A M14 x 2 hexagonal head bolt is used to clamp together two 15 mm steel plates. Young's modulus of the bolt and the plates can be taken as 207 GPa. (i)-Determine a suitable length for the bolt. (ii)-Determine the bolt stiffness (iii)-Determine the stiffness of the members

Answer:

a). Soderberg method

Explanation:

A straight line joining the endurance limit, [tex]S_{e}[/tex] on the ordinate and to the yield strength,[tex]S_{yt}[/tex]  on the abscissa is know as Soderberg line.

   The Soderberg line is the most conservative failure criteria and in this there is no need to consider yielding point in this case.

The equation for Soderberg is given by

[tex]\frac{\sigma _{m}}{S_{yt}}+\frac{\sigma _{a}}{S_{e}}=1[/tex]

where [tex]\sigma _{m}[/tex] is mean stress

           [tex]\sigma _{a}[/tex] is amplitude stress

Answer:

strains for the respective cases are

0.287

0.318

0.127

and for the entire process 0.733

Explanation:

The formula for the true strain is given as:

[tex]\epsilon =\ln \frac{l}{l_{o}}[/tex]

Where

[tex]\epsilon =[/tex] True strain

l= length of the member after deformation

[tex]l_{o} = [/tex] original length of the member

Now for the first case we have

l= 1.6m

[tex]l_{o} = 1.2m[/tex]

thus,

[tex]\epsilon =\ln \frac{1.6}{1.2}[/tex]

[tex]\epsilon =0.287[/tex]

similarly for the second case we have

l= 2.2m

[tex]l_{o} = 1.6m[/tex]   (as the length is changing from 1.6m in this case)

thus,

[tex]\epsilon =\ln \frac{2.2}{1.6}[/tex]

[tex]\epsilon =0.318[/tex]

Now for the third case

l= 2.5m

[tex]l_{o} = 2.2m[/tex]

thus,

[tex]\epsilon =\ln \frac{2.5}{2.2}[/tex]

[tex]\epsilon =0.127[/tex]

Now the true strain for the entire process

l=2.5m

[tex]l_{o} = 1.2m[/tex]

thus,

[tex]\epsilon =\ln \frac{2.5}{1.2}[/tex]

[tex]\epsilon =0.733[/tex]

Answer:

(b)False

Explanation:

[tex]I_{xy}[/tex] defined as

      [tex]I_{xy}[/tex] =[tex]\int \left (x\cdot y\right )dA[/tex]

Where x is the distance from centroidal x-axis

           y is the distance from centroidal y-axis

          dA is the elemental area.

The product of x and y can be positive or negative ,so the value of  [tex]I_{xy}[/tex] can be positive as well as negative .

So from the above expressions we can say that the product of [tex]I_{x},I_y[/tex] is different from [tex]I_{xy}[/tex] .

Answer:

Force on the bolt = 24.525 kN

Force on the 1st hinge = 8.35 kN

Force on the 2nd hinge = 16.17 kN

Explanation:

Given:

height = 2 m

width =1 m

depth of the door from the water surface = 1.5 m

Therefore,

[tex]\bar{y}[/tex] =1.5+1 = 2.5 m

Hydrostatic force acting on the door is

[tex]F= \rho \times g\times \bar{y}\times A[/tex]

[tex]F= 1000 \times 9.81\times 2.5\times 2\times 1[/tex]

         = 49050 N

         = 49.05 kN

Now finding the Moment of inertia of the door about x axis

[tex]I_{xx}=\frac{1}{12}\times b\times h^{3}[/tex]

[tex]I_{xx}=\frac{1}{12}\times1\times 2^{3}[/tex]

               = 0.67

Now location of force, [tex]y^{*}[/tex]

[tex]y^{*}=\bar{y}+\frac{I_{xx}}{A\times \bar{y}}[/tex]

[tex]y^{*}=2.5+\frac{0.67}{2\times 1\times 2.5}[/tex]

             = 2.634

Therefore, calculating the unknown forces

[tex]F=F_{A}+R_{B}+R_{C} = 49.05[/tex]  ------------------(1)

Now since [tex]\sum M_{R_{A}}=0[/tex]

∴ [tex]R_{B}\times L+R_{C}\times L-F\times \frac{1}{2}=0[/tex]

  [tex]R_{B}+R_{C}-F\times \frac{1}{2}=0[/tex]

  [tex]R_{B}+R_{C}=\frac{F}{2}[/tex]

  [tex]R_{B}+R_{C}=24.525[/tex]        -----------------------(2)

From (1) and (2), we get

[tex]R_{A} = 49.05-24.525[/tex]

                = 24.525 kN

This is the force on the Sliding bolt

Taking [tex]\sum M_{R_{C}}=0[/tex]

[tex]F\times 0.706-R_{A}\times 0.84-R_{B}\times 1.68 = 0[/tex]

[tex]49.05\times 0.706-24.525\times 0.84-R_{B}\times 1.68 = 0[/tex]

[tex]R_{B}[/tex] =8.35 kN

This is the reaction force on the 1st hinge.

Now from (1), we get

[tex]R_{C}[/tex] =16.17 kN

This is the force on the 2nd hinge.

Answer: a) angle, geometry and coordination number

Explanation: Crystal lattice is described as arrangement of groups of atoms inside three dimensional structure of crystal. It has a particular geometry in which atoms are placed in a symmetry. The also have angle in which placement of atoms are done. Co-ordination number also determines the crystal lattice by counting the atoms with which it is bonded. Thus, option (a) is the correct option.

Answer:

T = 212.8125°C

Explanation:

Given

radius of the wire, [tex]r_{0}[/tex] = 5 mm 0.005 m

heat generated, g = 5 x [tex]10^{7}[/tex] W/[tex]m^{3}[/tex]

outer surface temperature, [tex]T_{S}[/tex] = 180°C

Thermal conductivity, k = 8 W / m-k

Now maximum temperature occurs at the center of the wire

that is at r=0,

Therefore, [tex]T_{o}=T_{S}+\frac{g\times r_{o}^{2}}{4\times k}[/tex]

                  [tex]T_{o}=180+\frac{5\times 10^{7}\times 0.005^{2}}{4\times 8}[/tex]

                 [tex]T_{o}=219.0625[/tex]°C

Therefore, temperature at r = 2 mm

[tex]\frac{T-T_{S}}{T_{O}-T_{S}}= 1-\left (\frac{r}{r_{O}}  \right )^{2}[/tex]

[tex]\frac{T-180}{219.0625-180}= 1-\left (\frac{2}{5}  \right )^{2}[/tex]

Therefore, T = 212.8125°C

Answer:

True

Explanation:

An aircraft is subject to 3 primary rotations

1) About longitudinal axis known as rolling

2) About lateral axis known as known as pitching

3) About the vertical axis known as yawing

The rolling of the aircraft induces torsion in the body of the aircraft thus the fuselage structure should be capable of carrying torsion

Answer:

30.12345° can be written as : 30°7'20.42''

Or,

30 degrees 7 minutes and 20.42 seconds.

Explanation:

1 degree consists of 60 arc minutes.  

1 arc minutes consists of 60 arc seconds.  

Thus, 30.12345° can be written as:

30.12345°= 30° + 0.12345°

1° = 60'

So,

0.12345° = 0.12345*60' = 7.407'

Thus, 7.407' can be written as:

7.407' = 7' + 0.407'

1' = 60''

So,

0.407' = 0.407*60'' = 20.42''

Thus,

30.12345° can be written as : 30°7'20.42''

Answer: d) All of the above

Explanation: Polymers are the substances that have molecular structure with having same bonds in the entire molecule together.There are light weight substance which occur natural as well as artificially. They are also categorized  as thermoplastics ,thermosets, and elastomers. They also have the property of being stretching and bending under the pressure or load they are also instable. Therefore, all the options are correct statement about polymers.

Answer:stress=79.56MPa

strain=[tex]3.8\times 10^{-4}[/tex]

Young Modulus=209.36 GPa

Explanation:

Given data

d=20 mm

Length[tex]\left ( L\right )[/tex]=80mm

[tex]\Delta {L}[/tex]=[tex]3.04\times 10^{-2}[/tex]mm

Load=[tex]25\times 10^{3}[/tex]N

[tex]\left ( i\right )[/tex]

Stress=[tex]\frac{Load\ applied}{cross-section}[/tex]

Stress=[tex]\frac{25\times 10^{3}}{314.2}[/tex]

Stress=79.56MPa

[tex]\left ( ii\right )[/tex]

Strain=[tex]\frac{Change\ in\ length}{Length}[/tex]

Strain=[tex]\frac{3.04\times 10^{-3}}{80}[/tex]

Strain=[tex]3.8\times 10^{-4}[/tex]

[tex]\left ( iii\right )[/tex]

young modulus[tex]\left ( E\right )[/tex]=[tex]\frac{Stress}{Strain}[/tex]

E=[tex]\frac{79.56\times 10^{6}}{3.8\times 10^{-4}}[/tex]

E=209.36GPa

Answer:

FALSE

Explanation:

REYNOLDS NUMBER :Reynolds number is used to indicate whether the fluid flow past a body or turbulent. it is a dimensionless number

REYNOLDS NUMBER OF A INTERNAL TURBULENT FLOW: For a flow in a pipe experimental observation show that the critical reynolds number is about  2300 for the practical purpose . so the reynolds number can not be so high as 500000

Answer:

speed = 16.44 m/s

Acceleration = 71.36 m/s²

Explanation:

Given data

Speed ( N) = 240 rpm

angle  = 45°

stoke length(L)  = 750 mm

length of rod ( l )  = 1500 mm

To find out

the piston speed and acceleration

Solution

we find speed by this formula

speed = r ω (sin(θ) + (sin2(θ)/ 2n))  ...................1

here we have find  r and ω

ω = 2[tex]\pi[/tex] N / 60

so ω = 2[tex]\pi[/tex] × 240 / 60

ω =  25.132 rad/s

n = l/r =  1500/750 = 2

we know  L = 2r

so r = L/2 = 750/2 = 375 mm

put these value in equation 1

speed = 375 × 25.132 (sin(45) + (sin2(45)/ 2×2))  

speed = 16444.811823 mm/s = 16.44 m/s

Acceleration = r ω² (cos(θ) + (cos2(θ)/ n))  ...................2

put the value  r, ω and n in equation 2

Acceleration = r ω² (cos(θ) + (cos2(θ)/ n))

Acceleration  = 375 × (25.132)² (cos(45) + (cos2(45)/2))  

Acceleration = 71361.363659 = 71.36 m/sec²

Answer:

mechanism of energy transfer in system is depend on Heat and Work:

Explanation:

Heat :Heat is described as the type of energy transmitted by a temperature difference between two structures (or a system and its environment).

Work:it is  is an interaction of energy between a system and its environment. In the form of  work   it can cross the boundaries of a closed system. if energy crossing boundary of the system is not heat then it must be work..

Answer: d) a & b

Explanation: Composite materials are made up of two or more different types of phases which include dispersed phase and matrix phase as most important phases.

Answer:

Isobaric process

Explanation:

The process in which the system pressure remain constant is called is called isobaric process. The word "iso"means same and baric means pressure.

At constant pressure, the work done is given by :

[tex]W=p\times \Delta V[/tex]

Where

W is the work done by the system

p is the constant pressure

[tex]\Delta V[/tex] is the change in volume

So, the correct option is (c) " isobaric process ".

Answer:

Given:

laminar flow

and since velocity of flow is doubled, we consider [tex]v_{n}[/tex] as new velocity and [tex]v_{o}[/tex] as original velocity

Explanation:

As per laminar flow, thickness, t is given by

t = [tex]\frac{4.91x}{\sqrt( R_{ex}) }[/tex]

t =  [tex]\frac{4.91x}{\sqrt{\frac{\rho vx}{\mu }}}[/tex]

t = [tex]\frac{4.91x\mu }{\sqrt{\rho vx}}[/tex]

where,

[tex]R_{ex}[/tex] = Reynold's no.

therefore,

t ∝ [tex]\frac{1}{\sqrt{v} }[/tex]

Now,

[tex]\frac{t_{n} }{t_{o} }[/tex] = [tex]\sqrt{(\frac{v_{o} }{v_{n} })}[/tex]

[tex]\frac{t_{n} }{t_{o} }[/tex] = [tex]\sqrt{(\frac{v_{o} }{2v_{o} } )} =\frac{1}{\sqrt{2} }[/tex]

therefore,

[tex]t_{n}:t_{o} = 1:\sqrt{2}[/tex]

Answer:

L = 46.35 m

Explanation:

GIVEN DATA

\dot m  = 0.25 kg/s

D = 40 mm

P_1 = 690 kPa

P_2 = 650 kPa

T_1 = 40° = 313 K

head loss equation

[tex][\frac{P_1}{\rho} +\alpha \frac{v_1^2}{2} +gz_1] -[\frac{P_2}{\rho} +\alpha \frac{v_2^2}{2} +gz_2] = h_l +h_m[/tex]

where[tex] h_l = \frac{ flv^2}{2D}[/tex]

[tex]h_m minor loss [/tex]

density is constant

[tex]v_1 = v_2[/tex]

head is same so,[tex] z_1 = z_2 [/tex]

curvature is constant so[tex] \alpha = constant[/tex]

neglecting minor losses

[tex]\frac{P_1}{\rho}  -\frac{P_2}{\rho} = \frac{ flv^2}{2D}[/tex]

we know[tex] \dot m[/tex] is given as[tex] = \rho VA[/tex]

[tex]\rho =\frac{P_1}{RT_1}[/tex]

[tex]\rho =\frac{690 *10^3}{287*313} = 7.68 kg/m3[/tex]

therefore

[tex]v = \frac{\dot m}{\rho A}[/tex]

[tex]V =\frac{0.25}{7.68 \frac{\pi}{4} *(40*10^{-3})^2}[/tex]

V = 25.90 m/s

[tex]Re = \frac{\rho VD}{\mu}[/tex]

for T = 40 Degree, [tex]\mu = 1.91*10^{-5}[/tex]

[tex]Re =\frac{7.68*25.90*40*10^{-3}}{1.91*10^{-5}}[/tex]

Re = 4.16*10^5 > 2300 therefore turbulent flow

for Re =4.16*10^5 , f = 0.0134

Therefore

[tex]\frac{P_1}{\rho}  -\frac{P_2}{\rho} = \frac{ flv^2}{2D}[/tex]

[tex]L = \frac{(P_1-P_2) 2D}{\rho f v^2}[/tex]

[tex]L =\frac{(690-650)*`10^3* 2*40*10^{-3}}{7.68*0.0134*25.90^2}[/tex]

L = 46.35 m

Answer:

The given statement for temperature and convection is False.

Explanation:

Convection is not a function of temperature to the fourth power but it depends linearly on temperature. the below equation shows the linear relation of heat transfer due to convection and temperature:

Q = [tex]H_{c}A(T_{hot} - T_{cold} )[/tex]

Whereas, radiation is a function of temperature to the fourth power.

The Stefan-Boltzmann law gives the relationship between an object's temperature and the amount of radiation it emits. The law is given by:

[tex]Q=\sigma T^{4}[/tex]

Answer:

Explanation:

Thermostatic expansion valve is mainly a throttling device commonly used in air conditioning systems and refrigerators.

It is an automatic valve that maintains proper flow of refrigerant in the evaporator according to  the load inside the evaporator. When the load in the evaporator is higher the valve opens and  allows the increase in flow of refrigerant and when the load reduces the valve closes a bit and  reduces the flow of refrigerant. This process leads to higher efficiency of compressor as well as the whole refrigeration system.  Thus TEV works to reduce the pressure of refrigerant from higher condenser pressure to the lower evaporator pressure. It also keeps the evaporator active.      

Answer:

a). TRUE

Explanation:

Absolute zero temperature is the lowest possible temperature that can be achieved where no heat energy remains in the body. Absolute zero temperature is 0 k in the Kelvin scale and -273.16 degree Celsius in Centigrade scale.

             All bodies with temperature greater than absolute zero emits energy in the form of electro magnetic radiation. Two laws namely Stefan Boltzmann law and Wein's law gives the basis of the fact that bodies with temperature greater than absolute zero temperature emits electromagnetic radiation.

Stefan Boltzmann law : It states the relationship between temperature of the body and radiations that it can emit.

                         E = σ. [tex]T^{4}[/tex]

where E = radiation emissions

           σ =  Stefans Boltzmann constant

           t is temperature

Wein's Law : It states the temperature of the object and the wavelength at which the body emits maximum radiations.

[tex]\lambda _{max} = \frac{b}{T}[/tex]

where λ is wavelength

           b  is a constant

           T is temperature

Answer:

Explanation:

WATER CONTENT IN AIR-the water content of the air varies from place to place and from time to time because water content in air is dependent on temperature if temperature is change then water content also change water exist in air as a solid liquid and gas

RELATIVE HUMIDITY-Relative humidity is the ratio of partial pressure of water vapor to the equilibrium vapor pressure of water at a given temperature  relative humidity depends on temperature and pressure of the system

Enthalpy-when a substance changes at constant pressure enthalpy tells how much heat and work was added or removed from the substance

enthalpy is equal to the sum of system internal energy and product of its pressure and volume.it is denoted H

Answer:

Power needed to pump=4.79 KW.

Explanation:

Given that:[tex]T_{1}=283K,T_{2}=313K,Q_{H}=50KW[/tex]

We know that coefficient of performance of heat pump

 COP=[tex]\dfrac{T_{H}}{T_{H}-T_{L}}[/tex]

So COP=[tex]\dfrac{313}{313-283}[/tex]

      COP=10.43

COP=[tex]\frac{Q_{H}}{W_{in}}[/tex]

      10.43 =[tex]\frac{50}{W_{in}}[/tex]

[tex]W_{in}[/tex]=4.79 KW

So power needed to pump=4.79 KW.

Answer:

a). absorber, generator and liquid pump

Explanation:

The Vapour absorption system consists of compression, expansion, condensation and evapouration processes. This system uses ammonia, lithium bromide or water as refrigerant.

                  An absorber, pump and generator is used in place of a compressor in the vapour compression refrigeration system. The operation is smooth in vapour absorption system since all the moving elements are in the pump only. This system make use of low energy like heat and can work on lower evapourator pressure. It has low Coefficient of performance.

Answer:

The solar panel efficiency in converting solar energy in electrical energy is 18%.

Explanation:

The solar panel's  efficiency can be defined as:

[tex] n= \frac{Pe}{Ps}*100\%[/tex]

Where Pe and Ps are the output electrical power and input solar power respectively. The electrical is computing in terms of the voltage and current delivered:

[tex]Pe=I.V[/tex]

[tex]Pe=4.8 A * 15 V[/tex]

[tex]Pe= 72 AV = 72 W [/tex]

The net solar power of panel is found by multiplying the solar intensity by the panel area in square meters:

[tex]Ps = Is.Ap[/tex]

[tex]Ps = 1000 W/m^2 *(0.8 m * 0.5 m)[/tex]

[tex]Ps = 1000 W/m^2 *(0.40 m^2)[/tex]

[tex]Ps = 400 W [/tex]

Finally the panel efficience n is:

[tex] n= \frac{72 W}{400 W}*100\%[/tex]

[tex] n= 0.18*100\% = 18\%[/tex]

Answer:

(a) .01

Explanation:

there is relation between friction factor and stanton number and friction factor that is stanton number is half of friction factor

stanton number =[tex]\frac{friction factor}{2}[/tex]

.005=[tex]\frac{friction factor}{2}[/tex]

friction factor =2×.005

friction factor=.01

Answer:

The options a)- A blast furnace is used and d)-Coke is used to produce the heat are FALSE.

Explanation:

Aluminium is a chemical element and the most abundant metal present in the Earth's crust. An aluminium ore is called bauxite. Aluminium is extracted from its ore by the process of electrolysis, called the Hall–Héroult process. The extraction of aluminium is an expensive process as it requires large amount of electricity. The bauxite is purified to produce aluminium oxide. Then, aluminium is extracted from the aluminium oxide.

Therefore, the refining of aluminum from its ore does not involve the use of a blast furnace and coke to produce heat.

Answer:

  Rotary engine was early known by the name of internal combustion engine. It convert heat from a high pressure of combustion. The main advantage of rotary engine is that it can be operate with less number of vibration. It works on the principle of converting pressure into rotating motion. In rotary engine the expansion pressure is applied on the flank rotor.  

Answer: The rotary engine works on the same basic principle as the piston engine: combustion in the power plant releases energy to power the vehicle. However, the delivery system in the rotary engine is wholly unique. The piston engine performs four key operations: intake, compression, combustion, and exhaust.

Explanation:

Answer:

Q = 0.118 [tex]m^{3}[/tex]/s

Explanation:

Given :

diameter of the pipe, d = 150 mm

                                       = 0.15 m

Pitot tube co efficient, [tex]C_{v}[/tex] = 1.05

manometer reading is given, x = 167 mm

                                                   = 0.167 m

From manometer reading,we can find the difference between the manometer height, h

 [tex]h =x\times\left [ \frac{S_{m}}{S_{w}}-1 \right ][/tex]

[tex]h =0.167\times\left [ \frac{13.6}{1}-1 \right ][/tex]

h = 2.1042 m

Now, average velocity is v = [tex]C_{v}[/tex][tex]\sqrt{2.g.h}[/tex]

                                            = [tex]1.05\times \sqrt{2\times 9.81\times 2.1042}[/tex]

                                            = 6.74 m/s

Area of the pipe, A = [tex]\frac{\pi }{4}\times d^{2}[/tex]

                                = [tex]\frac{\pi }{4}\times 0.15^{2}[/tex]

                                = 0.0176 [tex]m^{2}[/tex]

Therefore, flow rate is given by, Q = A.v

                                                          = 0.0176 X 6.74

                                                          = 0.118[tex]m^{3}[/tex]/s

Answer:

A) Body forces-

  Body forces is the forces which acts throughout the volume of the body.     It is basically distributed over the volume and mass of the element of the body. In a body force other body exerts a force without being contract.  

For example : Gravity forces, electromagnetic forces, centrifugal forces.

B) Surface forces-

   Surface forces is the forces which are distributed all over the free surface of the body. Surfaces forces can be further divided into two perpendicular components as: normal forces and shear forces.

For example : Pressure forces and viscous forces.              

Answer:

b). False

Explanation:

A refractory material is a type of material that can withstand high temperatures without loosing its strength. They are used in reactors, furnaces, kilns, etc.

    Refractory materials are certain super alloys and ceramics materials.

Properties of refractory materials :

1. Refractory materials have high melting point.

2.They acts barriers between high heat zone and low heat zone.

3. The specific heat of refractory material is very low.

4. Refractories that have high bulk densities are better in quality.

Hence, Refractory materials have a very high melting temperature.