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Contents list

1. Part 1
   • Working of steam turbine
   • T-S diagram Description
2. Task A
   • Explanation of First law of thermodynamics
3. Task B
   • Viscosity
   • Kinematic viscosity
   • Properties of viscous fluids
   • Different Viscosity measurement techniques/Instruments
   • Shear force affecting the Newtonian fluid details
4. Task C
   • Analysis of Fluid system and hydraulic machines
   • Buckingham’s Pi theorem
   • Importance of Reynolds number (Re)
   • Dimensionless Analysis using Buckingham’s Pi theorem
5. Reference list
   • Bibliography

Part 1

Working:

The working of steam turbine involves hot water entering into the boiler. The steam is generated as a result of water entering into the boiler. The main aim of this is to generate the electricity, steam is allowed to pass through a generator .Water is formed when steam is allowed to flow through the condenser. The process is repeated by sending the water back into the boiler (Bruckner, 1999).

Plant layout

Rankine cycle is employed in steam power plants. All the components can be mounted to the steam power plant. The use of a superheater , economizer and an evaporator is to increase the efficiency of the power plant .The economizer in power plant  is used as a heater for the water that is fed and heat is obtained from the flue gas chamber. The water is fed to the Plant economizer before feeding it to the steam turbine.

The economizer starts working by extracting heat of the gases to increase the temperature of the feed water. When cycle is complete steam power plant produces heat by burning of coal and it converts heat energy into electrical energy.

The steam is superheated at the entry or inlet of the turbine because the steam might cool at the entrance of the turbine from the boiler result into the condensation from gas. As a result, the steam is passed through a super-heater and purpose is to increase the temperature of the steam before entering into the turbine thus it prevent it from condensing and releases form of internal energy.

Ts Diagram Description

• Process/cycle 1–2: When pumping of water from low pressure (LP) to high pressure (HP) is carried out. This pumping require a internal energy while water is in a fluid state.
• Process/Cycle 2–3: From process 2-3 the hot water enters the boiler after that heating process is achieve by the burning of coal. The water is then transformed into steam. The input energy can be determined with the help of steam tables,chart etc.
• Process/Cycle 3–4: The steam from the boiler is passed  through a superheater before entering into the turbine. The steam coming out of the turbine decreases in temperature and vapour resulting in condensation. The output of work produced can be determined with the help of calculations.
• Process/Cycle 4–1: After that the steam then enters into the condenser and .steam is condensed from vapour state or liquid state and then again enters into the boiler. The same process is repeated throughout the cycle.

Task A

According to the First law of thermodynamics:

The first law of thermodynamics is a special case of conservation of energy kind and Its direct application in heat engines. It takes into account for internal energy (E). Energy can be transferred in the form of heat and work.

According to first law of thermodynamics,

∆E (internal)=Q+ W

where                                                               ∆E is the internal energy

∆Q is the heat supplied

∆W is the work done on the system

A heat engine employs heat which is one form of energy to carry out work and sends out the additional heat which cannot be employed through the exhaust. Thermodynamics can be defined as the relationship study between heat and work. The first law is the basic principle behind the working of a heat engine. The first law is in tandem with the law of conservation of energy. The first law of thermodynamics states that energy can neither be created can nor be destroyed but can be transferred from one form of energy to the another.

The law of conservation of energy states that energy can neither be created nor destroyed but can be transformed from one form of energy to the other. Therefore it is quite evident that the first law of thermodynamics is related to heat supplied (H_supplied) and work done ( by the system on the surroundings.

Heat engines usually work in a continuous and cyclic manner, by proving energy in the form of heat to one part of the cycle and employing the energy produced in the first half of the cycle to carry out sufficient amount of work in the other part of the cycle.

Therefore it is quite evident that the first law of thermodynamics is related to heat supplied and work done (∆W) by the system on the surroundings.

The properties of perfect gases mainly depend on the following three constraints by the

1. The Pressure (P) exerted by the gas
2. The Volume (V) occupied by the gas.
3. The Temperature (T) of the gas.

According to the Boyle’s Law and Charles law together gives the General Gas equation

The characteristic gas equation is a modified form of general gas equation

PV=mRT

The specific heat of a substance may be defined as the quantity of heat needed to increase the temperature of its mass through 1. It is quite evident that all the substances including solids and liquids have the same specific heat. Gas tends to have different specific heats based on the heating conditions. The different types of specific heats are following as:

1. Specific heat at constant volume (C_v)
2. Specific heat at constant pressure (C_p)

Specific heat at constant pressure (C_v):

The quantity of heat needed to increase the temperature of its mass through 1 at constant pressure is called Specific heat at constant pressure. It is represented by (C_v).

Work was done by the gas at constant pressure= m.c_p (T2 – T1 )

Specific heat at constant volume (C_v):

The quantity of heat needed to increase the temperature of its mass through one degree Celsius at constant volume is called Specific heat at constant volume. It is denoted by (C_v).

Work was done by the gas at constant volume= m.c_p (T2 – T1 )

Where, C_p = Specific heat at constant pressure

C_v = Specific heat at constant volume

T₁ = Initial Absolute temperature or the gas

T₂= Final Absolute temperature of the gas

V₁= Initial volume of the gas

V₂ = Final volume of the gas

P = pressure

Relation Between Two Specific Heats for a perfect gas

Substituting the two equations we get

According to problem,

P₁V₁ = P₂V₂ = P₃V₃=⋯constant

For a polytrophic process,

PVⁿ = constant

Where n – polytropic index,

(120)×(1) = 60×4ⁿ
4ⁿ = 2
Hence ,n (Polytropic index) = 0.513

Thermodynamic processes

• Adiabatic process (Zero heat transfer): It may be defined as the thermodynamics process in which no heat (Q) transferred or exchange between a thermodynamic system as well as its surroundings.
  
• Isobaric process or Isopestic process(P=Constant): It may be explained in which the pressure always remains constant is known as constant pressure process or Isopestic process.
  Work done (W) = P (V_F-V_I)
• Isochoric process or Isometric process (V=Constant): It may be defined as the thermodynamic process in which the volume is always remains constant and also known as constant volume process.
  Work done (W) = 0
• Isothermal process(T=Constant) is defined as the process in which the temperature is constant and also known as constant temperature process.
  
• Isenthalpic process is defined as the process where there is no change in enthalpy between a thermodynamic system and its surroundings (Gaskell and Laughlin, 2017).

Task B

Viscosity

Viscosity is the property of fluid and which provided resistance to the fluid with help of shear stress and also offer resistance to one layer of the fluid over adjacent layer. There are two factors which affect the viscosity are cohesion and molecular momentum.

According to the Newton’s law of viscosity
=> shear stress ∝ shear strain.

Mathematically,

Kinematic viscosity

It can be defined as the ratio of dynamic viscosity (μ) to the density of the fluid (ρ) is known as kinematic viscosity (ϑ).

Properties of viscous fluids

The fluids based on their properties of viscosity can be classified into the following:

1. Ideal Fluid:A fluid which is having no viscosity and is incompressible in nature is called an ideal fluid. Practically, Ideal fluids doesn’t exist.
2. Real Fluid: A fluid which is having viscosity is called real fluids and compressible in nature. Real Fluid implies friction effect and it is considered to be real fluids.
   Example: Oil and Kerosene etc.
3. Newtonian Fluid:The fluids which follows or obey’s a Newton’s law of viscosity are called Newtonian fluids. For this kind of fluid viscosity is entirely depend upon pressure and temperature of liquid fluid.
   Example: Water and emulsions etc.
4. Non-Newtonian Fluid:The fluids that doesn’t follow the Newton’s law of viscosity are known as Non-Newtonian fluids.
   Example : Paste ,Gel and polymer solutions etc.
5. Ideal Plastic Fluid: The fluids having apparent viscosity and it decreases with increase in shear rate and shear stress more than their yield stress is called an ideal plastic fluid.

Viscosity Measurement Techniques

It can be measured using the following methods:

1. Capillary Viscometer– Capillary Viscometer is viscosity measuring instrument basically used to measure pressure drop ( In this viscometer capillary tubes are mounted and it measure the time for the capillary tube to fill the volume of liquid (V_liquid) to pass through the length of the tube (l).
2. Ford Cup type Viscometer – It is basically a simple gravity device and used to measure viscosity of fluid. At the bottom side there is hole or restriction orifice for passing liquid. This arrangement is also known as flow through restriction type.
3. Rotational Viscometer– It determine the viscosity by calculating the resistance of shaft and sometime used to measure the absolute viscosity. This is also known as Brook field viscometer.

Shear Force Affecting the Newtonian Fluid

Newtonian Fluid: The fluids that follows or obey’s the Newton’s law of viscosity are known as Newtonian fluids.

Newton’s law of viscosity states that the shear stress is directly proportional to the shear strain

Therefore if the fluid undergoes shear thickening or shear thinning then the shear stress might affect the Newtonian fluid.

Task C

Analysis of Fluid system and hydraulic machines

A hydraulic fluid system is basically used for transferring and converting fluid energy in the form of useful work. That fluid energy is called as available energy and it is combination Kinetic energy (K.E), Potential energy (P.E) and other energies. The hydraulic machine is kind of tool which convert hydraulic energy into mechanical form of energy and vice-versa.

Dimensional Analysis: The Dimensional analysis is mathematical technique which is used to learn dimension and basically deals with dimension of physical quantities and because of this flow phenomenon is influences .Sometime used for research and reference work as well as for model testing purposes .This phenomenon is known as dimensional analysis

Dimensional variables: The quantities that vary against each other are termed as dimensional variables.

Dimensional constants: They remain constant and are allowed to be the same. They have no dimensions and are considered as pure constants.

Buckingham ‘ s Pi theorem

The dimensions are analyzing by Rayleigh’s Method. The relationship between the variables can be obtain through a method called Buckingham’s π. Buckingham ‘ s Pi theorem state that:

Suppose there are n type variables in a application problem and these variables contains m- type primary dimensions (for i.e M,L,T ) the equation can be relate the the variables will have (n-m) kind of dimensionless groups.

Importance of Reynolds number (Re)

The Reynolds number (Re)  is play very important role in dimensional analysis and It indicate if the flow of fluid will be either laminar or turbulent in nature. It is defined as the ratio between fluid dynamics force and the viscous forces. Sometime Reynolds number is known as dimensionless variables.

Dimensionless analysis using Buckingham Pi theorem for industrial purpose:

When shaft is rotating with N rpm in steam and gas turbine then power (P) will be generated and dimensionless analysis will comes into the picture.

Notations:

P – Power
D – Diameter of impeller
N – Rotation speed

ρ,μ-Density of fluid flowing and Dynamic viscosity respectively

Now we can express all quantities in the function of above variables.

f(P,D,N,μ,ρ ) = 0

Total Number of variables=5

Total Number of dimensions=3 (i.e.M-Mass,L-length and T-Time)

So,Number of dimensionsless groups=Total number of variables-Total dimensions

=> 5-3=2

Selection of variables : D,N and ρ .

Variable	Dimensions
N	[T-1]
D	[L]
ρ	[M1L-3]

From above we can co-relate:

ρ = [M¹L^-3]

=> [M] = ρ [L¹]

=> Now, Dimension of Power (P) = [ML²T^-3]

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