RRB JE ME (CBT II) Mock Test- 2 - Mechanical Engineering MCQ

The equilibrium of a body submerged in a liquid requires that the body’s weight acting through its centre of gravity should be collinear with an equal hydrostatic lift acting through the centre of buoyancy.

• Stable Equilibrium: If the body returns to its original position by retaining the originally vertical axis as vertical
• Unstable Equilibrium: If the body does not return to its original position but moves further from it
• Neutral Equilibrium: If the body neither returns to its original position nor increases its displacement further, it will simply adapt its new position

The relative position of the centre of gravity (G) and centre of buoyancy (B) of a body determines the stability of a submerged body.

Stable Equilibrium: B is above G

Unstable Equilibrium: B is below G

Neutral Equilibrium: B coincides with G

Bernoulli's equation along streamlines

Total Head (H) = Pressure head (P/ρg) + Kinetic head (v2/2g) + Potential head (z)

Total Dynamic Head (H) = Static Head ((P/ρg) + z) + Dynamic Head (v²/2g)

Bernoulli's equation along streamlines

Total head (H) = Pressure head (P/ρg) + Kinetic head (v^2/2g) + Potential head (z)

Total head (H) = Hydraulic gradient line ((P/ρg) + z) + Kinetic head (v²/2g)

The line representing the sum of pressure head, datum head, and velocity head with respect to some reference line is known as total energy line (T.G.L).

The line representing the sum of pressure head and potential head or datum head with respect to some reference line is the hydraulic gradient line (H.G.L) which is always above compared to the centre line of conduct.

Streaklines are the loci of points of all the fluid particles that have passed continuously through a particular spatial point in the past. Thus, dye steadily injected into the fluid at a fixed point extends along a streak line.

Pathlines are the trajectories that individual fluid particles follow. These can be thought of as "recording" the path of a fluid element in the flow over a certain period. The fluid streamlines will determine the direction the path takes at each moment in time.

For steady flow, path lines, streamlines, and streaklines coincide.

Centre of pressure is the point of application of the total pressure force on the surface. It can be found by applying the principle of moments i.e. the sum of the moments of the resultant force about an axis is equal to the sum of the moments of the component force about the same axis.

• A venturi meter is a device used to measure the flow rate of a fluid of liquid flowing through a pipe.

• The venturi meter always have a smaller convergent portion and a larger divergent portion.

• This ensures a rapid converging passage and a gradual diverging passage in the direction of flow to avoid the loss of energy due to the separation.

• In the course of flow through the converging part, the velocity increases in the direction of flow according to the principle of continuity, while the pressure decreases according to Bernoulli’s theorem.

• The velocity reaches its maximum value, and pressure reaches its minimum value at the throat.

• Subsequently, a decrease in the velocity and an increase in the pressure take place in the course of flow through the divergent part.

• The angle of convergence ≈ 20°, Angle of divergence = 6° - 7° → It should be not greater than 7° to avoid flow separation.

• Piezometer is the simplest form of manometer used for measuring gauge pressure.

• One end of this manometer is connected to the point where the pressure is to be measured, and the other end is open to the atmosphere.

• As one end is open to the atmosphere so it can’t be used for measuring the gas pressure

• Gas pressure cannot be measured by means of piezometers because a gas forms no free atmosphere surface and it can’t be used when large pressures in the lighter liquid are to be measured.

Cavitation is the phenomenon of the formation of vapour bubbles of a flowing liquid in a region where the pressure of the liquid falls below the vapour pressure of the fluid and sudden collapsing of these bubbles in the region of higher pressure.

In centrifugal pumps the cavitation may occur at the inlet of the impeller of the pump or at the suction side of the pumps, where the pressure is considerably reduced.

Hence if the pressure at the suction side of the pump drops below the vapour pressure of the liquid then cavitation may occur.

In order to determine whether cavitation will occur in any portion of the suction side of the pump, the critical value of Thoma’s cavitation factor (σ) is calculated.

H = Head developed by the pump

H_S = Suction pressure head in m of water

H_V = Vapour pressure head in m of water

h_LS = Head lost due to friction in the suction pipe

If the value of σ is greater than σc (Critical cavitation factor), the cavitation will not occur in that pump.

So, the cavitation can be reduced by reducing the suction head.

A hygrometer, also known as a psychrometer, is a device that is used to measure the humidity in the air.

A thermometer is a device that measures temperature or a temperature gradient.

A piezometer is a device used to measure liquid pressure in a system by measuring the height to which a column of the liquid rises against gravity.

The difference between the saturation temperature and the temperature of sub cooled liquid at that pressure is called the Degree of subcooling.

Subcooling is beneficial as it increases the refrigeration effect by reducing the throttling loss at no additional specific work input.

Also, subcooling ensures that only liquid enters the throttling device leading to its efficient operation.

Effect of Subcooling:

• Increase the refrigeration effect
• Work input remains same
• Increase in COP

Heat transfer at constant pressure:

δQ_P = mc_pΔT

310 = 2 × c_p (35 – 25) = 20 c_p

c_p = 31/2 = 15.5 J/mol K

R = c_p – c_v ⇒ c_p = c_p – R = 15.5 – 8.3 = 7.2 J/mol K

Heat transfer at constant volume:

δQ = mcvΔT

δQ, = 2 × 7.2 × (35 – 25) = 144 J

The term steady implies no change with time at any point within the medium, while transient implies variation with time or time dependence.

Therefore, the temperature or heat flux remains unchanged with time during steady heat transfer through a medium at any location, although both quantities may vary from one location to another.

During transient heat transfer, the temperature varies typically with time as well as position.

Given:

h₁ = h₂ = 30 W/m²K

L = 15 cm = 0.15 m

k = 0.10 W/mK

The overall heat transfer coefficient, U:

U = 15/226 = 0.07 W/m2K

U ≈ 0.1 ≈ k

The first law of thermodynamics is a restatement of the law of conservation of energy. It states that energy cannot be created or destroyed in an isolated system; energy can only be transferred or changed from one form to another.

When heat energy is supplied to a gas, two things may occur:

• The internal energy of the gas may change
• The gas may do some external work by expanding

According to the first law of Thermodynamics:

δQ = δW + ΔU

When a system executes a process, the change in stored energy of the system is numerically equal to the net heat interaction minus the network interaction during the process:

ΔU = δQ – δW where U is the internal energy which is introduced by this law.

For the cyclic process: ΔU = 0

The first law of thermodynamics states that for a cyclic process, the cyclic integral of heat is equal to the cyclic integral of work.

The second law of thermodynamics introduces the concept of entropy.

Concept:

The efficiency of Carnot Engine:

Calculation:

Case 1:

η₁ = 40% = 0.4, T_L1 = 300 K

Case 2:

If we need to increase the efficiency by 50% of original, efficiency = 40% + (50/100) × 40% = 40% + 20% = 60%

η₂ = 60% = 0.6, T_L2 = T_L1 = 300 K

Increase in source temperature:

ΔT = T_H2 – T_H1 = 750 – 500 = 250 K

internal energy: U = u (T, V)

For a real gas, the internal energy if a function of both the temperature and the specific volume.

That is,

U = f(T,u)

For ideal gas (∂U/∂V)_T = 0

∴ U = U (T) only

Important Points

For an ideal gas (no intermolecular interactions and no molecular volume), appropriate equation of state would be: PV = nRT ⇒ V = nRT/P i.e. V = f(T,P,n)

There are many equations of state describing real gases. These equations take in consideration molecular volume and interactions. The most well-known such equation is the Van der Waals equation.

The internal energy of an ideal gas is a function of temperature only and is independent of pressure and volume. u = u(T)

Knocking in CI engines occurs because of an ignition lag in the combustion of fuel between the time of injection and the time of actual burning.

As the ignition lag increases, the amount of fuel accumulated in the combustion chamber increases; and when combustion actually takes place, an abnormal amount of energy is suddenly released causing an excessive rate of pressure rise which results in a knock.

Hence a good CI engine fuel should have a short ignition lag so that it will ignite more easily.

The CI engine knock can be controlled by reducing the delay period. The delay is reduced by the following :

a. High charge temperature

b. High fuel temperature

c. Good turbulence

d. Injection of fuel just before TDC

In order to decrease the tendency of knock it is necessary to start the actual burning as early as possible after the injection begins. In other words, it is necessary to decrease the ignition delay and thus decrease the amount of fuel present when the actual burning of the first few droplets starts.

Important Point :

• In the SI engine, knocking occurs near the end of combustion whereas in the CI engine, knocking occurs near the beginning of combustion.

The radiation energy emitted by a body per unit time is given by

E_b = ϵAσT⁴

Where ϵ is emissivity of the body.

σ = The Stefan – Boltzmann constant = 5.67 × 10-8 W m^-2K^-4

Calculation:

For same material and same temperature: E ∝ A

thermal conductivity of a material can be defined as the rate of heat transfer through a unit thickness of the material per unit area per unit temperature difference. The thermal conductivity of a material is a measure of the ability of the material to conduct heat. A high value for thermal conductivity indicates that the material is a good heat conductor, and a low value indicates that the material is a poor heat conductor or insulator. The thermal conductivities of some common materials at room temperature are given as

K_water < K_mercury < K_copper < K_Silver

PVⁿ = C

• n = 0 ⇒ P = C ⇒ Constant Pressure Process (Isobaric Process)
• n = 1 ⇒ PV = C ⇒ Constant Temperature Process (Isothermal process)
• n = γ ⇒ PV^γ = C ⇒ Adiabatic Process
• n = ∞ ⇒ V = C ⇒ Constant Volume Process (Isochoric process)

Area under P-V diagrams represents the work done.

For compression between two volumes, we can see that area is maximum for the adiabatic process.

So work done on the gas will be maximum for the adiabatic process.

Concept:

Wien’s displacement law

For a black body emissive spectrum, the wavelength λmax giving the maximum emissive power at a temperature is inversely proportional to the absolute temperature.

λ_max = C/T

λ_maxT= C

λ₁T₁ = λ₂T₂

The radiation energy emitted by a black body per unit time is given by:

E_b = σAT⁴

The radiation energy emitted by a body per unit area per unit time is given by:

E_b = ϵσT⁴

Calculation:

E₂ = 16 × E₁

The modulus of resilience is defined as the maximum energy that can be absorbed per unit volume without creating a permanent distortion (i.e. The proof of resilience per unit volume of a body is called modulus of resilience).

σ_t = Eɑ△T = 250 x 10⁹ x 10 x 10^-6 x 150 = 375 MPɑ

The shear force is of at point is given by the slope of the bending moment diagram at that point.

Where,

V = shear force

M = bending moment

The value of distributed load at any point is equal to the slope of the shear force diagram at that point.

Modulus of rigidity is associated with the change in the shape of a body.

Note:

Young’s Modulus of Elasticity is associated with the change in the length of a body.

Bulk Modulus of Elasticity is associated with the change in the volume of a body.