw and clearly indicate the restoration time and yback time on the typical

waveform of a time base voltage.

(b) Derive the relation between the slope, transmission and displacement errors

(c) Explain how UJT is used for sweep circuit? [6+4+6]

6. (a) What do you mean by synchronization ?

(b) What is the condition to be met for pulse synchronization?

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(c) Compare sine wave synchronization with pulse synchronization? [4+6+6]

7. (a) Explain the basic principles of sampling gates using series switch and also give

the applications of sampling gates.

(b) Explain the e ect of control voltage on gate output of unidirectional sampling

gate using diode with some example. [8+8]

8. (a) What are the basic logic gates which perform almost all the operations in

Digital communication systems.

(b) Give some applications of logic gates.

(c) Define a positive and negative logic systems.

(d) Draw a pulse train representing a 11010111 in a synchronous positive logicdigital system. [4+4+4+4]

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2. (a) A symmetrical 10 kHz square wave whose peak -to-peak excursion are ±10V

with respect to ground is impressed upon the diode clamping circuit shown in

figure 2a. The Diodes has R = 100 , R = a and V = 0. Sketch the steadyf r

state output waveform Indicating clearly the voltage levels.

Figure 2a

(b) Explain positive peak voltage limiters above and below reference level. [8+8]

3. (a) Sketch neatly the waveforms of current & voltages for a transistor switch withcapacitance loading circuit.

(b) What are catching diodes? [12+4]

4. Regeneration is possible in the fixed-bias transistor ip- op if the base-to-base

voltage gain exceeds unity. Verify that this gain condition is satisfied provided that

h Rc > R . Assume that for each stage the current gain is |A | = h 1 andfe 1 I F E that the input resistance R is small compared with either R or R . [16]

i 1 2

5. (a) With the help of a neat circuit diagram and waveforms explain the working

of a transistor Miller time base generator.

(b) Find the component values of a bootstrap sweep generator, given Vcc=18V,

Ic(sat) = 2mA and hfe(min)=30. [8+8]

6. (a) Draw the circuit diagram of an astable multivibrator to obtain frequency di- vision by 5. Explain its working with waveforms.

(b) What is phase jitter? Discuss the significance of it in a frequency divider.[8+8]

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7. (a) What is sampling gate? Explain how it di er from Logic gates?

(b) What is pedestal? How it e ects the output of a sampling gates?

(c) What are the drawbacks of two diode sampling gate? [6+6+4]

8. (a) Draw and explain the circuit diagram of a diode AND gate for positive logic.

(b) Derive the output equation for a diode OR gate for positive logic. [8+8]

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2. (a) Determine V for the network shown in figure 2a for the given waveform. o

Assume ideal Diodes.

Figure 2a

(b) Draw the basic circuit diagram of positive peak clamper circuit and explain

its operation. [8+8]

3. Write Short notes on:

(a) Diode switching times

(b) Switching characteristics of transistors

(c) FET as a switch. [4+8+4]

4. Write short notes on:

(a) Gate width of mono-stable multivibrator.

(b) Astable multivibrator as a voltage to frequency converter with circuit andwaveform. [8+8]


of a transistor Bootstrap time base generator.

(b) i. In the circuit shown in Figure 5 L=200mH, and it is required that the

current in L increases from zero to100mA in 1ms. Find V ? Assume cc

R =0 and V = 0.L CE(sat)

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ii. If R , consisting of the diode resistance alone, is 10 ohms draw the wave-d

forms of i and V indicating voltage levels and time constants. [8+8]L CE

Figure 5

6. (a) Explain the factors which in uence the stability of a relaxation divider with

the help of a neat waveforms.

(b) A UJT sweep operates with Vv = 3V, Vp=16V and =0.5. A sinusoidalsynchronizing voltage of 2V peak is applied between bases and the natural

frequency of the sweep is 1kHz, over what range of sync signal frequency will

the sweep remain in 1:1 synchronism with the sync signal? [8+8]

7. (a) What is pedestal? Draw and explain the sampling gate which cancel the

pedestal.

(b) What are the applications a sampling gates? Explain any one application indetail. [8+8]

8. (a) What are the basic logic gates which perform almost all the operations in

Digital communication systems.

(b) Give some applications of logic gates.

(c) Define a positive and negative logic systems.

(d) Draw a pulse train representing a 11010111 in a synchronous positive logic

digital system. [4+4+4+4]

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2. (a) For the circuit shown in figure 2a an input voltage V linearly from 0 to 150Vi

is applied. Sketch the output waveform V to the same time scale. Assume0

ideal diodes.

Figure 2a

(b) What in meant by a d.c restoration circuit and explain? [12+4]

3. (a) Sketch neatly the waveforms of current & voltages for a transistor switch with

capacitance loading circuit.

(b) What are catching diodes? [12+4]

4. What is a monostable multivibrator? Explain with the help of a neat circuit di-

agram the principle of operation of a monostable multivibrator, and derive anexpression for pulse width. Draw the wave forms at collector and Bases of both

transistors. [16]


of a transistor current time base generator.

(b) Design a transistor bootstrap ramp generator to provide an output amplitudeof 12V over a time period of 2ms. The input signal is a negative going pulse

with an amplitude of 5 V, a pulse width of 2ms and the time interval between

pulses is 0.5ms. The load resistance is 1Kohms and the ramp is to be linear within 1%. The supply is to be ±15v. take h = 80. [8+8]

fe(min)

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6. (a) What do you mean by synchronization ?

(b) What is the condition to be met for pulse synchronization?

(c) Compare sine wave synchronization with pulse synchronization? [4+6+6]

7. (a) What is sampling gate? Explain how it di er from Logic gates?

(b) What is pedestal? How it e ects the output of a sampling gates?

(c) What are the drawbacks of two diode sampling gate? [6+6+4]

8. (a) Draw the circuit diagram and explain the working of a diode transistor logic

gate.

(b) Explain the wired AND logic with the help of circuit diagram. [8+8]

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OOP THROUGH JAVA

( Common to Mechanical Engineering, Mechatronics, Metallurgy &

Material Technology, Production Engineering and Automobile Engineering)Time: 3 hours Max Marks: 80



1. Distiguish between the following terms:

(a) Objects and classes

(b) Data abstraction and data encapsulation

(c) Inheritance and polymorphism

(d) Dynamic binding and message passing. [16]

2. (a) What is the di erence between equality of objects and equality of objects and

equality of references that refer to them?

(b) What is the di erence between a public member and a private member of aclass?

(c) write an application that computes the value of ex by using the formula:e = 1 + x/1! + x /2! + x /3! + .......... [4+4+8]2 3 x

3. (a) Define Absract class? Explain with a suitable example.

(b) Write a sample program to demonstrate the order of initialization of the base

classes and derived classes. Now add member objects to both the base andderived classes, and show the order in which their initialization occurs during

construction. [8+8]

4. Prove that all the methods in an interface are automatically public. [16]

5. What is Error? What is Exception? Are they totally di erent or related? As a pro-grammer what is the di erence in handling an error and an exception. With the help

of a simple java program explain the concepts error and exception. [2+2+2+4+6]

6. With the help of an example program explain how you handle all mouse related

events. [16]

7. Brie y explain the components of AWT. [16]

8. Write a program to illustrate the usage of the following methods of StringBu erclass. Explain the output in each case. Delete(), setChatAt(), deleteChatAt(),

append(), chatAt(), getChars(). [16]

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OOP THROUGH JAVA





1. (a) Describe the structure of a typical java program

(b) Enumerate the rules for creating identifiers in java

(c) What are the conventions followed in java for naming identifiers? Give exam-

ples? [6+4+6]

2. (a) How does String class di er from the StringBu er class?

(b) Write program to do the following: [6+10]

i. To output the question “who is the inventor of java”?

ii. To accept an answer

iii. To print out “Good” and then stop, if the answer is correct.

iv. To output the message “try again”, if the answer is wrong

v. To display the correct answer when the answer is wrong even at the third

attempt.

3. (a) Define Absract class? Explain with a suitable example.

(b) Write a sample program to demonstrate the order of initialization of the base

classes and derived classes. Now add member objects to both the base andderived classes, and show the order in which their initialization occurs during

construction. [8+8]

4. Write a program to create an interface containing a static inner class. Implement this interface and create an instance of the inner class. [16]

5. (a) When do you use Nested try statements. Explain nested try statements withthe help of an example java program.

(b) Explain nested try statements in the context of method calls with the help of

an example java program. [8+8]

6. Explain in detail about the following event classes:

(a) ComponentEvent

(b) ContainerEvent

(c) FocusEvent. [6+5+5]

7. What are JWindow and JLabel? What are their uses? Explain the steps involvein creating them with java skeleton code. [8+8]

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8. Write short notes on:

(a) ”whois” port

(b) URL connection class

(c) Datagram packet. [5+5+6]

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OOP THROUGH JAVA





1. (a) What is a variable? What is scope of a variable?

(b) What is type casting? Why is required in programming?

(c) Write a while loop to find the smallest n such that n is greater than 10,000.2

[4+4+8]

2. (a) What is the di erence between equality of objects and equality of objects andequality of references that refer to them?

(b) What is the di erence between a public member and a private member of a

class?

(c) write an application that computes the value of ex by using the formula:

e = 1 + x/1! + x 2 /2! + x 3 /3! + .......... [4+4+8]x

3. Create a 3-level inheritance hierarchy. Each class in the hierarchy should have afinalize( ) method, and it should properly call the base-class version of finalize( ).

Demonstrate that your hierarchy works properly. [16]

4. What is interface? How do you define an interface? Explain with a suitable exam-

ple. [16]

5. (a) Why thread is called light weight task and process heavy weight task.

(b) What are the di erent things shared by di erent threads of a single process. What are the benefits of sharing?

(c) Is multithreading suitable for all types of applications. If yes explain any suchapplication. If no, explain any application for which multithreading is not

desired.[4+4+8]

6. Give class hierarchy related to Panel and Frame. Brie y explain all the classes.

[16]

7. (a) Explain the di erent steps in the life cycle of an applet.

(b) Develop an applet that receives three numeric values as inputs from the user

and then displays the largest of three on the screen. Write a HTML programand test the applet. [8+8]

8. (a) How does StringTokenizer implements Enumeration?

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(b) Write a program to display the employee number, employee name, department

number, salary of an employee using a StringTokenizer class. [8+8]

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OOP THROUGH JAVA





1. Write a program that will compute the following series:

(a) 1/1 + 1/2 + 1/3 + ...... + 1/n

2(b) 1/1 + 1/2 + 1/2 + ....... + 1/2 . [8+8]n

2. (a) What is the di erence between equality of objects and equality of objects andequality of references that refer to them?

(b) What is the di erence between a public member and a private member of a

class?

(c) write an application that computes the value of ex by using the formula:

e = 1 + x/1! + x /2! + x /3! + .......... [4+4+8]2 3 x

3. (a) How can you prevent a class from Inheritance?Explain with an example.

(b) How can you prevent a method from overriding? Explain with an example.

(c) What is the use of this keyword in java. [6+6+4]

4. Create three interfaces, each with two methods. Inherit a new interface from the

three, adding a new method. Create a class by implementing the new interface andalso inheriting from a concrete class. Now write four methods, each of which takes

one of the four interfaces as an argument. In main( ), create an object of your class

and pass it to each of the methods. [16]

5. (a) What is multithreading? What are its advantages?

(b) compare process based and thread based multitasking. [6+10]

6. What are the components and other graphical user interface elements that can

act as source of events? What are the events that can be generated by the above

elements? Explain. [16]

7. (a) Write brie y applet display methods.

(b) Write a java program to form a calculator. [8+8]

8. (a) What is the di erence between Internet address and InetAddress?

(b) Explain datagrams. [8+8]

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ADVANCED DATA STRUCTURE( Common to Computer Science & Engineering and Electronics &

Computer Engineering)Time: 3 hours Max Marks: 80



1. (a) When are copy constructors called?

(b) What is Virtual Destructor?

(c) What is the di between “new” and “operator new” ?

(d) What is a local class? Why can it be useful? [4+4+4+4]

2. What is template? Explain about function templates and class templates with

suitable examples. [16]

3. (a) Explain about try, catch, throw keywords in C++?

(b) Write a program to illustrate the exception handling mechanism in C++.

[8+8]

4. (a) What is a Sparse Matrix? Explain about the linear list representation of a

sparse matrix?

(b) Write a C++ program to implement addition of two sparse matrices? [8+8]

5. Develop a class for hash table using linear probing and neverUsed concept to handle

an erase operation. Write complete C++ code for all the methods. Include a

method to reorganize the table when (say) 60% of the empty buckets have neverused equal to false. The reorganization should move pairs around as necessary and

leave a properly configured hash table in which neverUsed is true for every emptybucket. [16]

6. What is an AVL Tree? Explain about the di erent rotation patterns in AVL trees

for balancing with appropriate examples? [16]

7. (a) Explain the various operations used in Splay tree.

(b) Write a deletion algorithm of B-tree. [8+8]

8. (a) Explain the construction of su x trie with an example.

(b) Write brute force algorithm? Compute the performance of an algorithm.[8+8]

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1. (a) Each class has some special member-functions, which calls can be insertedby the compiler into a code without explicit instruction of the programmer.

Enumerate such functions, members and cases, when implicit calls can arise.

(b) If when creating a variable the programmer explicitly did not initialize it, in

some cases, the compiler itself would give it a certain, predefined initial value,and in some cases the initial value would be unpredictable. What does it

depend on? [8+8]

2. (a) What is a “virtual member function”?

(b) How can C++ achieve dynamic binding yet also static typing?

(c) What’s the di erence between how virtual and non-virtual member functions

are called? [5+5+6]

3. Create a program that opens a file (the first argument on the command line) and

searches it for any one of a set of words (the remaining arguments on the commandline). Read the input a line at a time, and write out the lines (with line numbers)

that match to the new file. [16m]

4. (a) Define a sparse matrix? Explain its representation? Write the program that gives the header for the class sparse Matrix which uses row major mapping of

a sparse matrix into an arrayList.

(b) Write the methods get (theRow, the Column) and set (theRow, theCol-umn, theValue) for a sparse matrix. [10+6]

5. What is Hashing? Explain the di erent Hash table representations in detail? [16]

6. Define a Binary Search Tree? Write the procedures to perform insertion, deletion

and searching in a binary search tree? [16]

7. (a) Write a program for visualization of a key insertion algorithm in a B-tree.

(b) Describe insertion operation in a red black tree with an example. [8+8]

8. (a) Brie y describe about Pattern matching. List some of Pattern matching al-

gorithms.

(b) Write an algorithm for deleting a string from a compressed trie and also ana-

lyze its time complexity. [6+10]

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1. (a) Give an overview of C++ class structure?

(b) Compare the C++ class with C structure. [8+8]

2. (a) Write a program to overload prefix and postfix operators?

(b) Write a program to overload new and delete operators? [8+8]

3. (a) Explain about ios ags in C++ with suitable program.

(b) Explain about the manipulators in C++. [8+8]

4. (a) Write a method called removeRange(fromIndex, toIndex) that removes

all elements in the specified index range from a list/ chain. What is the

complexity of this method?

(b) Write a method called lastIndexOf(theElement) that returns the index ofthe rightmost occurrence of theElement. If theElement is not present

then it returns -1. [16]

5. (a) What is skip list representation of dictionary? Write the structure to represent node in a skip list. What are the data members to be included in the class

skipList.

(b) Write a method in C++ to search a skip list and save the last node encountered

at each level. [8+8]

6. Define a class called binarySearchTree to represent a Binary search tree. Extendthis class by adding a public method outputInRange (Low,High) that outputs,

in ascending order of key, all elements in a binary search tree whose key lies between

Low and High. Use recursion and avoid entering sub trees that cannot possiblycontain any elements with keys in desired range. [16]

7. (a) What is Splay tree? Explain the operations of Splay tree with an example.

(b) Give the properties of red black tree. [10+6]

8. (a) Explain the construction of the kmp ow chart with an example.

(b) Explain the search engines. [10+6]

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1. (a) Explain about parameter passing mechanism in C++?

(b) Explain about the various storage classes in C++? [8+8]

2. What do you mean by run time polymorphism and how to implement run timepolymorphism using virtual functions in C++? [16]

3. (a) Why should we use iostream instead of the traditional cstdio?

(b) Why does a program go into an infinite loop when someone enters an invalid

input character?

(c) How can we get std::cin to skip invalid input characters? [5+6+5]

4. (a) Write a method to return the Indexth element in a list/chain. What is its

time complexity?

(b) Write a method to Erase the Indexth element in a list/chain. What is its

time complexity? [8+8]

5. (a) What is the structure to represent node in a skip list. Write the constructorfor skipList.

(b) Write a method in C++ to find a pair with key theKey in a dictionary usingskip list representation? What is its complexity? [8+8]

6. Define a Binary Search Tree? Write the procedures to perform insertion, deletion

and searching in a binary search tree? [16]

7. (a) Prove that net T be a B-tree of order m and height h. Let d = [m/2] and let n be the number of elements in T.

i. 2d - 1 = n = m - 1h-1 n

ii. log (n + 1) = h = log + 1n+1m d 2

(b) Explain the advantages of splay tree in representation of dictionaries. [10+6]

8. (a) Describe about search engine and inverted files.

(b) Explain the main features of Boyer-Moore algorithm. [10+6]

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SET - 1 Code No: W0801

II B.Tech I Semester (R05) Supplementary Examinations, May- 2011

FLUID MECHANICS FOR CHEMICAL ENGINEERS

(Chemical Engineering)



1. What are the different types of nanometers? ex plain with neat figure and give their

applications also. (16M)

2. a) A pipeline tapers from 8 cm diameter to 4 cm diameter. If the discharge through the pipe is

100 lit/sec, find the average v elocities at the two sections. (8M)

b) Define “stream line “, stream tube” and kinetic viscosity (8M)

2 3. Oil of viscosity 0.01kgf sec/m and specific gravity of 0.9 flows through a horizontal pipe of22.5cm diameter. If the pressures drop p er meter length of the pipe is 0.12 k gf/cm . Determine

i) the rate of flow ii) N (16M)R e

4. Define friction factor? Derive the equation for friction loss from sudden contraction of cross

section. (16M)

5. What is isentropic flow? Describe the flow through variable area conduits and derive the

relevant equ ations. (16M)

6. a) What is fluidization? Derive the equation for minimum fluidization velocity.

b) Describe about different types of fluidization (8M+8M)

7. a)describe about differen t types of valves and give their applications

b) What is NPSH? Derive its equation (10M+6M)

8. A pitot static tube having a coefficient of 0.98 is p laced at the centre of pipeline in which

benzene is flowing. A nanometer attached to the p itot tube contains mercury and benzene and

shows a reading of 10cm. calculate the velocity at the centre line of the pipe. Specific gravity

of benzene is 0.88. (16M)

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1. A simple U- tube manometer is installed across an orifice meter. The mano meter is filled with

mercur y (sp. gravity=13.6), and the liquid above the mercury is CCl (sp.gravity=1.6). The42manometer r eads 200mm. what is the pressure difference over the manometer in N/m?

(16M)

2. What is Bernoulli’s equation? Derive it and explain all the notations used. (16M)

3. Oil of specific gravity 0.82 is pumped through a horizontal pipe line of 15 cm diameter, 3 km

long at the rate of 900 lit/min. The pump has an efficiency of 60% and requires10 HP to pump

the oil. Determine the dynamic viscosity of the oil and verif y whether the flow is laminar orturbulent. (16M)

4. Define (8×2=16M)

i) mach number v) Acoustical velocity

ii) Sub sonic flow vi) Asterisk conditioniii) Sonic flow vii) Stagnation temperature

iv) Supersonic flow viii) Friction factor

5. Describe about different process of compressible f low (16M)

6. a) Differentiate between free settling and hindered settling

b) particles of sphalerite (sp. gravity=4) are settling under the force of of gravity in CCl of at4020 C (sp.gravity =1.594). The diameter o f the particles is 0.1mm, the volume fraction of

sphalerite in CCl is 0.2 ,what is the settling velocity of sphalerite?40Data: the viscosity of CCl at 20 C =10.3cp (16M) 4

7. Describe th e construction details of a centrifugal pump with a neat diagram. (16M)

8. An orifice meter consisting of 10 cm diameter orifice in a 25 cm diameter pipe has coefficient

of 0.65. The pipe delivers oil of 0.8 specific gravity. The p ressure differen ce on the two sides

of the orifice plate is measured by a mercury oil differ ential manometer. If the differential

gauge reads 80 cm of mercury, calculate the rate of flow in lit/sec. (16M)

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01. The temper ature of the earth’s atmosphere drops about 5C for every1000m of elevation

0above the earth’s surface. If the air temp erature at ground level is 15C and the pressure 760

mmHg, at what elevation is the pressure 380 mmHg ? Assume that air behaves as an ideal

gas. (16M)

2. a)explain about Newtonian & non-Newtonian fluids using shear stress Vs velocity gradient

diagram (8M)

b) Define boundar y layer ? Explain about laminar and turbulent flow in bou ndary layers

(8M)

3. A Newtonian fluid is in laminar flow in a circular channel, derive the relationship between

average velocity and maximum velocity and prov e that V/u max =0.5 (16M)

4. What is friction factor? Derive the equation for friction loss from sudden ex pression of cross

section. (16M)

5. What is choking? Derive the equations for adiabatic frictional flow. (16M)

6. Derive the equations for one- dimensional motion of a particle throu gh a fluid by writing the

force balance on the particle (16M)

7. Discuss the classification of pumps and describe the characteristic curves of a centrifugal

pump. (16M)

8. How do you measur e the flow of fluids in industry? Describe about venturi meter with a neatsketch? (16M)

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1. Describe about continuous gravity d ecanter with neat figure and derive the equations (16M)

2. a)defin e transition length and give the equation to calculate it (6M+10M)

b) Estimate the transition length at the entrance to a15mm tube through which 100% glycerol0 3at 60 C fallowing at a velocity of 0.3m/s. the density of glycerol is 1240kg /m

3. a)Define ‘f riction factor’ and derive the relation between skin friction and wall shear

b) Derive Hagen - poiseuille equation (10M+6M)

4. a) find the loss of head due to friction in pipe of 1m diameter and 15 km long. The velocity of

water in the pipe is 1m/sec. Take f=0.005 (10M+6M)

b) Differentiate between incompressible and compressible fluids with examples

5. What is isothermal frictional flow? Derive the equations for isothermal frictional flow

(16M)

6. a) What is drag? Explain different types of drag

b) Derive Ergun equation (6M+10M)

7. a) Discuss about differ ent types of v alves? (8M+8M)

b) Differentiate between positive displacement pumps and centrifugal pumps

8. Describe about orifice meter with a neat figure, compare it with venturi meter. (16M)

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ADVANCED DATA STRUCTURES AND ALGORITHMS

( Common to Information Technology and Computer Science & Systems

Engineering)Time: 3 hours Max Marks: 80



1. (a) What is a class? How do you define class in C++?

(b) Explain about the data members and member functions of a class?

(c) Explain about access control mechanism in C++? [5+5+6]

2. (a) Write a program to illustrate the concept of method overriding with suitable

example.

(b) Explain about the abstract class with an example. [8+8]

3. (a) Write a program to count the no of blank spaces, characters, words in a giventext file.

(b) write a program to copy the contents of one file to other. [8+8]

4. (a) What is a heap ? Di erentiate between heap and binary search tree.

(b) Show that log n is O(n ).3 1/3

(c) Brie y explain about Hashing. [5+5+6]





6. (a) Prove that the insertion of a new node in a red-black tree with n nodes in

(logn) time in the worst case.

(b) Derive the amortized complexity of a find, insert or delete operation performedon a splay tree with n elements. [8+8]

7. (a) Write and explain the Breadth first generation of a solution AND/OR tree.

(b) Explain when quick sort is preferred to merge sort and vice-versa. [10+6]

8. (a) Write a control abstraction algorithm of Greedy method.

(b) Solve the following 0/1 knapsack problem using dynamic programmingn=3, (W ,W , W ) = (2, 3, 3) (P , P , P ) =(1,2,4) and m=6. [8+8]

1 2 3 1 2 3

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1. (a) What is the default data hiding type for a class? Why are data members

hidden? How would you access them?

(b) In a printf statement, what are the codes for integer? oat? string? How can

you choose how many numbers occur before and after the decimal point for

a oat? How can you pad zeroes to the beginning of an integer to make it aspecific length? [8+8]

2. (a) Write a program to illustrate the concept of method overriding with suitable

example.

(b) Explain about the abstract class with an example. [8+8]

3. (a) How does that funky while (std :: cin >> foo) syntax work?

(b) Why does input seem to process past the end of file?

(c) Should we end output lines with std::endl or ‘\n ? [5+5+6]

4. (a) What is meat by Profiling ? Explain it with an example.

(b) Trace the heap sort algorithm to sort the following list of numbers

8, 20, 9, 4, 15, 10, 7, 22, 3, 12. [8+8]





6. (a) What is a B- tree? How do we define the height of it?

(b) Write the procedure to search for an element of a B- Tree? What is its time

complexity? [8+8]

7. Write and explain the divide and conquer Merge sort algorithm? Compute its time

Complexity. [16]

8. (a) Show how Prim’s algorithm can be implemented using heap. What would be

the time complexity of the algorithm.

(b) What is the time complexity of traveling sales person problem using dynamicprogramming. [10+6]

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1. (a) What is an object? How do you create in C++?

(b) How do you create array of objects ? Explain with suitable program? [8+8]

2. What is operator overloading? Explain how to overload the operators in C++ by

taking any five operators. [16]

3. (a) Explain about ios ags in C++ with suitable program.

(b) Explain about the manipulators in C++. [8+8]

4. (a) What is heap? Write an algorithm for implementing priority Queue usingheap.

(b) If f(n) + a n +............a n + a and a > 0 then prove that f(n) = (n ). mm1 0 mm

[8+8]

5. (a) Explain the linear probing method in Hashing? Explain its performance anal-

ysis?

(b) What is hashing with Chains? Explain? Compare this with Linear Probing?[8+8]

6. What is a B- tree? Explain how the insertion, deletion can be performed in a

B-Tree with appropriate example? [16]

7. Write and explain a non recursive algorithm for post order traversal of a Binary

tree with an example. [16]

8. (a) What is Spanning tree? Explain the Prim’s algorithm with an example.

(b) Find the shortest path between all pairs of nodes as shown in the figure.8bby

using TSP. [8+8]

Figure 8b

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1. (a) Each class has some special member-functions, which calls can be inserted

by the compiler into a code without explicit instruction of the programmer.

Enumerate such functions, members and cases, when implicit calls can arise.

(b) If when creating a variable the programmer explicitly did not initialize it, in

some cases, the compiler itself would give it a certain, predefined initial value,

and in some cases the initial value would be unpredictable. What does itdepend on? [8+8]

2. Define Inheritance? How many types of inheritances are there? Explain each with

suitable examples. [16]

3. (a) Why should we use iostream instead of the traditional cstdio?

(b) Why does a program go into an infinite loop when someone enters an invalid

input character?

(c) How can we get std::cin to skip invalid input characters? [5+6+5]

4. Write and explain UNION and find algorithms with weighting and collapsing rule.[16]

5. Develop a class for hash table using linear probing and neverUsed concept to handlean erase operation. Write complete C++ code for all the methods. Include a

method to reorganize the table when (say) 60% of the empty buckets have never

used equal to false. The reorganization should move pairs around as necessary andleave a properly configured hash table in which neverUsed is true for every empty

bucket. [16]

6. (a) Write an algorithm of Red-Black tree insertion.

(b) Explain the operation of splay trees with an example. [8+8]

7. (a) Show that the inorder and post order sequences of a binary tree uniquely

define the binary tree.

(b) Explain the AND/OR graph with an example. [8+8]

8. (a) What is dynamic programming technique? How does it di er from divide and

conquer technique.

(b) Solve the Greedy Knapsack problem where

m=25, n=3, P = (25,24,17) and W = (16,14,9). [8+8]

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MECHANICS OF FLUIDS(Aeronautical Engineering)



1. (a) Calculate the specific weight, specific mass, specific volume and specific gravityof a liquid having a volume of 6 m and weight of 44 kN.3

(b) Distinguish between simple manometer and a di erential manometer. [8+8]

2. (a) In a three dimensional incompressible ow, the velocity components in y and

z-direction are v = ax - by +cz ; w = bx -cy +az x. Determine the missing3 2 2 3 2 2

component of velocity distribution such that continuity equation is satisfied.

(b) How is the continuity equation based on the principle of conservation of massstated? And explain how the control volume approach will help indevicing

continuity equation. [8+8]

3. An open circuit wind tunnel draws air from the atmosphere through a well con-toured nozzle. In the test section, where the ow is straight and nearly uniform,

a static pressure tap is drilled into the tunnel wall. A manometer connected to

the tap shows that the wall pressure within the tunnel is 45 mm of water be-

low atmospheric. Assume that air is incompressible and at 25 C, pressure is 1000

Kpa(absolute). Calculate the velocity in the wind tunnel section. Density of wateris 999kg/m and characteristic gas constant for air is 287 J/Kg K. [16] 3

4. (a) Explain the di erent types of hydraulic similarities that must exist between a

prototype and its model.

(b) Water ows in a 200mm diameter pipe. Two pitot tubes are installed in thepipe , one on the Centerline and the other 50mm from the centerline. If

the velocities at the two point are 4m/s and 3m/s respectively, calculate the

reading on the di erential mercury manometer connected to the two tubes.[7+9]

5. (a) Explain with a neat sketch the boundary layer characteristics when a uid is

owing over a at plate.

(b) A thin at plate 0.3 m wide and 0.6 m long is suspended and exposed parallel

to air owing with a velocity of 3 m/sec. Calculate drag force on both sidesof the plate when the 0.3 m edge is oriented parallel to free stream. Consider

ow to be laminar and assume for air kinematic viscosity is 0.18 stokes anddensity is 1.2 kg/m . [10+6] 3

6. A pipeline ABC 180 m long is laid on an upward slope of 1 in 60. The length of

portion AB is 90 m and its diameter is 0.15 m. At B the pipe section suddenlyenlarges to 0.30 m diameter and remains so for the remainder of its length BC, 90

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m. A ow of 50 litres per second is pumped into the pipe at its lower end A and is

discharged at the upper end C into a closed tank. The pressure at the supply endA is 137.34 kN/m . Sketch [16]2

(a) the total energy line

(b) the hydraulic gradient line and also find the pressure at discharge end C. Take

f = 0.02 in h = flV 2 f 2gD

7. (a) Define the terms Kinetic energy correction factor and momentum correction

factor.

(b) The Radial clearance between a hydraulic plunger and the cylinder wall is 0.1

mm, the length of the plunger is 300 mm and diameter 100 mm. Find the

velocity of leakage and rate of leakage past the plunger at an instant when thedi erence of the pressure between the two ends of the plunger is 9m of water.

Take mu = 0.0127 Poise. [6+10]

8. (a) Derive an expression for velocity of sound. How is it governed by the coe cientof compressibility and molecular weight of gas.

(b) Calculate the velocity of sound [8+8]

i. in air 100 C0

ii. in CO at 70 C0 2

iii. in water.

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1. (a) A lubricating oil of viscosity µ undergoes steady shear between a fixed lower

plate and an upper plate moving at speed V. The clearance between the plates

is t. Show that a linear velocity profile results if the uid does not slip at either

plate.

(b) Describe with a neat sketch a micro-manometer used for very precise mea-surement of small pressure di erence between two points. [8+8]

2. (a) When 2500 litres of water ows per minute through a 0.3m diameter pipe

which later reduces to a 0.15 diameter pipe, calculate the velocities of ow in

the two pipes.

(b) How are uid ows classified?

(c) What are the properties of a ‘stream tube’. [6+6+4]

3. 250 Lit /s of water is owing in a pipe having a diameter of 300mm. If the pipe

is bend by 135 (that is change from initial to final direction is 135 ), Find the0 0

magnitude and direction of the resultant force on the bend. The pressure of under

owing is 39.24 N/cm . [16]2

4. (a) Explain and di erentiate between Pitot tube and Pitot Static Tube.

(b) Water ows through a rectangular channel 1m wide and 0.5m deep and then

over a sharp crested cipolletti weir of crust length 0.6m. If the water level inthe channel is 0.225m above the weir crest. Calculate the discharge over the

weir. Take Cd = 0.6 and make correction for the velocity of approach. [7+9]

5. Water of kinematic viscosity 1.02 ×10 m /sec is steadily owing over a smooth-6 2

at plate at zero angle of attack with a velocity 1.6 m/sec. The length of the plate

is 0.3m. Calculate

(a) The thickness of boundary layer at 15 cm from the leading edge and

(b) Shear stress at trailing edge of the plate.

Assume a parabolic profile. Take density = 1000 kg/m [16]3

6. (a) How the loss of energy at the entrance to the pipe and exit from the pipe isto be determined?

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

discharges freely into the atmosphere at the other end. For the first 30 m of its

length from the tank, the pipe is 100 mm diameter and its diameter suddenly

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enlarged to 200 mm. The height of the water level in the tank is 10 m above

the centre of the pipe. Determine the rate of ow. Take 4f = 0.04 for bothsections of the pipe and consider minor losses. [6+10]

7. (a) Sketch the Reynolds apparatus and explain how the laminar ow can be

demonstrated with the help of this apparatus?

(b) Oil of absolute viscosity 1.5 poise and relative density 0.85 ows through

a 30cm diameter pipe .If the head losses in a 3000M length of a pipe is

20M.estimate the friction factor by assuming the ow to be laminar. [8+8]

8. (a) what is the relation between pressure and density of a compressible uid for?

i. Isothermal process

ii. Adiabatic process.

(b) A gas is owing through a horizontal pipe at a temperature of 4 C. The0

diameter of the pipe is 8cm and at a section I in the pipe, the pressure is

30.3N/cm (gauge). The diameter of the pipe changes from 8cm to 4cm at the2

section II, where pressure is 20.3N/cm (gauge). Find the velocities of the gas 2

at these sections assuming an isothermal process. Take R=287.14Nm/Kg.K

and atmosphere pressure=10N/ cm . [6+10] 2

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1. (a) A lubricating oil of viscosity µ undergoes steady shear between a fixed lower

plate and an upper plate moving at speed V. The clearance between the platesis t. Show that a linear velocity profile results if the uid does not slip at either

plate.

(b) Describe with a neat sketch a micro-manometer used for very precise mea-surement of small pressure di erence between two points. [8+8]

2. (a) The velocity potential function for a two-dimensional ow is

f = x (2y - 1) At a point P(4,5) determine:

i. The velocity and

ii. The value of stream function.

(b) Di erentiate between the rotational and irrotational ows. [10+6]

3. A 60 reducing bend is connected in a pipeline, the diameters at the inlet and 0

outlet of the bend being 500mm and 250mm respectively. Find the force extendedby water on the bend if the intensity of pressure at inlet to bend is 9N/cm and 2

rate of ow of water is 500lit/sec. [16]

4. (a) What is the significance of the following non dimensional numbers in the

theory of Similarity?

i. Reynolds number

ii. Froude number and

iii. Mach Number.

(b) A venturimeter its axis vertical, the inlet and throat diameters being 90 mmand 45 mm respectively. The throat is 150 mm above inlet and Cd =0.96, oil

of specific gravity 0.8 ows up through the meter at a rate of 0.01 m /s. Find3

the pressure di erence between inlet and throat. [6+10]




to air owing with a velocity of 3 m/sec. Calculate drag force on both sides

of the plate when the 0.3 m edge is oriented parallel to free stream. Considerow to be laminar and assume for air kinematic viscosity is 0.18 stokes and

density is 1.2 kg/m . [10+6] 3

6. (a) Derive Darcy-Weisbach equation for loss of head in a pipe.

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(b) Two tanks are connected by a 300 mm diameter 1000 m long pipe. Find the

rate of ow if the di erence of water level in the tank is 10 m. Take 4f = 0.04

and ignore minor losses. [10+6]

7. (a) Define the terms Kinetic energy correction factor and momentum correction

factor.

(b) The Radial clearance between a hydraulic plunger and the cylinder wall is 0.1

mm, the length of the plunger is 300 mm and diameter 100 mm. Find thevelocity of leakage and rate of leakage past the plunger at an instant when the

di erence of the pressure between the two ends of the plunger is 9m of water.Take mu = 0.0127 Poise. [6+10]

8. (a) What is meant by co-e cient of compressibility ?

(b) A di user of area 2:1 operates at the inlet conditions P =500KN/m , T21 1

=500K, Mach number M =0.6, K=1.4. Estimate the following at the exit1

[8+8]

i. Velocity

ii. pressure

iii. Temperature

iv. Mach number.

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1. (a) A lubricating oil of viscosity µ undergoes steady shear between a fixed lower plate and an upper plate moving at speed V. The clearance between the plates

is t. Show that a linear velocity profile results if the uid does not slip at either plate.

(b) Describe with a neat sketch a micro-manometer used for very precise mea-

surement of small pressure di erence between two points. [8+8]

2. (a) What is the irrotational velocity field associated with the potential f = 3x - 2

3x +3y +16t + 12zt. Does the ow field satisfy the incompressible continuity 2 2

equation?

(b) Show that the streamlines and equipotential lines formla net of mutually per- pendicular lines. [8+8]

3. (a) What is Euler’s equation of motion? How will you obtain Bernoulli s equation

from it?

(b) The water is owing through a pipe having diameters 20 cm and 10 cm at

section I and II respectively. The rate of ow through pipe is 35 Lit/Sec.

The section 1 is 6 m above datum and section I I is 4 m above datum. If the

pressure at section I is 39.24 N / c m , find the intensity of pressure at section 2

I I. [6+10]

4. (a) What is the significance of the following non dimensional numbers in the

theory of Similarity?

i. Reynolds number

ii. Froude number and

iii. Mach Number.

(b) A venturimeter its axis vertical, the inlet and throat diameters being 90 mm

and 45 mm respectively. The throat is 150 mm above inlet and Cd =0.96, oil of specific gravity 0.8 ows up through the meter at a rate of 0.01 m /s. Find3

the pressure di erence between inlet and throat. [6+10]




to air owing with a velocity of 3 m/sec. Calculate drag force on both sidesof the plate when the 0.3 m edge is oriented parallel to free stream. Consider

ow to be laminar and assume for air kinematic viscosity is 0.18 stokes anddensity is 1.2 kg/m . [10+6] 3

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6. (a) Derive Darcy-Weisbach equation for loss of head in a pipe.

(b) Two tanks are connected by a 300 mm diameter 1000 m long pipe. Find the

rate of ow if the di erence of water level in the tank is 10 m. Take 4f = 0.04

and ignore minor losses. [10+6]

7. (a) Derive an expression for the velocity distribution for viscous ow through a

circular pipe.

(b) An Oil of viscosity 0.1 Pascal - sec and specific gravity 0.9 is owing through

a circular pipe of diameter 50 mm and of length 300 m. The rate of ow of

uid through the pipe is 3.5 lit / sec. Find the pressure drop in a length of300 m and also the shear stress at the pipe wall. [8+8]

8. (a) Derive Bernoulli’s equation for compressible ow undergoing adiabatic pro-

cess?

(b) Find the Mach number when an aero plane is ying at 1100Km/hr through

still air having a pressure of 7 N/ cm and temperature -5 C. Wind velocity2 0

may be taken as zero. Take R=287.14J/KgK. Calculate the pressure, temp

and density of air at stagnation point on the nose of the plane. Take K=1.4.[8+8]

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STRENGTH OF MATERIALS -I Civil Engineering

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