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Desklib is an online library for study material with solved assignments, essays, dissertations, and more. This case study analysis covers the fundamentals of mechanics, truss overview, stress-strain graph, fluid pressure measuring equipment, and fluid basics. The content includes subject B.Sc Combined Engineering, Mechanical Engineering Science, course code 107EN, and college/university Coventry University Group.

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COVENTRY UNIVERSITY GROUP

CASE STUDY ANALYSIS

B.Sc Combined Engineering

Mechanical Engineering Science

107EN – Full Time Assignment

Student Name:

Student ID:

CASE STUDY ANALYSIS

B.Sc Combined Engineering

Mechanical Engineering Science

107EN – Full Time Assignment

Student Name:

Student ID:

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Contents

CASE STUDY A........................................................................................................

1. Case Study Fundamentals............................................................................

2. Exercise........................................................................................................

CASE STUDY B........................................................................................................

3. Truss Overview.............................................................................................

4. Stress-Strain Graph......................................................................................

CASE STUDY C........................................................................................................

5. Fluid Pressure Measuring equipment.........................................................

6. Fluid Basics..................................................................................................

CASE STUDY A........................................................................................................

1. Case Study Fundamentals............................................................................

2. Exercise........................................................................................................

CASE STUDY B........................................................................................................

3. Truss Overview.............................................................................................

4. Stress-Strain Graph......................................................................................

CASE STUDY C........................................................................................................

5. Fluid Pressure Measuring equipment.........................................................

6. Fluid Basics..................................................................................................

CASE STUDY A

1. Case Study Fundamentals

(a) The fundamental of mechanics

The concept of mechanics is based on these three

fundamental quantities: mass, force and time along with

the three Newton’s law of motion. The latter is normally

the independent variable such that interaction of the

other two occurs within a predefined boundary designated

as space. For the purpose of simple analysis, particles and

objects are normally assumed to be moving on a rigid

plane hence two dimensional analyses is pursued.

Otherwise, in complex analysis, the three dimensional

analysis considers the motion of the object in all the three

basic directions. Mathematically, the directions are x, y

and z. Besides, the system of force equilibrium is often

considered and this is encapsulated by the three

fundamental laws of motion.

(b) Branches of mechanics

The major branches of mechanics are dynamics and

statics. The former mainly deals with motion of objects

and particles at rest or those moving with uniform velocity

throughout while the latter deals with motion of objects

that move with changing velocity over a given period.

1. Case Study Fundamentals

(a) The fundamental of mechanics

The concept of mechanics is based on these three

fundamental quantities: mass, force and time along with

the three Newton’s law of motion. The latter is normally

the independent variable such that interaction of the

other two occurs within a predefined boundary designated

as space. For the purpose of simple analysis, particles and

objects are normally assumed to be moving on a rigid

plane hence two dimensional analyses is pursued.

Otherwise, in complex analysis, the three dimensional

analysis considers the motion of the object in all the three

basic directions. Mathematically, the directions are x, y

and z. Besides, the system of force equilibrium is often

considered and this is encapsulated by the three

fundamental laws of motion.

(b) Branches of mechanics

The major branches of mechanics are dynamics and

statics. The former mainly deals with motion of objects

and particles at rest or those moving with uniform velocity

throughout while the latter deals with motion of objects

that move with changing velocity over a given period.

Furthermore, in dynamics, there are two main sub

branches: kinetics and kinematics.

(c) Types of motions in mechanics

The basic types of motions include: Linear and non-linear

where the former deals with motion in a straight fashion

from point 1 to point 2 while the latter deals with motion

in a curvilinear manner such that the particle traces a

curved path on a plane or space

(d) The five SUVAT equations

S= Ut +1/2at2 .............(1)

V2= U2+2as.................(2)

V=U+ at......................(3)

S= Ut-1/2at2................(4)

S= t(u+v)/2 ................(5)

(e) Meaning of SUVAT

These are equations of linear motion in which acceleration

is assumed constant all over and in free fall case, often

acceleration value is same as value of gravity (9.81m/s2).

They often involve displacement S, velocity (both final V

and initial U), acceleration A and time t hence the

acronym SUVAT

(f) Components of a curvilinear motion

There are two components: tangential and normal

components. The former describes motion of particle such

branches: kinetics and kinematics.

(c) Types of motions in mechanics

The basic types of motions include: Linear and non-linear

where the former deals with motion in a straight fashion

from point 1 to point 2 while the latter deals with motion

in a curvilinear manner such that the particle traces a

curved path on a plane or space

(d) The five SUVAT equations

S= Ut +1/2at2 .............(1)

V2= U2+2as.................(2)

V=U+ at......................(3)

S= Ut-1/2at2................(4)

S= t(u+v)/2 ................(5)

(e) Meaning of SUVAT

These are equations of linear motion in which acceleration

is assumed constant all over and in free fall case, often

acceleration value is same as value of gravity (9.81m/s2).

They often involve displacement S, velocity (both final V

and initial U), acceleration A and time t hence the

acronym SUVAT

(f) Components of a curvilinear motion

There are two components: tangential and normal

components. The former describes motion of particle such

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that it is always orthogonal to the movement of particle.

The tangential component is parallel to the direction of

particle such that should it come off the curve, the particle

will trace this direction.

2. Exercise

Given:

The train engine at point E has a velocity of 20 m/s and an

acceleration of 14 m/s2 acting in the direction as shown in

figure 1

(i) The acceleration vector equation

This is given by: a= atut+ anun

(ii) The values of the tangential and normal components of

the acceleration

at=v’ut= 0.27601u2t2

an=(v2/ρ)un= 142/29.58= 6.626Un m/s

(iii) The value of ˙v from the tangential component of the

acceleration

v’=ut/at= 1/3.623 ut= 0.27601ut m/s2

(iv) The value of radius of curvature ρ (r) from the normal

component of the acceleration

ρ=[1+(dy/dx)2]1.5/ /d2y/dx2/ or we can use:

ρ=v2/an = 202/14sin75= 29.58 m

(v) The magnitude of the acceleration vector

The tangential component is parallel to the direction of

particle such that should it come off the curve, the particle

will trace this direction.

2. Exercise

Given:

The train engine at point E has a velocity of 20 m/s and an

acceleration of 14 m/s2 acting in the direction as shown in

figure 1

(i) The acceleration vector equation

This is given by: a= atut+ anun

(ii) The values of the tangential and normal components of

the acceleration

at=v’ut= 0.27601u2t2

an=(v2/ρ)un= 142/29.58= 6.626Un m/s

(iii) The value of ˙v from the tangential component of the

acceleration

v’=ut/at= 1/3.623 ut= 0.27601ut m/s2

(iv) The value of radius of curvature ρ (r) from the normal

component of the acceleration

ρ=[1+(dy/dx)2]1.5/ /d2y/dx2/ or we can use:

ρ=v2/an = 202/14sin75= 29.58 m

(v) The magnitude of the acceleration vector

The magnitude of acceleration vector is given by:

a= (at2+ an2)0.5

Now an= a sin 75= 14sin75= 13.522

And at= acos75= 14cos75= 3.623

Hence a= /13.5222+3.6232/0.5 = (13.1404+182.844)0.5 =195.980.5 = 13.99m/s2

CASE STUDY B

3. Overview of Trusses

(a) Description of truss

Truss is a rigid framework composed of rigid members

that are either in tension or compression and unitarily

supports structures such as roofing in buildings (Scribd, 2018).

(b) Truss Configuration

a= (at2+ an2)0.5

Now an= a sin 75= 14sin75= 13.522

And at= acos75= 14cos75= 3.623

Hence a= /13.5222+3.6232/0.5 = (13.1404+182.844)0.5 =195.980.5 = 13.99m/s2

CASE STUDY B

3. Overview of Trusses

(a) Description of truss

Truss is a rigid framework composed of rigid members

that are either in tension or compression and unitarily

supports structures such as roofing in buildings (Scribd, 2018).

(b) Truss Configuration

The two common configuration include: the pitched truss

which is triangular in basic shape while flat truss is

composed of parallel members as shown in figures 2(a)

and 2(b) below;

Figure 2(a): Pitched truss

Figure 2(b): Flat truss

(c) Condition for equilibrium

The basic criteria for static equilibrium in truss are:

(i) Sum of all forces in the x-direction must be zero;

similarly, sum of forces in the other two directions,

that is, y and z, must also be zero

which is triangular in basic shape while flat truss is

composed of parallel members as shown in figures 2(a)

and 2(b) below;

Figure 2(a): Pitched truss

Figure 2(b): Flat truss

(c) Condition for equilibrium

The basic criteria for static equilibrium in truss are:

(i) Sum of all forces in the x-direction must be zero;

similarly, sum of forces in the other two directions,

that is, y and z, must also be zero

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(ii) Sum of moments in all directions must be zero, that

is, Sum of Mx=0, My=0 and Mz= 0

(d) Assumptions in truss analysis

It is assumed that the members are fixed to each other

and that there is buckling in members under stress, in

other words, they are rigid.

(e) Ways to determine if a truss is theoretical determinant

or in-determinant

In determinant case, the equations of statics are just

sufficient to determine the required parameters while in

in-determinant, there are extra theorems that must be

used to adequately define the system. For instance,

Castiglione’s theorem often comes in handy.

4. Stress-Strain Graph

Each test sample is 10 mm in diameter with a gage length of

50mm.

is, Sum of Mx=0, My=0 and Mz= 0

(d) Assumptions in truss analysis

It is assumed that the members are fixed to each other

and that there is buckling in members under stress, in

other words, they are rigid.

(e) Ways to determine if a truss is theoretical determinant

or in-determinant

In determinant case, the equations of statics are just

sufficient to determine the required parameters while in

in-determinant, there are extra theorems that must be

used to adequately define the system. For instance,

Castiglione’s theorem often comes in handy.

4. Stress-Strain Graph

Each test sample is 10 mm in diameter with a gage length of

50mm.

Figure 2: Engineering stress - strain graph

(a) Types of mechanical forces that can act on a body

(b) Definition of :

(i) Stress can be defined as the force acting per unit

surface area in an engineering material that

causes deformation or fracture. That is stress=

Force/Area (Engineeringtoolbox.com, 2018)

(ii) strain and the mathematical relationship between

them

Strain is the result of stress in materials such that

it designates the ratio of change in length to the

original length of material (Scribd, 2018).

(a) Types of mechanical forces that can act on a body

(b) Definition of :

(i) Stress can be defined as the force acting per unit

surface area in an engineering material that

causes deformation or fracture. That is stress=

Force/Area (Engineeringtoolbox.com, 2018)

(ii) strain and the mathematical relationship between

them

Strain is the result of stress in materials such that

it designates the ratio of change in length to the

original length of material (Scribd, 2018).

The two are related as: Strain = Stress/Young’s

modulus that is έ = ϭ/E

(c) Material with the lowest yield stress is A. Its value is

320MPa

(d) Material with the lowest ultimate tensile strength is B.

Its value is 500MPa

(e) Material with a larger modulus of elasticity is B. Its

value= gradient (in the elastic region)=

(400-200)/(0.00025-0.0001)= 200/0.00015= 133.33GPa

CASE STUDY C

5. Fluid Pressure Measuring equipment

Critical analysis:

(a) The type of equipment to use in measuring the

pressure

A pressure transducer (capacitive) can be used to

measure the pressure as it easily integrates well

with the system that requires complex sensing to

optimize the flow process (Brighthub Engineering, 2018).

(b) Flow rate of the fluid (beer) during transportation

of the fluid (beer) from the production unit through

the pipe to the filler and coupling machine

Liquid flow meter can be used, it measures flow

rates in real-time and has a digital readout unlike

the conventional analogue types.

modulus that is έ = ϭ/E

(c) Material with the lowest yield stress is A. Its value is

320MPa

(d) Material with the lowest ultimate tensile strength is B.

Its value is 500MPa

(e) Material with a larger modulus of elasticity is B. Its

value= gradient (in the elastic region)=

(400-200)/(0.00025-0.0001)= 200/0.00015= 133.33GPa

CASE STUDY C

5. Fluid Pressure Measuring equipment

Critical analysis:

(a) The type of equipment to use in measuring the

pressure

A pressure transducer (capacitive) can be used to

measure the pressure as it easily integrates well

with the system that requires complex sensing to

optimize the flow process (Brighthub Engineering, 2018).

(b) Flow rate of the fluid (beer) during transportation

of the fluid (beer) from the production unit through

the pipe to the filler and coupling machine

Liquid flow meter can be used, it measures flow

rates in real-time and has a digital readout unlike

the conventional analogue types.

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6. Fluid Basics

(a) Definition of Fluid

A fluid mainly designates liquid and gas states

such that they easily yield to pressure and move

freely without separation of mass of particles.

(b) Properties of Fluid

-Can easily flow under slight pressure changes

-In Newtonian Fluid, the pressure changes are

often assumed uniform

-Can easily be compressed

-Easily occupies the available space evenly

through flow (in liquid) and diffusion (gas)

-Fluid kinetic energy varies linearly as

temperature

(c) Real life application of some of these properties

-The car braking system is actuated via fluid

pressure transmission

-Compressed air is normally used to drive

systems in aircraft

-The hydraulic jack is used to lift heavy object

such as vehicles via fluid pressure mechanism.

(a) Definition of Fluid

A fluid mainly designates liquid and gas states

such that they easily yield to pressure and move

freely without separation of mass of particles.

(b) Properties of Fluid

-Can easily flow under slight pressure changes

-In Newtonian Fluid, the pressure changes are

often assumed uniform

-Can easily be compressed

-Easily occupies the available space evenly

through flow (in liquid) and diffusion (gas)

-Fluid kinetic energy varies linearly as

temperature

(c) Real life application of some of these properties

-The car braking system is actuated via fluid

pressure transmission

-Compressed air is normally used to drive

systems in aircraft

-The hydraulic jack is used to lift heavy object

such as vehicles via fluid pressure mechanism.

(d) The equation of state as applies to fluid.

Thi is given by PV= mRT (in gaseous state).

References

Brighthub Engineering. (2018). Pressure Measurement Devices - Inclined Manometer, Bourdon

Gauge, Diaphragm Gauge, Bellows, Pressure Transducers, Electronic Pressure Sensors.

[online] Available at: https://www.brighthubengineering.com/hydraulics-civil-engineering/

43777-pressure-measurement-pressure-measurement-devices/ [Accessed 4 Apr. 2018].

Engineeringtoolbox.com. (2018). Stress, Strain and Young's Modulus. [online] Available at:

https://www.engineeringtoolbox.com/stress-strain-d_950.html [Accessed 4 Apr. 2018].

Scribd. (2018). Fundamentals of Engineering Mechanics | Force | Euclidean Vector. [online]

Available at: https://www.scribd.com/document/241787088/Fundamentals-of-Engineering-

Mechanics [Accessed 4 Apr. 2018].

Scribd. (2018). Trusses, Types, Configuration andConnections | Truss | Civil Engineering.

[online] Available at: https://www.scribd.com/document/115008353/Trusses-Types-

Configuration-and-Connections [Accessed 4 Apr. 2018].

Thi is given by PV= mRT (in gaseous state).

References

Brighthub Engineering. (2018). Pressure Measurement Devices - Inclined Manometer, Bourdon

Gauge, Diaphragm Gauge, Bellows, Pressure Transducers, Electronic Pressure Sensors.

[online] Available at: https://www.brighthubengineering.com/hydraulics-civil-engineering/

43777-pressure-measurement-pressure-measurement-devices/ [Accessed 4 Apr. 2018].

Engineeringtoolbox.com. (2018). Stress, Strain and Young's Modulus. [online] Available at:

https://www.engineeringtoolbox.com/stress-strain-d_950.html [Accessed 4 Apr. 2018].

Scribd. (2018). Fundamentals of Engineering Mechanics | Force | Euclidean Vector. [online]

Available at: https://www.scribd.com/document/241787088/Fundamentals-of-Engineering-

Mechanics [Accessed 4 Apr. 2018].

Scribd. (2018). Trusses, Types, Configuration andConnections | Truss | Civil Engineering.

[online] Available at: https://www.scribd.com/document/115008353/Trusses-Types-

Configuration-and-Connections [Accessed 4 Apr. 2018].

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