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All questions of Full Mock Tests Series for Mechanical Engineering Exam

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The steady flow energy equation:
Q = m(h2 – h1) is applicable for:
  • a)
    Nozzle
  • b)
    Turbine
  • c)
    Compressor
  • d)
    Boiler
Correct answer is option 'D'. Can you explain this answer?

Knowledge Hub answered
From Steady Flow Energy Equation (S.F.E.E.)
For Boiler: W=0, no work is done by the boiler,
Change in kinetic and potential energy is neglected.
i.e. Q=m(h2−h1)
For Nozzle: Q=0, as the nozzle is perfectly insulated,
W=0, no work is done by nozzle, \(v_{1}
For Turbine: Q=0, for the adiabatic or perfectly insulated turbine,
Change in kinetic and potential energy is neglected
i.e. W=m(h1−h2)
for Compressor: Q=0, for an adiabatic or perfectly insulated turbine,
Change in kinetic and potential energy is neglected
i.e. W = m (h2 − h1)

In a cam drive, it is essential to offset the axis of a follower to
  • a)
    Decrease the side thrust between the follower and guide
  • b)
    Decrease the wear between follower and cam surface
  • c)
    Take care of space limitation
  • d)
    Reduce the cost
Correct answer is option 'B'. Can you explain this answer?

Rajesh Khanna answered
When the motion of the follower is along an axis away from the axis of the cam center, it is called an off-set follower.
Follower with zero offsets and Follower with offset
If the follower movement is a displacement from the cam centre, then the follower is called an offset follower, offsetting results in reduced forces and stresses.
The offsetting eccentricity should be in the direction to improve force components tending to jam the translating follower in its bearing guide and decrease the wear between follower and cam surface.

Transmission angle is the angle between
  • a)
    Output link and fixed link
  • b)
    Input link and fixed link
  • c)
    Input link and coupler
  • d)
    Output link and coupler
Correct answer is option 'D'. Can you explain this answer?

Aarav Sharma answered
Transmission angle is the angle between the output link and the coupler in a mechanism. It is an important parameter in the analysis and design of mechanisms, as it affects the motion and efficiency of the system. The correct answer is option 'D', which states that the transmission angle is the angle between the output link and the coupler.

Explanation:
- Transmission angle is an important concept in the study of mechanisms. It is defined as the angle between the output link and the coupler in a mechanism. The output link refers to the link that provides the desired output motion, while the coupler is the link that connects the input and output links.
- The transmission angle is a measure of the misalignment between the output motion and the desired motion. A smaller transmission angle indicates a more efficient transfer of motion, while a larger transmission angle indicates a less efficient transfer of motion.
- In a mechanism, the input link is connected to the fixed link, which provides a stable base for the mechanism. The fixed link does not move during the operation of the mechanism. Therefore, the transmission angle is not related to the input link and the fixed link.
- Similarly, the transmission angle is not related to the input link and the coupler. The input link provides the input motion to the mechanism, while the coupler connects the input and output links. The transmission angle is not affected by the input link and the coupler.
- The correct answer is option 'D', which states that the transmission angle is the angle between the output link and the coupler. This is the angle that determines the efficiency of the motion transfer in a mechanism.
- By analyzing the transmission angle, engineers can optimize the design of mechanisms to minimize the transmission angle and improve the efficiency of motion transfer. This can lead to more reliable and efficient mechanisms in various applications.

During sensible heating of moist air, enthalpy
  • a)
    Increases
  • b)
    Decreases
  • c)
    Remains same
  • d)
    Can increase or decrease
Correct answer is option 'A'. Can you explain this answer?

Rajesh Khanna answered
Sensible heating
During this process, the moisture content of air remains constant, and its temperature increases as it flows over a heating coil. The heat transfer rate during this process is given by:
Qh = ma(hB−ho) = macpm(TB−To)
where cpm is the humid specific heat (≈1.0216 kJ/kg dry air), tangent direction, and ma is the mass flow rate of dry air (kg/s).
Sensible heating process
on psychrometric chart
During sensible heating of moist air, enthalpy increases.
Sensible cooling:
During this process, the moisture content of air remains constant, but its temperature decreases as it flows over a cooling coil.
Sensible cooling process
on psychrometric chart

Figure out the odd point in the following
  • a)
    Proportional limit
  • b)
    Elastic limit
  • c)
    Yield point
  • d)
    Fracture point
Correct answer is option 'D'. Can you explain this answer?

Tanvi Shah answered
Proportional limit, Elastic limit, and yield point are points before metal failure, but fracture point is a point of failure where metal fractures.
  • So it is evident from the graph that the strain is proportional to stress or elongation is proportional to the load giving a straight-line relationship. This law of proportionality is valid up to a point A. Point A is known as the limit of proportionality or the proportionality limit.
  • For a short period beyond point A, the material may still be elastic in the sense that the deformations are completely recovered when the load is removed. The limiting point B is termed as Elastic Limit.
  • Beyond the elastic limit, plastic deformation occurs, and strains are not totally recoverable. There will be thus permanent deformation or permanent set when the load is removed. These two points are termed upper and lower yield points, respectively. The stress at the yield point is called the yield strength.
  • A further increase in the load will cause marked deformation in the whole volume of the metal. The maximum load which the specimen can withstand without failure is called the load at the ultimate strength. The highest point ‘E' of the diagram corresponds to the ultimate strength of a material.
  • Beyond point E, the bar begins to form the neck. The load falls from the maximum until a fracture occurs at F.

Separation of flow occurs when pressure gradient:
  • a)
    Tends to approach zero
  • b)
    Becomes negative
  • c)
    Changes abruptly
  • d)
    Reduces to a value when vapour formation starts
Correct answer is option 'C'. Can you explain this answer?

Knowledge Hub answered
  • Flow separation occurs when the boundary layer travels far enough against an adverse pressure gradient that the speed of the boundary layer relative to the object falls almost to zero.
  • It has been observed that the flow is reversed in the vicinity of the wall under certain conditions.
  • A favourable pressure gradient is one in which the pressure decreases in the flow direction (i.e., dp/dx < 0)="">
  • It tends to overcome the slowing of fluid particles caused by friction in the boundary layer.
  • This pressure gradient arises when the freestream velocity U increases with x, for example, in the converging flow field in a nozzle.
  • On the other hand, an adverse pressure gradient is one in which pressure increases in the flow direction (i.e., dp/dx > 0)
  • It will cause fluid particles in the boundary layer to slow down faster than that due to boundary-layer friction alone.
  • If the adverse pressure gradient is severe enough, the fluid particles in the boundary layer will actually be brought to rest.
  • When this occurs, the particles will be forced away from the body surface (a phenomenon called flow separation) as they make room for following particles, ultimately leading to a wake in which flow is turbulent.

Which of the following statements does NOT apply to the volumetric efficiency of a reciprocating air compressor?
  • a)
    It decreases with an increase in inlet temperature
  • b)
    It increases with a decrease in pressure ratio
  • c)
    It increases with a decrease in clearance ratio
  • d)
    It decreases with an increase in clearance to stroke ratio
Correct answer is option 'A'. Can you explain this answer?

Bank Exams India answered
In actual compressors, a small clearance is left between the cylinder head and piston to accommodate the valves and to take care of thermal expansion and machining tolerances.
A large clearance volume results in low volumetric efficiency and hence large cylinder dimensions increase the contact area between the piston and cylinder and so, increases friction and work.
Volumetric efficiency is given by:
Where c = Clearance ratio.
P2/P1=Pressure;ratio
As the clearance ratio increases, the volumetric efficiency of the reciprocating compressor decreases as the pressure ratio increases.

A thin cylindrical shell under internal pressure can fail along the
  • a)
    Longitudinal joint
  • b)
    Circumferential joint
  • c)
    Longitudinal as well as circumferential joint
  • d)
    None
Correct answer is option 'C'. Can you explain this answer?

Sagar Sharma answered
Understanding Failure Modes of a Thin Cylindrical Shell
A thin cylindrical shell subjected to internal pressure can fail due to various factors. The failure can occur along specific joints, and understanding these is crucial in engineering applications.
Failure Along Longitudinal and Circumferential Joints
- Circumferential Joint Failure: This is typically the primary failure mode. The internal pressure exerts a hoop stress, which is greatest at the circumferential direction. As a result, the shell is more susceptible to failure here.
- Longitudinal Joint Failure: While the longitudinal direction has lower stress compared to the circumferential, it can still fail under significant internal pressure. This is especially true if there are defects or weaknesses along the joint.
Combined Failure Potential
- Simultaneous Failure: In many cases, the failure can occur along both the longitudinal and circumferential joints. This is due to imperfections in the material or construction that may lead to weaknesses in both directions.
- Material Fatigue and Flaws: Over time, materials can experience fatigue, and any pre-existing flaws can exacerbate the risk of failure in either direction.
Conclusion
In summary, the correct answer to the failure modes of a thin cylindrical shell under internal pressure is option 'C'—the potential for failure along both longitudinal and circumferential joints. Understanding these failure mechanisms is vital for ensuring the integrity and safety of cylindrical pressure vessels in various applications.

The temperature strain in a bar is ________ to the change in temperature.
  • a)
    Indirectly proportional
  • b)
    Directly proportional
  • c)
    Independent
  • d)
    Equal
Correct answer is option 'B'. Can you explain this answer?

Rajesh Khanna answered
When the temperature of the material changes, there will be a corresponding change in dimension.
When a member is free to expand or contract due to the rise or fall of the temperature, no stress will be induced in the member.
But, if the material is constrained (i.e., the body is not allowed to expand or contract freely), change in length due to rise or fall of temperature is prevented, stresses are developed in the body, known as thermal stress.
The change in length (ΔL) due to change in temperature is found to be directly proportional to the total length of the specimen. Stresslength of the member (L) and to the change in temperature (ΔT).
ΔL ∝ L ΔT
ΔL = αLΔT
Where α is known as the coefficient of thermal expansion and is defined as the change in a unit length of the material due to a unit change in temperature.
Temperature strain: ϵ = change in length/original length
So thermal strain is directly proportional to the change in temperature.
Thermal Stress = Strain × E = αΔTE

The air standard Otto cycle consists of
  • a)
    Two constant volume and two isentropic processes
  • b)
    Two constant pressure and two isentropic processes
  • c)
    Two constant pressure and two constant volume processes
  • d)
    None of the above
Correct answer is option 'A'. Can you explain this answer?

Learners World answered
Air standard Otto cycle consists of two constant volume and two isentropic processes.
Process 1–2: An adiabatic (isentropic) compression
Process 2–3: A constant-volume heat addition
Process 3–4: An Adiabatic (isentropic) expansion
Process 4–1: A constant-volume heat rejection

For laminar flow in a pipe, average velocity is equal to:
  • a)
    2 Umax
  • b)
    Umax
  • c)
    0.5 Umax
  • d)
    0.25 Umax
Correct answer is option 'C'. Can you explain this answer?

Om Desai answered
For a fully developed laminar viscous flow through a circular pipe, the maximum velocity is equal to twice the average velocity.
i.e. Vmax=2×Vavg
Vavg=0.5×Vmax
Point to be remembered:
For the fully developed laminar flow through the parallel plates, the maximum velocity is equal to the (3/2) times of the average velocity.
i.e.

Select the option that is related to the third term in the same way as the second term is related to the first term.
SECOND: CDENOS:: FIRST:?
  • a)
    FIRST
  • b)
    FIRTS
  • c)
    RFITS
  • d)
    IRFTS
Correct answer is option 'A'. Can you explain this answer?

Om Desai answered
Given the first term SECOND and the second term is CDENOS.
Here, the alphabets of the given second term are arranged in alphabetical order.
SECOND → CDENOS
Similarly, the third term FIRST will be written as
FIRST → FIRST (since all the alphabets are already in alphabetical order)
Hence, “FIRST” is the correct answer.

In an engine, the fluctuation of speed is ± 2% of mean speed. Then coefficient of fluctuation of speed is
  • a)
    0.01
  • b)
    0.03
  • c)
    0.05
  • d)
    0.04
Correct answer is option 'D'. Can you explain this answer?

Rhea Reddy answered
Concept:
The difference between the maximum and minimum speeds during a cycle is called the maximum fluctuation of speed. The ratio of the maximum fluctuation of speed to the mean speed is called the coefficient of fluctuation of speed (Cs).
Calculation:
ωmax – ωmin = ± 2% of ωmean
⇒ ωmax – ωmin = 4% of ωmean⇒ ωmax – ωmin = 0.04 ωmean
⇒

The design of thin cylindrical shells is based on
  • a)
    Radial stress
  • b)
    Hoop stress
  • c)
    Longitudinal stress
  • d)
    Arithmetic mean of the hoop and the longitudinal stress
Correct answer is option 'B'. Can you explain this answer?

Learners World answered
The wall of a cylindrical shell subjected to internal pressure has to withstand tensile stresses of the following two types:
Circumferential or hoop stress, and (b) Longitudinal stress
Longitudinal stress:
Hoop stress:
We see that the longitudinal stress is half of the circumferential or hoop stress. Therefore, the design of a pressure vessel must be based on the maximum stress i.e., hoop stress.

Lathe bed is usually made of_______.
  • a)
    Structural steel
  • b)
    Stainless steel
  • c)
    Cast iron
  • d)
    Mild steel
Correct answer is option 'C'. Can you explain this answer?

Bank Exams India answered
Lathe is a machine tool that holds the job in between the centre and base and rotates the job, and rotates the job on its own axis.
Main parts of Lathe:

According to the linear law of machine, when P is the effort and w is the load, then.
  • a)
    P = mw + c
  • b)
    P = pmc
  • c)
    P = mw - c
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Rhea Reddy answered
The law of the machine is (where P = Effort applied to lift the load, m = A constant which is equal to the slope of the line, W = Load lifted, and C = Another constant which represents the mechanical friction.)

During the colonial period, British capital was mainly invested in:
  • a)
    Infrastructure
  • b)
    Industry
  • c)
    Agriculture
  • d)
    Services
Correct answer is option 'C'. Can you explain this answer?

Om Desai answered
During the British Raj(from 1858 to 1947), the Indian economy essentially remained stagnant, growing at the same rate (1.2%) as the population. India experienced deindustrialization during this period. After 1857, the inflow of British capital and enterprise into India rose to an appreciable extent. The bulk of the imperialist capital was mainly invested in the externally oriented sectors like plantations, jute, and coal, and the trading and banking infrastructure established to service this sector. This ultimately led to the perpetuation of the subordination of Indian capital to the British capital with the ulterior motive of feeding Britain and other countries with cheap raw materials and food.

An orifice meter, having an orifice of diameter ‘d’ is fitted in a pipe of diameter D. For this orifice meter, what is the coefficient of discharge Cd?
  • a)
    A function of Reynolds number only
  • b)
    A function of d/D only
  • c)
    A function of d/D and Reynolds number
  • d)
    Independent of d/D and Reynolds number
Correct answer is option 'C'. Can you explain this answer?

Aisha Gupta answered
An orifice meter provides a simpler and cheaper arrangement for the measurement of flow through a pipe. An orifice meter is essentially a thin circular plate with a sharp-edged concentric circular hole in it.
Cd is defined as the ratio of the actual flow and the ideal flow and is always less than one.
For the orifice meter, the coefficient of discharge Cd depends on the shape of the nozzle, the ratio of pipe to nozzle diameter, and the Reynolds number of the flow.

In limits and fits system, basic shaft system is one whose
  • a)
    Lower deviation is zero
  • b)
    Upper deviation is zero
  • c)
    Minimum clearance is zero
  • d)
    Maximum clearance is zero
Correct answer is option 'B'. Can you explain this answer?

Rhea Reddy answered
Hole basis system: The hole is kept as a constant member (i.e. when the lower deviation of the hole is zero).
Shaft basis system: When the shaft is kept as a constant member (i.e. when the upper deviation of the shaft is zero).

In a thermocouple, the potential between the two functions is due to the temperature gradient along the conductors in the circuit. This effect is named as
  • a)
    Peltiers effect
  • b)
    Thomson's effect
  • c)
    Seebak effect
  • d)
    Maxwell's effect
Correct answer is option 'B'. Can you explain this answer?

Rhea Reddy answered
Thomson effect, the evolution or absorption of heat when an electric current passes through a circuit composed of a single material that has a temperature difference along its length. This heat transfer is superimposed on the common production of heat associated with the electrical resistance to currents in conductors.

The depth of a fluid is measured in vertical Z – direction; X and Y are the other two directions and are mutually perpendicular. The static pressure variation in the fluid is given by
  • a)
    dp/dz = g
  • b)
    dp/dz = 0
  • c)
    dp/dz = ρg
  • d)
    dp/dz = −ρg
Correct answer is option 'D'. Can you explain this answer?

Bank Exams India answered
The pressure at any point in a fluid at rest is obtained by the Hydrostatic Law, which states that the rate of increase of pressure in a vertically downward direction must be equal to the specific weight of the fluid at that point.
p = ρgh
Pressure distribution profile
dp/dz = -ω = -pg
dp = -ω.dz
It indicates that a negative pressure gradient exists upward along any vertical.
Thus, the pressure decreases in the upward direction and increases in the downward direction with a magnitude equal to a specific weight.

Find out the wrong term: 3, 2, 8, 9, 13, 22, 18, 32, 23, 42
  • a)
    8
  • b)
    9
  • c)
    13
  • d)
    22
Correct answer is option 'B'. Can you explain this answer?

Aarav Sharma answered
Incorrect Term in the Given Series

The given series is: 3, 2, 8, 9, 13, 22, 18, 32, 23, 42

To find out the incorrect term in the given series, we need to identify the pattern followed in the series. On observing the series, we can see that:

- The first two terms (3 and 2) are consecutive odd numbers in reverse order.
- The next two terms (8 and 9) are consecutive even numbers in ascending order.
- The next two terms (13 and 22) are consecutive odd numbers in ascending order.
- The next two terms (18 and 32) are consecutive even numbers in ascending order.
- The last two terms (23 and 42) are consecutive odd numbers in ascending order.

Hence, we can see that the pattern followed is that the series alternates between consecutive odd and even numbers in reverse and ascending order, respectively.

Now, we need to identify the term that does not follow this pattern. On observing the series, we can see that:

- 3 and 2 are consecutive odd numbers in reverse order.
- 8 and 9 are consecutive even numbers in ascending order.
- 13 and 22 are consecutive odd numbers in ascending order.
- 18 and 32 are consecutive even numbers in ascending order.
- 23 and 42 are consecutive odd numbers in ascending order.

Hence, we can see that the term '2' does not follow the pattern as it is the only term that is not a consecutive even or odd number in the series.

Therefore, the incorrect term in the given series is '2'.

A submerged body will be in stable equilibrium if the
  • a)
    Centre of buoyancy B is below the centre of gravity G
  • b)
    Centre of buoyancy B coincides with G
  • c)
    Centre of buoyancy B is above the metacentre M
  • d)
    Centre of buoyancy B is above G
Correct answer is option 'D'. Can you explain this answer?

Aarav Sharma answered
Submerged Body in Stable Equilibrium

Stable equilibrium is the state of the body when it returns to its original position after a slight displacement. A submerged body is said to be in stable equilibrium if its centre of buoyancy is above the centre of gravity. Let's understand this concept in detail.

Centre of Buoyancy

The centre of buoyancy is the point through which the buoyant force acts on the body. It is the centroid of the displaced volume of fluid. The position of the centre of buoyancy depends on the shape and size of the body and the density of the fluid.

Centre of Gravity

The centre of gravity is the point through which the weight of the body acts. It is the centroid of the body. The position of the centre of gravity depends on the distribution of mass in the body.

Metacentre

The metacentre is the point of intersection of the vertical line passing through the centre of buoyancy and the new vertical line passing through the displaced centre of buoyancy when the body is tilted slightly.

Submerged Body in Stable Equilibrium

When a submerged body is in stable equilibrium, the following conditions are satisfied:

- The centre of buoyancy is above the centre of gravity.
- The metacentre is above the centre of gravity.

If the centre of buoyancy is below the centre of gravity, the body will be in unstable equilibrium, and if the centre of buoyancy coincides with the centre of gravity, the body will be in neutral equilibrium.

Conclusion

In conclusion, a submerged body is said to be in stable equilibrium if its centre of buoyancy is above the centre of gravity. This condition ensures that the body returns to its original position after a slight displacement. The metacentre should also be above the centre of gravity to maintain stable equilibrium.

Cutting and forming operations can be performed in a single operation in a _______ die.
  • a)
    Progressive
  • b)
    Combination
  • c)
    Simple
  • d)
    Compound
Correct answer is option 'B'. Can you explain this answer?

Sagar Sharma answered
Combination Die:
Combination dies are designed to perform cutting and forming operations in a single operation. This type of die is commonly used in industries where efficiency and productivity are crucial. Here is why combination dies are preferred for such operations:

Efficiency:
- Combination dies eliminate the need for multiple setups and operations, saving time and increasing productivity.
- By combining cutting and forming processes into a single die, manufacturers can streamline their production processes.

Versatility:
- Combination dies can be customized to perform a variety of cutting and forming operations, making them versatile for different manufacturing needs.
- They can produce complex shapes and parts with precision and accuracy.

Precision:
- By integrating cutting and forming operations, combination dies ensure that the final product meets exact specifications and quality standards.
- This precision helps reduce waste and rework, leading to cost savings for the manufacturer.
In conclusion, a combination die is the ideal choice for performing cutting and forming operations simultaneously, offering efficiency, versatility, and precision in manufacturing processes.

The curl of a given velocity field (∇ x -V) indicates the rate of
  • a)
    Increase or decrease of flow at a point
  • b)
    Twisting of the lines of flow
  • c)
    Deformation
  • d)
    Translation
Correct answer is option 'C'. Can you explain this answer?

Rajesh Khanna answered
The curl indicates the rate of deformation.
The angular velocity vector is defined as:
The vorticity of a flow field is defined as:
Rate of rotation of fluid element ABCD about the ?-axis is defined as the average of the angular speeds of two mutually perpendicular lines AB (dx element) and AD (dy element):

When inspection doors on the walls of boilers are opened, the flame does not leap out because
  • a)
    These holes are small
  • b)
    Pressure inside is negative
  • c)
    Flame always travels in the direction of flow
  • d)
    These holes are located beyond the furnace
Correct answer is option 'B'. Can you explain this answer?

Om Desai answered
The flame does not leap out during the opening of the inspection door because there is negative pressure in the combustion area. Negative pressure is achieved in balanced draft boilers by using forced draft fans to force air into the boiler (pressuring it) and Induced draft fans to remove air from the boilers to create negative pressure.

Which material has the highest value of poisson's ratio?
  • a)
    Elastic Rubber
  • b)
    Wood
  • c)
    Copper
  • d)
    Steel
Correct answer is option 'A'. Can you explain this answer?

Rajesh Khanna answered
Elastic Rubber: 0.5
Wood: Because wood is orthotropic, 12 constants are required to describe elastic behaviour: 3 moduli of elasticity, 3 moduli of rigidity, and 6 Poisson’s ratios (vary from 0.02 to 0.47). These elastic constants vary within and among species and with moisture content and specific gravity.
Copper: 0.33
Steel: 0.27 - 0.30

The maximum shear stress in a shaft, of diameter ‘d’ subjected to torsion ‘T,’ is given by:
  • a)
    16T/πd3
  • b)
    up>(B) 64T/πd3
  • c)
    up>(C) 8T/πd3
  • d)
    up>(D) 32T/πd3
Correct answer is option 'A'. Can you explain this answer?

Rhea Reddy answered
Torsion Equation:
Where T is torque applied on the shaft in N−m
is the polar moment of inertia m4
T is shear stress in MPa, r is the radius of the shaft in m, G shear modulus or modulus of rigidity in MPa
θ is the angle of twist in radian, and 1 is the length of the shaft in m.Tmaxoccurs at rmax

Find the odd number/letters / word from the given alternative:
  • a)
    27
  • b)
    35
  • c)
    18
  • d)
    9
Correct answer is option 'B'. Can you explain this answer?

Aarav Sharma answered
Explanation:

To determine the odd number/letters/word from the given alternatives, we need to identify the pattern or rule that is being followed by the options. Let's analyze each option:

a) 27: This is an odd number. It can be expressed as 3 * 3 * 3, which is the cube of 3.

b) 35: This is an odd number. There doesn't appear to be any specific pattern or rule.

c) 18: This is an even number. It can be expressed as 2 * 3 * 3, which is the product of 2 and the square of 3.

d) 9: This is an odd number. It can be expressed as 3 * 3, which is the square of 3.

From the given options, the only odd number is 35. Therefore, the correct answer is option 'B'.

Summary:

- Option 'A' (27) is an odd number.
- Option 'B' (35) is an odd number.
- Option 'C' (18) is an even number.
- Option 'D' (9) is an odd number.
- The odd number/letters/word among the given alternatives is option 'B' (35).

A long fin extends from the external surface of a cylinder through which hot fluid flows; the excess temperature at the tip of the fin would be
  • a)
    Zero
  • b)
    Ambient temperature
  • c)
    higher than ambient temperature
  • d)
    Lower than ambient temperature
Correct answer is option 'A'. Can you explain this answer?

Rhea Reddy answered
Determination of fin length is an important step in designing a fin once its cross-sectional area has been determined. The longer the fin, the larger is the surface area, and the higher is the heat transfer. However, it is not necessary that the fin should be infinitely long for maximum heat transfer. It has been observed that the temperature drops along the fin exponentially and reaches an environmental temperature at some point along the fin length. Beyond this point, the length of the fin does not contribute to the heat transfer; therefore, designing extra-long fin results in material waste, excessive weight, and increased size at increased cost without any benefit in return.

To replace a pipe of diameter D by n parallel pipes of diameter d, the formula used is
  • a)
    d = D/n
  • b)
    d = D/n1/2
  • c)
    d = D/n3/2
  • d)
    d = D/n2/5
Correct answer is option 'D'. Can you explain this answer?

Aarav Sharma answered
Replacing a Pipe with Parallel Pipes

To replace a pipe of diameter D with n parallel pipes of diameter d, the formula used is:

d = D/n^0.4

Explanation:

- The formula for the hydraulic diameter of a pipe is given by:

Dh = 4A/P

where Dh is the hydraulic diameter, A is the cross-sectional area of the pipe, and P is the wetted perimeter of the pipe. For a circular pipe, the hydraulic diameter is simply the diameter of the pipe.

- The formula for the flow rate (Q) through a pipe is given by:

Q = (π/4)D^2v

where v is the velocity of the fluid in the pipe.

- If we replace the single pipe of diameter D with n parallel pipes of diameter d, the total cross-sectional area of the parallel pipes is n times the cross-sectional area of the single pipe. Therefore, the velocity of the fluid in the parallel pipes will be n times less than the velocity in the single pipe to maintain the same flow rate (Q).

- Using the continuity equation, we can relate the velocity of the fluid to the cross-sectional area of the pipe:

Q = Av

where A is the cross-sectional area of the pipe.

- Combining the above equations, we get:

(π/4)D^2v = n(π/4)d^2(v/n)

Simplifying this equation, we get:

d = D/n^0.4

Therefore, the formula used to replace a pipe of diameter D with n parallel pipes of diameter d is:

d = D/n^0.4

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