Answer:
e.All of the above
Explanation:
A fluid should be change
a.When its acidity increase
b.When its become contaminated
c.At operating temperature
Generally fluid is used in fluid power.Fluid power means transmission of power by using pressurized fluids.
Fluid power works on Pascal's and Bernoulli law.
From the above option we can say that all option is right for fluid .
Thin film deposition is a process where: a)-elemental, alloy, or compound thin films are deposited onto a bulk substrate! b)-Phosphatization is also applied c)-Zinc plating is also applied d)-None of the above
Answer:
(A) elemental, alloy, or compound thin films are deposited on to a bulk substrate
Explanation:
In film deposition there is process of depositing of material in form of thin films whose size varies between the nano meters to micrometers onto a surface. The material can be a single element a alloy or a compound.
This technology is very useful in semiconductor industries, in solar panels in CD drives etc
so from above discussion it is clear that option (a) will be the correct answer
The gas expanding in the combustion space of a reciprocating engine has an initial pressure of 5 MPa and an initial temperature of 1623°C. The initial volume is 0.05 m^3 and the gas expands through a volume ratio of 20 according to the law PV^1.25 = constant. Calculate: a) Work transfer b) Heat transfer
Answer:
a). Work transfer = 527.2 kJ
b). Heat Transfer = 197.7 kJ
Explanation:
Given:
[tex]P_{1}[/tex] = 5 Mpa
[tex]T_{1}[/tex] = 1623°C
= 1896 K
[tex]V_{1}[/tex] = 0.05 [tex]m^{3}[/tex]
Also given [tex]\frac{V_{2}}{V_{1}} = 20[/tex]
Therefore, [tex]V_{2}[/tex] = 1 [tex]m^{3}[/tex]
R = 0.27 kJ / kg-K
[tex]C_{V}[/tex] = 0.8 kJ / kg-K
Also given : [tex]P_{1}V_{1}^{1.25}=C[/tex]
Therefore, [tex]P_{1}V_{1}^{1.25}[/tex] = [tex]P_{2}V_{2}^{1.25}[/tex]
[tex]5\times 0.05^{1.25}=P_{2}\times 1^{1.25}[/tex]
[tex]P_{2}[/tex] = 0.1182 MPa
a). Work transfer, δW = [tex]\frac{P_{1}V_{1}-P_{2}V_{2}}{n-1}[/tex]
[tex]\left [\frac{5\times 0.05-0.1182\times 1}{1.25-1} \right ]\times 10^{6}[/tex]
= 527200 J
= 527.200 kJ
b). From 1st law of thermodynamics,
Heat transfer, δQ = ΔU+δW
= [tex]\frac{mR(T_{2}-T_{1})}{\gamma -1}+ \frac{P_{1}V_{1}-P_{2}V_{2}}{n-1}[/tex]
=[tex]\left [ \frac{\gamma -n}{\gamma -1} \right ]\times \delta W[/tex]
=[tex]\left [ \frac{1.4 -1.25}{1.4 -1} \right ]\times 527.200[/tex]
= 197.7 kJ
An aircraft increases its speed by 2% in straight and level flight. If the total lift remains constant determine the revised CL as a percentage of its original value to three significant figure
Answer:
96.1%
Explanation:
We know that lift force
[tex]F_L=\dfrac{1}{2}C_L\rho AV^2[/tex]
------------(1)
Where [tex]C_L[/tex] is the lift force coefficient .
ρ is the density of fluid.
A is the area.
V is the velocity.
Now when speed is increased by 2 % and all other parameter remains constant except [tex]C_L[/tex] .
Let;s take new value of lift force coefficient is [tex]C_L'[/tex] .
[tex]F_L=\dfrac{1}{2}C_L'\rho A(1.02V)^2[/tex]
-----------(2)
Now from equation 1 and 2
[tex]C_L\times V^2=C_L'\times1.0404 V^2[/tex]
⇒[tex]C_L'=0.961C_L[/tex]
So we can say that revised value of lift force coefficient is 96.1% of original value.
Reliability is defined as the_______that a component or system will perform its intended function for a specific period of time.
Answer:
Probaility
Explanation:
The reliability of a component, system or unit can be defined as the probability that that component can operate for a certain period of time (mission time) without losing its function.
Briefly describe the ionic bonding and covalent bonding. What is the key difference between these two bonding
Answer:
Explanation:
Ionic bonding are formed when two opposite ion attract each other. Ionic bond is generally between metal and non metal. Example NaCl
Covalent bonding is the bonding which is formed by the sharing of electron pair covalent bond is generally between two non metal.Example H₂O
Ionic bond is generally electrostatic in nature which lead to attraction of positive and negative ion
ionic bond does not have definite shape where covalent has definite shape
melting point of covalent bond is low where as ionic bond have high melting point.
Why is it important (in the context of systems engineering management) to become familiar with analytical methods? Provides some specific examples.
Understanding analytical methods is essential in systems engineering for problem-solving and system comprehension, with real-world applications in areas like environmental monitoring.
Explanation:The importance of analytical methods in systems engineering management is crucial for problem-solving and comprehending the physics of the situation. Analytical methods help in selecting the right system and developing solutions efficiently. For instance, in the field of environmental monitoring programs, the use of analytical methods aids in assessing system health and trends accurately.
A_____ transducer is a device that can convert an electronic controller output signal into a standard pneumatic output. A. pneumatic-to-current (P/I) B. voltage-to-pneumatic (V/P) C. current-to-pneumatic (I/P) D. pneumatic-to-voltage (P/V)
Answer:
The correct answer is
option C. current to pneumatic (V/P)
Explanation:
A current to pneumatic controller is basically used to receive an electronic signal from a controller and converts it further into a standard pneumatic output signal which is further used to operate a positioner or control valve. These devices are reliable, robust and accurate.
Though Voltage and current to pressure transducers are collectively called as electro pneumatic tranducers and the only electronic feature to control output pressure in them is the coil.
The response of an inductor to current is most directly similar to the response of the capcitor (a) current (b) voltage (c) resistance (d) inductor
Answer:
(b) vpltage
Explanation:
we know the expression for voltage across the inductor V=L[tex]\frac{di}{dt}[/tex] which clearly shows voltage across the inductor is directly proportional to rate of change of current similarly current across the capacitor I=C[tex]\frac{dv}{dt}[/tex] from the expression we can see that current across the capacitor is directly proportional to rate of change of voltage. so from above discussion it is clear that response of an iductor to current is similar to response of capacitor to voltage
What is a cascade refrigeration system?
Answer Explanation:
CASCADE REFRIGERATION SYSTEMS :
cascade refrigeration systems are commonly used in the liquefaction of natural gas and some other gases
cascade refrigeration system is also known as freezing system. It uses two types of refrigerants having different boiling points.this system is employed to obtain temperature of -40 to -80It allows stable ultra low temperature operationexamples of cascade refrigeration system: LNG (Liquefied natural gas ) plants mostly used cascade refrigeration system
ADVANTAGES OF CASCADE REFRIGERATION SYSTEMS:
energy is saved because the system allows the use of refrigerant gasesthe running cost is inexpensive repair is easyA cascade refrigeration system utilizes multiple linked refrigeration cycles to achieve ultra-low temperatures not possible with a single cycle. It features a cascade control mechanism for precise temperature management, using heat exchangers to interconnect and sequentially cool each stage.
Explanation:Understanding Cascade Refrigeration SystemsA cascade refrigeration system is a complex refrigeration strategy that employs multiple refrigeration cycles linked together to achieve cooling. Typically, these systems are utilized in environments requiring very low temperatures, which cannot be efficiently or cost-effectively achieved through a single refrigeration cycle. The essence of a cascade system lies in its deployment of two or more refrigeration units in series, each referred to as a "stage," with each successive stage operating at a lower temperature range than its predecessor.
The interconnection between these stages involves a heat exchanger, where a refrigerant from one cycle cools the condenser of the next lower temperature cycle. This process is crucial for achieving the desired low temperatures. One common application is in industrial refrigeration, where maintaining precise low temperatures is critical for process efficiency and product quality.
A key feature of cascade refrigeration systems is the use of cascade control, which enhances system responsiveness to temperature changes and maintains tight control over the process. This control mechanism consists of a master-slave relationship, where the output of one control loop (master) serves as the setpoint for the next (slave), creating a highly integrated control environment. Such setup enables rapid adjustment to changing operating conditions, ensuring the system swiftly responds to disturbances while maintaining the desired temperature levels.
What is an atom? a. it is a property of material b. it is specification of any material c. it the part of a substance d. it is a grain boundary
Answer:
Out of the multiple options provided,
option (c) it is the part of a substance
is correct
Explanation:
An atom is basically the smallest particle of matter or we can call it as building block of matter. It is as a brick to the wall or a cell to the body.
Matter is build up of a large number of these atoms. Atoms carbon(C), hydrogen(H), oxygen(O) combines to form molecules such as carbon dioxide([tex]CO_{2}[/tex]), water([tex]H_{2}O[/tex]), methane([tex]CH_{4}[/tex]), etc and then these molecules combines to form a substance.
It cannot be property, neither can it be specification of any material as these two characterizes the material and it can't be grain boundary for sure as grain boundary is the interface between two grain or crystal particles.
This shows that the smallest unit of matter is atom and it is the part of a substance
We can recycle glass as many time as we want. a)-True b)-False
Answer: True
Explanation: Yes , we can recycle glass endlessly, as many times as we want without the degradation of quality and purity factor because they are made from the widely available domestic components for example:- sand , limestone etc. These material are responsible for the successful recycling process of glass which does not produce any loss.
What is the theoretical density in g/cm3 for Lead [Pb]?
Answer:
11.34 g/cm3
Explanation:
At room temperature, where it is in a solid state, it is 11.34 [tex]\frac{g}{cm^{3}}[/tex]. While at melting temperature, at 327.5 ° C, it is 10.66 [tex]\frac{g}{cm^{3}}[/tex]
What is an example of a linear actuator?
Answer and Explanation :
LINEAR ACTUATOR-In simple terms a linear actuator is a mechanical device that creates motion in a straight line. Linear actuators are used in machine tools and industrial machinery, in computers peripherals such as drives and printers in valve and dampers and it is used where linear motion is required.
EXAMPLE OF LINEAR ACTUATOR: There are many types of motors that are used in a linear system these include DC MOTOR (with brush or brushless) STEPPER MOTOR a linear actuator can be used to operate a large valve in refinery. Hydraulic pump is an also a good example of linear actuator.
Describe the operational principle of a unitary type air conditioning equipment with a suitable sketch.
Answer:
Operational Principle of a Unitary Type Air Conditioning Equipment:
A unitary air conditioning system is basically a room type air conditioning system which comprises of an outdoor unit, a compressor for compressing
coolant, a heat exchanger (outdoor) for heat exchange, an expander attached to the heat exchanger for expansion of coolant and a duct.
It continuously removes heat and moisture from inside an occupied space and cools it with the help of heat exchanger and condensor in the condensing unit and discharges back into the same occupied indoor space that is supposed to be cooled.
The cyclic process to draw hot air, cool it down and recalculation of ther cooled air keeps the indoor occupied space at a lower temperature needed for cooling at home, for industrial processes and many other purposes.
refer to fig 1
Which of the following describes the action of a capacitor? (a) creates a de resistance (b) converts ac into de (c) opposes changes in the flow of current (d) stores electrical energy
Answer:
From the multiple choices provided for the action of capacitor, option
(d) stores electrical energy
is correct
Explanation:
A capacitor is basically a two terminal device that stores electrical energy in the electric field in its vicinity. It is apassive element.
The property of a capacitor to store electrical energy or the effect of a capacitor is known as its capacitance. The capacitance of a capacitor is given by:
Q = CV or C = [tex]\frac{Q}{V}[/tex]
It is originally known as condensor and it can be said that a capacitor adds capacitance to the circuit.
The resistivity of mercury drops suddenly to zero at a critical temperature, maki mercury a superconductor below that temperature. ( True , False )
Resistance zero meaning superconductor, so True.
Product service life is determined by a. estimates b. market forces c. liability d. property tests e. failure analysis f. all of the above
Answer: d) property tests
Explanation: Product service life can be referred as the life that define the service that can be provided by the product manufactured.The service life contains the testing and calculation of the product's quality, reliability, maintenance factor etc. These factors are known as the property of the product and so is calculated by the property test. Therefore option (d) is the correct option because other option does not define the factors for defining the product service life.
The specific heat of aluminum is approximately 900 J/kg°C. If the temperature of a 5 kg specimen needs to be raised from 30°C to 1000°C, the amount of heat required will be equal to Select one: a)- 4365 kJ b)- 4365 Btu c)- 4365W d)- None of the above
Answer:
a) 4365 kJ
Explanation:
In any thermodynamic system, any heat change is accompanied by the change in temperature. The relation between heat released/gained in a system and the temperature is:
Q=mcΔT
where,
Q is the amount of heat absorbed or released
m is the mass
ΔT is the change in temperature
c is called the specific heat.
Specific heat is defined as heat gained by 1 unit mass of any sample to raise the temperature of the sample by 1 °Celsius.
Thus, from the question:
Mass of aluminum =5 kg
Final temperature = 1000°C
Initial temperature = 30°C
ΔT = (1000 -30)°C = 970°C
Specific heat of aluminum = 900 J/kg°C
Thus, Amount of heat required:
Q = 5 kg×900 J/kg°C×970°C = 4365000 J
The conversion of J into kJ is shown below:
1 J = 10⁻³ kJ
Thus, Heat gained by aluminum =4365000 ×10⁻³ J = 4365 kJ
What are units for heating capacity? Mark all that apply: a)- Tons b)- kJ/kg c)- kW d)- Btu
Answer:
(b) kJ/kg
Explanation:
The ratio of amount of energy required to change the temperature of the substance by certain magnitude and this magnitude of temperature change is known as heat capacity of the substance.
The expression for Heat capacity is:
C=E/ΔT
Where,
C is the Heat capacity
E is the energy absorbed/released
ΔT is the change in temperature
The SI unit of heat capacity is J/K.
(a) Tons represents the unit of mass (1000 kg)
(c) kW represents the unit of power (1000 W)
(d) Btu represents the unit of heat (1055 J)
The units from the options that can be a unit of heat capacity is (b) kJ/kg.
Two one-kilogram bars of gold are initially at 50°C and 300°C. The bars are brought in contact with each other. What is their final temperature, the entropy change of each block, and the total entropy generation in the process.
Given:
[tex]T_{1}[/tex] = 50°C = 273+50 =323 K
[tex]T_{2}[/tex] = 300°C = 273+300 =573 K
Solution:
We know that:
specific heat for gold, c = 0.129 J/g°C
Also, change in entropy, ΔS is given by:
[tex]\Delta S = cln\frac{T_{f}}{T_{i}}[/tex]
After the bars brought in contact with each other,
final temperature, [tex]T_{f}[/tex] = [tex]\frac{T_{1}+T_{2}}{2}[/tex]
final temperature, [tex]T_{f}[/tex] = [tex]\frac{323+573}{2}[/tex] = 448K
Now, entropy for first gold bar, using eqn-1
[tex]\Delta S = cln\frac{T_{f}}{T_{1}}[/tex]
[tex]\Delta S_{1} = 0.129ln\frac{448}{323}[/tex] =0.042 J/K
[tex]\Delta S_{2}[/tex] = 0.129ln [tex]\frac{448}{573}[/tex] = - 0.032 J/K
Total entropy generation,
[tex]\Delta S_{1}[/tex] = [tex]\Delta S_{1}[/tex] + [tex]\Delta S_{2}[/tex]
[tex]\Delta S[/tex] = 0.042 + (- 0.032) = 0.010 J/K
A light pressure vessel is made of 2024-T3 aluminum alloy tubing with suitable end closures. This cylinder has a 90mm OD, a 1.65mm wall thickness, and Poisson's ratio 0.334. The purchase order specifies a minimum yield strength pf 320 MPa. What is the factor of safety if the pressure-release valve is set at 3.5 MPa?
Given:
Outer Diameter, OD = 90 mm
thickness, t = 0.1656 mm
Poisson's ratio, [tex]\mu[/tex] = 0.334
Strength = 320 MPa
Pressure, P =3.5 MPa
Formula Used:
1). [tex]Axial Stress_{max}[/tex] = [tex]P[\frac{r_{o}^{2} + r_{i}^{2}}{r_{o}^{2} - r_{i}^{2}}][/tex]
2). factor of safety, m = [tex]\frac{strength}{stress_{max}}[/tex]
Explanation:
Now, for Inner Diameter of cylinder, ID = OD - 2t
ID = 90 - 2(1.65) = 86.7 mm
Outer radius, [tex]r_{o}[/tex] = 45mm
Inner radius, [tex]r_{i}[/tex] = 43.35 mm
Now by using the given formula (1)
[tex]Axial Stress_{max}[/tex] = [tex]3.5[\frac{45^{2} + 43.35^{2}}{45^{2} - 43.35^{2}}][/tex]
[tex]Axial Stress_{max}[/tex] = [tex]3.5\times 26.78[/tex] =93.74 MPa
Now, Using formula (2)
factor of safety, m = \frac{320}{93.74} = 3.414
A properly installed window quilt can provide an additional insulation of R-4 to windows. For a window with a U-factor of 0.33, determine the percentage of heat lost for a quilt-covered win- dow compared to a bare window.
Answer:
Heat loss 67%.
Explanation:
We know that heat transfer
Q=AUΔT
Where U is the overall heat transfer coefficient ,A is the area and ΔT is the temperature difference.
Now heat transfer in terms of U-factor
[tex] Q_1=AU_1ΔT[/tex]
[tex] Q_2=AU_2ΔT[/tex]
Given that temperature difference is same in both condition so
[tex]\dfrac{Q_1}{U_1}=\dfrac{Q_2}{U_2}[/tex]
[tex]\dfrac{Q_1}{Q_2}=\dfrac{U_1}{U_2}[/tex]
[tex] heat\ loss=\dfrac{Q_2-Q_1}{Q_1}[/tex]
[tex] heat\ loss=\dfrac{U_2-U_1}{U_1}[/tex]
Given that[tex]U_2=0.33U_1[/tex]
[tex] heat\ loss=\dfrac{0.33U_1-U_1}{U_1}[/tex]
Heat loss 67%.
What is Differential Analysis in fluid mechanics?
Answer:
Differential analysis is used when it is needed to determine the detail information of the flow i.e. pressure or stress variation along any point.
Explanation:
In fluid mechanics, sometime situation arise in which we need to determine in detail about flow characteristics like stress and pressure variation.
To find these flow characteristics some relationship need to imply either at a point or at very small volume and analysis of flow at very small point is known as differential analysis.
Example: pressure and shear stress variation in a line of the wing of a plane.
As temperature decreases a ductile material can become brittle - ductile-to-brittle transition
Answer:
Yes ,at low temperature ductile material behaves like brittle.
Explanation:
Yes,as temperature decreases a ductile material can become brittle.
In metals ductile to brittle transition temperature is around 0.1 to 0.2 Tm(melting point temperature) and in ceramics ductile to brittle transition temperature is around 0.5 to 0.7 Tm(melting point temperature) .
We can easily see that from graph between fracture toughness and temperature.In the graph when temperature is low then the ductile material is behaving like brittle material.But when temperature is above a particular value then material behaves like ductile.
What do you understand by equilibrium of a system? What is meant by thermodynamic equilibrium? Explain in detail.
Answer:
Equilibrium of a system is defined as when the concentration of reactants and products of a chemical reaction are in equilibrium and their ratio does not vary. In another words we can say that, when the forward reaction rate is similar to the reverse reaction rate.
Thermodynamics equilibrium is defined as in an isolated system when there is no change in energy and entropy. It is determined by the its intensive properties like volume and pressure.
Water, in a 150 in^3 rigid tank, initially has a temperature of 70°F and an enthalpy of 723.5 Btu/lbm. Heat is added until the water becomes a saturated vapor. Calculate: a) The initial quality of the water b) The total mass of the water c) The temperature of the water at the final state.
Answer:
a)initial quality of water 0.724.
b)mass of water =2.45 kg
c)T=70°F
Explanation:
h=732.5 Btu/lbm
h=763.33 KJ/kg (1 Btu=1.05 kj)
T=70°F⇒T=21.1°C
[tex]V=150 in^3=0.002458m^3[/tex]
(a)From steam table
Properties of saturated steam at 21.1°C
[tex]h_f= 88.56\frac{KJ}{Kg} ,h_g= 2539.49\frac{KJ}{Kg}[/tex]
To find dryness fraction
[tex]h=h_f+x(h_g-h_f)\frac{KJ}{Kg}[/tex]
[tex]763.33=88.56+x(2539.49-88.56)\frac{KJ}{Kg}[/tex]
x=0.27
So initial quality of water 0.724.
(b)
[tex]v=v_f+x(v_g-v_f)\frac{m^3}{Kg}[/tex]
where v is specific volume
From steam table at 21.1°C
[tex]v_f= 0.001\frac{m^3}{Kg} ,v_g= 54.13\frac{m^3}{Kg}[/tex]
V=[tex]m_f\times v_f[/tex]
0.002458=[tex]m_f\times 0.001[/tex]
So mass of water =2.45 kg
(c)
Actually water will take latent heat ,it means that heating of will take place at constant temperature and constant pressure.So we can say that final temperature of water will remain same (T=70°F).
From your cooling load (8890.007 Btu/hr = 2.605kW, determine mass flow rate of refrigerants. Use the following "rule of thumb" estimate of a standard room of size 180 ft^2: 1 ton of refrigerant = 12,000Btu = 3.517 kW Rule of thumb: 1 ton cooling load = 300-400 ft^2
Answer:
0.740833917 ton/hr
Explanation:
Given:
Cooling load, 8890.007 Btu/hr = 2.605 kW
Room size = 180 [tex]ft^{2}[/tex]
According to the thumb rule
1 ton of refrigerant = 12000Btu
Hence for 8890.007 Btu/hr,
the mass flow rate of the refrigerant is =8890.007 / 12000
= 0.740833917 ton per hr
Hence, mass flow rate is 0.740833917 ton/hr
A steel rod 6mm in diameter is stretched with a tensile force of 400N. Calculate the tensile stress experienced by the steel rod
Answer:
Tensile stress is 14.15 N/[tex]mm^{2}[/tex]
Explanation:
When any object is subjected to an external force, the body offers a resisting force which is equal and opposite to the external load. This resisting force is called stress. Thus stress is defined as the force acting perpendicular to the given cross sectional area of the object.
Mathematically, stress , σ = [tex]\frac{force }{area}[/tex]
Given : Tensile force, F = 400 N
Diameter of the rod, d = 6 mm
Area of the rod is given by, A = [tex]\frac{\pi }{4}\times d^{2}[/tex]
= [tex]\frac{\pi }{4}\times 6^{2}[/tex]
=28.27 [tex]mm^{2}[/tex]
Therefore, the tensile tress is, σ = [tex]\frac{force }{area}[/tex]
= [tex]\frac{400 }{28.27}[/tex]
= 14.149 N/[tex]mm^{2}[/tex]
[tex]\simeq[/tex] 14.15 N/[tex]mm^{2}[/tex]
Thus, tensile stress experieced by the rod is 14.15 N/[tex]mm^{2}[/tex]
List the main activities of exploration??
Answer: Exploration includes plethora of activities and depend upon the kind of exploration a person is doing. But most include some of the basic activities like research , investigation, planning and execution.
Suppose we want to explore new petroleum sites then we would have to start with studying the geography of that area, then according to our research we will analyse the hot spots or the sector where probability of finding of oil field is highest, post that appropriate man power is skilled professionals, tools and machinery will be brought at the site so that execution can take place.
A circular plate with diameter of 20 cm is placed over a fixed bottom plate with a 1 mm gap between two plates filled with Kerosene at 40 degree C, shown in the following figure. Find the torque needed to rotate the top plate at 5 rad/s. The velocity distribution in the gap is linear and the shear stress on the edge of the rotating plate can be neglected.
Answer:
T = 1.17 x [tex]10^{-3}[/tex] N-m
Explanation:
Given :
Gap between the two plates , dy = 1 mm
dy = 1 x [tex]10^{-3}[/tex] m
Angular velocity of the top plate , ω = 5 rad/s
Diameter of the plate, D = 20 cm
Radius of the plate, R = 10 cm
= 0.1 m
Temperature of the kerosene = 40°C
Viscosity of kerosene at 40°C = 0.0015 Pa-s
Now let us take a small elemental ring of thickness dr at a radius r.
Therefore, area of this elemental ring of dr = 2πrdr
Now linear velocity at radius r = ω x r
5r m/s
Now applying Newtons law of viscosity we get,
Shear stress, τ = μ.[tex]\frac{du}{dy}[/tex]
[tex]\Rightarrow \frac{F_{s}}{A}=\mu .\frac{du}{dy}[/tex]
[tex]\Rightarrow \frac{F_{s}}{A}=\mu .\frac{5r-0}{1\times 10^{-3}}[/tex]
[tex]\Rightarrow \frac{F_{s}}{A}=\mu \times 10^{3}\times 5r[/tex]
[tex]F_{s}=\mu \times 10^{3}\times 5r\times 2\pi rdr[/tex]
[tex]F_{s}=5 \times 10^{3}\times \mu \times r\times 2\pi rdr[/tex]
[tex]F_{s}=\frac{18849}{400}\times r^{2}dr[/tex]
Now we know torque due to small strip,
dT = [tex]F_{s}[/tex] x r
dT = [tex]\frac{18849}{400}\times r^{3}dr[/tex]
Therefore total torque for r=0 to r=R can be calculated. So by integrating,
[tex]\int dT=\int_{0}^{R}\frac{18849}{400}\times r^{3}dr[/tex]
[tex]T = \frac{18849}{400}\times \frac{R^{4}}{4}[/tex]
[tex]T = 47.1225\times \frac{0.1^{4}}{4}[/tex]
T = 1.17 x [tex]10^{-3}[/tex] N-m