Mechanical Engineering Test - 4

Explanation:

Fourier number :

Fourier number is defined as the ratio of heat conducted to heat stored in the system.

• Also, it is defined as the ratio of operating time to diffusion time.

Biot number:

Biot number is the ratio of internal conduction resistance within solid to external convective resistance at body surface.

Nusselt number

It is the ratio of heat flow rate by convection process to the heat flow rate by the conduction process or it can be defined as the ratio of conductive thermal resistance to the surface convective resistance.

Thermal diffusivity:

where k is thermal conductivity in W/m-k, ρ is density in kg/m³ and c specific heat capacity in J/kg-K

It is the property of the material. The larger the value of α, the faster heat will diffuse through the material. A high value of α could result either from a high value of thermal conductivity or low value of thermal heat capacity ρc. Thermal diffusivity α has units of square meters per second.

Explanation:

The stress-strain diagrams for different type of materials are given below:

Concept:

Reversible work and irreversibility

• Reversible work (W_rev) is the maximum amount of useful work that can be produced as a system undergoes a process between the specified initial and final states.
• For a process that require work, reversible work represents the minimum amount of work necessary to carry out that process.
• The difference between the reversible work and the useful work (W) is due to irreversibility.
• The irreversibility is equivalent to the exergy destroyed.
• For a total reversible process, the actual and reversible work terms are identical, and thus the irreversibility is zero.
• Irreversibility represents the energy that could have been converted to work but could not be converted because of the effects like friction losses, heat transfer through the finite temperature difference, etc.
• If Heat transfer takes place from a reservoir which is at the almost same temperature to the system then sgen is zero. If we are using infinite reservoirs then it will always be the case as written above, therefore overall sgen will be zero and the whole process will be reversible.

The irreversibility (I) of the process is defined as

I = W_r – W

Where,

W_r = Reversible work

W = Actual work

If the reversible work equal irreversibility ,

⇒ W_r = I;

⇒ W = 0 

∴ Actual useful work is zero

Concept:

Using the equilibrium of forces in the vertical direction,

∑F_vertical = 0

Explanation:

Atomic packing factor

In the crystal structure, the atomic packing factor (APF) or packing efficiency or packing fraction is the fraction of volume in a crystal structure that is occupied by constituent particles. It is a dimensionless quantity and always less than unity.

The atomic packing factor of different crystal structures is given in the table below:

Important Point:

Co-ordination number: The coordination number of an atom is the number of atoms it is touching in a unit cell.

Concept:

Surface tension on a liquid droplet (Spherical droplet of water): Pressure intensity inside the droplet:

Surface tension on a hollow bubble (Soap bubble): Pressure intensity inside the droplet:

where σ is the surface tension of the liquid.

Concept:

The minimum number of teeth on the pinion is given by:

where, t_min = minimum number of teeth on the pinion, t = number of teeth on the pinion, T = number of teeth on the gear, A_p = Addendum fraction, ϕ = Pressure angle.

Calculation:

Given:

Pinion and gear have an equal number of teeth, i.e. t = T

Additional Information

Increasing teeth decreases interference

Interference is a phenomenon in which the addendum tip of gear undercuts into the addendum or base circle of a pinion.

This tooth interface can be reduced by increasing the number of teeth above a certain minimum number.

Explanation:

Reheating

• In the reheat cycle, the total expansion of steam from the boiler to condenser pressure is carried out in more than one stage with reheating of steam in between the stages.
• The main advantage of the reheat cycle is that it increases the dryness fractions of steam at the condenser inlet thus making it possible to use higher boiler pressure. It also increases the net-work output thus decreasing the mass flow rate of steam required for the same power output. 
• By reheating it's not sure that efficiency will increase, it may decrease also depending on the mean temperature of heat addition.
• Also, the mean temperature of heat addition doesn't always increase. It depends on the pressure in the reheater and entry pressure.

Concept:

Moment of inertia of a disc about an axis passing through centre and perpendicular to its plane is I_z.