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Content

1. Part A
   • Working
   • Ts Diagram Description
2. Task A
   • First Law of Thermodynamics
3. Task B
   • Viscosity
   • Kinematic Viscosity
   • Properties of Viscous Fluids
   • Different Viscosity Measurement Techniques
   • Shear Force Affecting the Newtonian Fluid
4. Task C
   • Fluid System and Hydraulic Machines
   • Buckingham’s Pi Theorem
   • Reynolds Number (Re)
   • Application Problem
5. References
6. Bibliography

Part A

Working

The working of steam turbine involves water entering into the boiler. The steam is produced as a result of water entering into the boiler. For the purpose of creating 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. (Gaskell and Laughlin, 2017).

Plant Layout

Rankine cycle is employed in steam power plants. A number of other components can be attached to the steam power plant. The use of a super heater, economizer and an evaporator the efficiency of the power plant is increased. The economizer is used as a heater for the water that is fed and heat is obtained from the flue gases. The water is fed to the economizer before feeding it to the turbine.

The economizer works by extracting heat of the gases to increase the temperature of the feed water. The steam power plant produces heat by burning of coal and converts heat energy into electrical energy.

The steam is superheated at the entry of the turbine because the steam might cool while entering into the turbine from the boiler resulting in condensation from gas. As a result the steam is passed through a super-heater to increase the temperature of the steam before entering into the turbine thereby preventing it from condensing and loose its internal energy.

Ts Diagram Description

• Process 1–2: Pumping of water from low pressure to high pressure is carried out. This pumping requires internal energy since water is in fluid state.
• Process 2–3: The hot water enters into the boiler. The heating process is achieved by burning of coal. The water is then converted into steam.The input energy o be determined can be calculated using hs-charts, steam tables etc.
• Process 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 vapor resulting in condensation. The output can be determined with the help of charts.
• Process 4–1: The steam then enters the condenser. The steam is condensed from vapor sate ro liquid state and again enters into the boiler. The process is repeated.

Task A

First Law of Thermodynamics

The first law of thermodynamics finds its application in heat engines. 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. First law of thermodynamics states that energy can neither be created nor destroyed but can be converted from one form of energy to the other.

The law of conservation of energy states that energy can neither be created nor destroyed but can be converted from one form of energy to the other. Therefore it is quite evident that first law of thermodynamics is related to heat 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.

∆U = Q – W
where ∆U is the internal energy
Q is the heat supplied
W is the work done by the system

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

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

1. Pressure exerted by the gas
2. Volume occupied by the gas.
3. Temperature of the gas.

Laws are governed to attain the changes that might occur. The combination of 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 is 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. A gas tends to have different specific heats based on the heating conditions. The different types of specific heats

1. Specific heat at constant volume
2. Specific heat at constant pressure

Specific heat at constant pressure

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 denoted by C_p.

Work done by the gas at constant pressure = M.C_P (T2 – T1)

Specific heat at constant volume

The quantity of heat needed to increase the temperature of its mass through 1 at constant volume is called Specific heat at constant volume. It is denoted by C_V.

Work done by the gas at constant volume = M.C_v (T2 – T1)

Relation Between Two Specific Heats for a Perfect Gas

where 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

C_P = Specific heat at constant pressure

C_V = Specific heat at constant volume

P = Constant pressure

Substituting the two equations we get

C_p – C_V = R/J

On solving integrating and differentiating the equations we get

P₁V₁ = P₂V₂ = P₃V₃ = …constant

Problem

For a polytrophic process

PVⁿ = constant

(120)(1) = (60)(4)n

4n = 2

n = 0.513

Thermodynamic Processes

• An adiabatic process is defined as the process where there is no heat transfer between a thermodynamic system and its surroundings.
• An isobaric process is defined as the process in which the pressure remains constant.
• An isochoric process is defined as the process in which the volume remains constant.
• An isothermal process is defined as the process in which the temperature remains constant.
• An 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 C

Viscosity

Viscosity is defined as the fluid property which provided resistance to the movement of one layer of the fluid over an adjacent layer.

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

Kinematic Viscosity

The ratio between dynamic viscosity and density of the fluid is called kinematic viscosity.

Properties of Viscous Fluids

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

1. Ideal Fluid:A fluid which has no viscosity and is incompressible is called an ideal fluid. Ideal fluids are considered to be as imaginary. This is because all fluids tend to have viscosity hence forth there is no ideal fluid.
2. Real Fluid: A fluid which comprises of viscosity are called real fluids. All fluids are considered to be real fluids. e.g. water.
3. Newtonian Fluid:The fluids that obey the Newton’s law of viscosity are called as Newtonian fluids.
4. Non-Newtonian Fluid:The fluids that disobey the Newton’s law of viscosity are called as Non-Newtonian fluids.
5. Ideal Plastic Fluid: The fluids which have shear stress more than their yield stress and the fluids should obey the Newton’s law of viscosity is called an ideal plastic fluid.

Different Viscosity Measurement Techniques

It can be measured using the following methods.

1. Capillary Viscometer– Capillary Viscometer is a method where capillary tubes are employed. The duration for the tube to fill the volume of liquid to pass through the length of the tube.
2. Zahn Cup– Zahn cup comprises of a small jar provided with a handle and containing a minute opening at the bottom. The duration it takes the cup to empty through the hole is related to viscosity.
3. Falling Sphere Viscometer-This method comprises of a sphere whose density is known. The sphere is dropped into the sample fluid and the duration taken by the sphere to reach a specified point is recorded and the viscosity is measured.
4. Vibrational Viscometer– It is employed to determine the damping of an electromechanical oscillating resonator submerged in the fluid.
5. Rotational Viscometer– It is employed to determine the torque that is needed to turn the object in a fluid as a function of that fluid’s viscosity.

Viscosity is defined as the fluid property which provides resistance to the movement of one layer of the fluid over an adjacent layer. (Hentschel, et.al, 2017).

Shear Force Affecting the Newtonian Fluid

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

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

shear stress ∝ shear strain

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

Task C

Fluid System and Hydraulic Machines

A fluid machine is considered as a device which is capable of converting the fluid energy that is stored into mechanical energy or converting mechanical energy into fluid energy. The fluid energy that is stored is available as potential, kinetic and intermolecular energy. The mechanical energy that is to be converted is done with the help of a rotating shaft. Machines that employ fluid as the means for doing work are called as hydraulic machines. (Hentschel, et.al, 2017).

Dimensional Homogeneity: The process of grouping variables based on their relationships it is termed as dimensionally homogeneous. The dimensionless quantities must be correct for any system of units and consequently each group of terms in the equation must have the same dimensional representation. This is also known as the law of dimensional homogeneity.

Dimensional Analysis: The systematic procedure of determining the variables in a physical phenomena and grouping them to form a set of dimensionless group 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 analysed using Rayleigh’s Method. The relationship between the variables can be obtained through a method called . Buckingham ‘ s Pi theorem states that:

 If there are n variables in a problem and these variables contain m primary dimensions (for example M, L, T) the equation relating all the variables will have (n-m) dimensionless groups.

Reynolds Number (Re)

The Reynolds number (Re) is a dimensionless quantity. It is used to determine or predict whether the flow is laminar or turbulent. The Reynolds number may be defined as the ration between inertial forces and viscous forces. (Bansal, R.K.,2014)

Application Problem

The power required by an agitator in a steam turbine is a function of the following variables:

1. Diameter of the agitator
2. Number of rotations of the impeller per unit time
3. Viscosity of liquid
4. Density of liquid

f (P, D, N, p, µ) = O

Number of variables = 5

Number of dimensions = 3 (i.e. M, L, T)

Number of dimensionless groups = 5-3 = 2

We need to choose the variables so as to represent the dimensions, and hence choose N, D

 In terms of dimensions, N = [T^-I]

therefore, [T] = N^-l

Similarly, D = [L],

[L] = D

p = [ML ^-3],

[M] = p[L³ ]

For the other variables:

The dimensions of power,

P, is [ML ² T ^-3]

Therefore, PM^-l L ^-2 T ³ must be dimensionless

π = P (pD³) ^-I (D)^-2 (N -1) ³

The dimensions of µ is [ML ^-1 T ^-1]

Therefore, µM^-1 L T must be dimensionless

π₂ = µ (p D³) ^-1 (D) (N^-I)

= µ (p^-I D^-3) (D) (N^-I)

π₂ = µ / p D² N

On solving both the equations we get

∆P / pv² = f ( L/ d ,vpd/µ)

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