Indrani Banerjee

In this article “Friction factor for turbulent flow” and friction factor for turbulent flow related several information will be discuss. The common method is to determine friction factor for turbulent flow is Moody diagram.

The friction factor is a physical parameter which is a dimensionless. The turbulent flow for a particular given type field is constant. The friction factor for turbulent flow only depends on the geometry of the channel and Reynolds number. The flow is called turbulent when Reynolds number is more than 3500.

What is the friction factor for turbulent flow?

Maximum system of the fluid in the nuclear facilities is work with the flow type of turbulent flow. The resistance of this flow obey the equation of Darcy – Weisbach.

The friction of the turbulent flow is measurement of the shear stress which is applied in the wall of a rod or pipe during the flow of turbulent. The flow of turbulent is obeying the equation of Darcy – Weisbach which is directly proportional to square of mean velocity of the flowing fluid in a certain area.

Turbulent flow:-

1. When the value of Reynolds number is more than 3500 this type of flow called turbulent flow.
2. Mathematical analysis of the turbulent flow is not too easy.
3. Velocity of the turbulent flow is too high.
4. Irregular movement is appearing in fluids which are flow in a motion in turbulent flow.
5. Average motion is appearing in which side fluid is flowing.
6. Turbulent flow in general very common type of flow.
7. The velocity profile of the flow turbulent in a certain area is quickly drops when it comes to the wall of the pipe or rod.
8. The velocity profile of the flow turbulent in a certain area is clearly flat when it comes to the center section of the rod or pipe.

Friction factor for turbulent flow formula:

The Colebrook–White equation is define as f for the Darcy friction factor, the function of for Reynolds number as R_e, pipe relative roughness express as, ε / Dh for both smooth pipes and rough pipes.

The friction factor for turbulent flow formula is,

or,

Where,

D_h (m , ft) = Hydraulic diameter for filling the fluid in circular conduits

D_h = D= Inside diameter of the area from where flow of turbulent is flowing

R_h (m , ft) = Hydraulic radius for filling the fluid in circular conduits

R_h = D/4 = Inside diameter of the area from where flow of turbulent is flowing/4

The equation of Colebrook is solved by numerically for its implicit nature. Now a day Lambert W function is also use to obtain outspoken reformulation the equation of Colebrook.

or,

We will get,

p^x = ax + b

Expanded forms:-

Additional mathematical form of the equation of Colebrook is,

Where,

1.7384…. = 2 log (2 * 3.7) = 2 log (7.4)

18.574 = 2.51 * 3.7 * 2

And,

Or,

Where,

1.1364…. = 1.7384… = – 2 log (2) = 2 log

(7.4) – 2 log (2) = 2 log (3.7)

9.287 = 18.574/2 = 2.51 * 3.7

How to calculate friction factor for turbulent flow?

The process of calculating friction factor for turbulent flow is given below,

1. At first we need to determine the value of Reynolds number for the turbulent flow using this formula,
2. ρ x V x D x μ
3. In the next step relative roughness should be calculated using k/D formula which value to under 0.01
4. In the final step use the Moody formula for the roughness with the help of Reynolds number,

Friction factor for turbulent flow in pipe:

The range friction factor for turbulent flow in pipe is

For smooth pipe,

0.04 At Re 4000 to 1.01 at Re 3 x 10⁶

For rough pipe,

0.045 At Re 4000 to 0.03 at Re 3 x 10⁶

Friction factor for turbulent flow in smooth pipe:

Friction factor for turbulent flow in smooth pipe can be explained by the help of Blasius correlation. Blasius correlation is the simplest form of determine the Darcy friction factor.

Blasius correlation is only applicable for turbulent flow in smooth pipes it is not applicable for turbulent flow in uneven pipes. The value of 100000 of Reynolds number Blasius correlation is valid. In some cases of turbulent flow in uneven pipes is applied only because of its simplicity.

Mathematical equation of Blasius correlation turbulent flow in uneven pipes is given below,

After that the equation is corrected and express as,

With,

Where,

f is a function for the,

D = Pipe diameter express as meter, feet

R = Curve radius express as meter, feet

H = Helicoidal pitch express as meter, feet

Re = Reynolds number which is dimensionless

Reynolds number valid for,

0 < H/D < 25.4

Friction factor for turbulent flow in rough pipe:

The Darcy friction factor for turbulent flow in rough pipe means value of Reynolds number is more than 4000 is expressed by Colebrook – White equation.

or,

Where,

D_h (m , ft) = Hydraulic diameter for filling the fluid in circular conduits

D_h = D = Inside diameter of the area from where flow of turbulent is flowing

R_h (m , ft)= Hydraulic radius for filling the fluid in circular conduits

R_h = D/4 = Inside diameter of the area from where flow of turbulent is flowing/4

The equation of Colebrook is solved by numerically for its implicit nature. Now a day Lambert W function is also use to obtain outspoken reformulation the equation of Colebrook.

or,

We will get,

p^x = ax + b

Expanded forms:-

Additional mathematical form of the equation of Colebrook is,

Where,

1.7384…. = 2 log (2 * 3.7) = 2 log (7.4)

18.574 = 2.51 * 3.7 * 2

And,

Or,

Where,

1.1364…. = 1.7384… = – 2 log (2) = 2 log

(7.4) – 2 log (2) = 2 log (3.7)

9.287 = 18.574/2 = 2.51 * 3.7

Friction factors for turbulent flow in curved pipes:

In order to calculate the pressure drop with in a coil or pipe the friction factor should be calculated at first.

Friction factors for turbulent flow in curved pipes is discuss below,

D = Internal diameter of the coil or pipe

R = Darius of the coil or pipe helix

De = Dean Number

Re_c = Transitional Reynolds number

f_c = Friction factor of the coil or pipe which smooth

f_rough = Friction factor for a rough coil or pipe

f_smooth = Friction factor for a smooth coil or pipe

When a single phase flow is appear in a pipe or coil which shaped is curved a secondary flow pattern is introduce in the coil or pipe, in this time friction factor and fluid behaviour start to changes.

As the effect of stabilization of fluid flow the output is comes increases the Reynolds number at that point when flow is enter to the coil or pipe the transition flow form laminar flow to the flow of turbulent.

This condition mathematical form is given below,

To calculate the friction factor in a pipe or coil the Dean number is needed,

After this we easily can determine the friction factor for a smooth coil or pipe.

For,

De < 11.6

f_c = 64/Re

For,

11.6 < De < 200

For, De > 2000

For calculation of totally turbulent flows determine the friction factor for a smooth coil or pipe using this equation,

The range is,

Moody diagram friction factor for turbulent flow:

In the flow of turbulent the relation between Reynolds number represent as Re, friction factor represent as f_D, and relative roughness represent as ∈/D is complicated.

The expression for Moody diagram friction factor for turbulent flow is,

Frequent Asked Questions:-

Question:- Write about the Darcy friction factor chart.

Solution:- Darcy friction factor chart is combination of four physical parameters such as, pressure loss coefficient, Reynolds number, and relative roughness of the coil or pipe and diameter ratio of the coil or pipe.

Darcy friction factor chart is dimensionless physical factor with the help of Darcy – Weisbach equation can be written as,

Pressure drop can be calculate as,

Or,

The expression for Darcy friction factor for laminar flow is,

f_D = 64/Re

In the flow of turbulent the relation between Reynolds number represent as Re, friction factor represent as f_D, and relative roughness represent as ∈/D is complicated.

The expression for Darcy friction factor for turbulent flow is,

In this article “Thermal insulation examples” will be discuss with its related several facts. Thermal insulation examples are not suitable for transferring the heat from one circumstance to another circumstance.

13+ Thermal Insulation Examples with several facts are listed below,

• Glass
• Asbestos
• Bakelite
• Mica
• Rubber
• Paper
• Silk or cotton
• Ceramics
• Dry air
• Wood
• Diamond
• Plastic
• Styrofoam

Thermal insulation examples:-

In our surroundings lots of insulators are present in solid state. The examples solid state insulators are,

Glass:-

1. The solid insulator example is glass. From the definition of thermal insulation we can get an idea that the heat cannot from one space to another space. The electrons which are present in the glass not able to carry heat just because of the electrons are participating chemical bonds for this reason the electrons are could not get free time to conducting heat and heat cannot flow from circumference to another circumference.
2. Ordinary glass is appropriate example of solid thermal insulator just one problem with the glass is it is brittle.
3. Dielectric constant in nature.
4. Glass has very less temperature coefficient.

Asbestos:-

1. The solid insulator example is Asbestos. The electrons which are present in the asbestos not able to carry heat just because of the electrons are participating chemical bonds for this reason the electrons are could not get free time to conducting heat and heat cannot flow from circumference to another circumference.
2. Not brittle
3. Resistance to heat
4. Resistance to wear
5. Flexible
6. High strength

Bakelite:-

1. Bakelite is heat proof.
2. Bakelite material is acid proof.
3. Bakelite is a material which is very strong in mechanically.
4. Bakelite is a polymer which made with monomers of formaldehyde and phenol.
5. Another solid insulator example is Bakelite. The electrons which are present in the Bakelite not able to carry heat just because of the electrons are participating chemical bonds for this reason the electrons are could not get free time to conducting heat and heat cannot flow from circumference to another circumference.

Mica:-

1. Highly reflective.
2. Flexible
3. Another example of thermal insulator is Mica. The electrons which are present in the mica not able to carry heat just because of the electrons are participating chemical bonds for this reason the electrons are could not get free time to conducting heat and heat cannot flow from circumference to another circumference.
4. Low thermal conductivity.
5. Mica affected by oil.
6. Mica is rigid.
7. In high temperature mechanically the mica became week.
8. High dielectric strength is about 30 kV/mm.

Rubber:-

1. Rubber is the insulator of thermal example. The electrons which are present in the rubber not able to carry heat just because of the electrons are participating chemical bonds for this reason the electrons are could not get free time to conducting heat and heat cannot flow from circumference to another circumference.
2. Rubber has tensile strength.
3. Tear resistance
4. Elongation
5. Abrasion resistance
6. Specific gravity
7. Tensile modulus
8. Hardness

Paper:-

1. The electrical property of the paper is adequately good.
2. Paper is made from wood pulp after that manila fibers are beaten and finally rolled into sheets.
3. Another solid insulator example is Paper. The electrons which are present in the paper not able to carry heat just because of the electrons are participating chemical bonds for this reason the electrons are could not get free time to conducting heat and heat cannot flow from circumference to another circumference.
4. Papers have dielectric strength near about 4 to 10 kV/mm.
5. Hygroscopic
6. The application of paper is wallpaper, filter paper, writing, toilet tissue, security paper and laminated worktops.

Silk or cotton:-

1. Elasticity
2. Light weight
3. Easy to use
4. Initial cost is low
5. Available
6. Silk or cottons have dielectric strength
7. Thermal insulator another example is Silk or cotton. The electrons which are present in the silk or cottons not able to carry heat just because of the electrons are participating chemical bonds for this reason the electrons are could not get free time to conducting heat and heat cannot flow from circumference to another circumference.
8. Silk or cottons can be used in various ways such as cooking oils, making of clothes, towels, sheets, currency paper, animal feed biofuels and many more.

Ceramics:-

1. Ceramics materials are brittle type
2. Hard
3. Nonmagnetic
4. Another solid insulator example is Ceramics. The electrons which are present in the ceramics not able to carry heat just because of the electrons are participating chemical bonds for this reason the electrons are could not get free time to conducting heat and heat cannot flow from circumference to another circumference.
5. Oxidation resistant
6. Prone to thermal shock
7. Ceramics are both thermal insulator and electrical insulator
8. Ceramics uses in cutting tools, in space industry.
9. Ceramics works as both thermal insulator and electrical insulator.

Dry air:-

1. Dry air is thermal insulator. The electrons which are present in the Bakelite not able to carry heat just because of the electrons are participating chemical bonds for this reason the electrons are could not get free time to conducting heat and heat cannot flow from circumference to another circumference.
2. Dry air not easily affected by heat
3. Exerts pressure
4. Can be compressed
5. Affected by altitude
6. Economical
7. Eco friendly
8. Light weight
9. Easy to use
10. Initial cost is low
11. Available

Wood:-

1. Wood has good amount of strength.
2. Wood is another example for thermal insulator. The electrons which are present in the wood not able to carry heat just because of the electrons are participating chemical bonds for this reason the electrons are could not get free time to conducting heat and heat cannot flow from circumference to another circumference.
3. Wood has both two characteristics such as tension and compression
4. Rigid
5. Relatively light weight
6. Easy to install
7. Economical
8. Eco friendly
9. Any type of size and shape can be given to wood.
10. Wood can be used in various fields such as packing, weapons, tools, paper, artwork, constructions and many more.

Diamond:-

1. Diamond is not brittle type
2. Another example is Diamond of thermal insulator. The electrons which are present in the diamond not able to carry heat just because of the electrons are participating chemical bonds for this reason the electrons are could not get free time to conducting heat and heat cannot flow from circumference to another circumference.
3. Diamonds have thermal conductivity
4. Combustibility
5. Compressive strength
6. Tear resistance

Plastic:-

1. Plastic is water resistant
2. Plastic is shock resistant
3. Another example is plastic of thermal insulator, the electrons which are present in the plastic not able to carry heat just because of the electrons are participating chemical bonds for this reason the electrons are could not get free time to conducting heat and heat cannot flow from circumference to another circumference.
4. Light weight
5. Easy to install
6. Maintenance cost in very minimal
7. Easy to give size and shape
8. Combustibility
9. Compressive strength
10. Recyclable

Styrofoam:-

1. Styrofoam is another example of thermal insulator. Thermal insulator material means from where heat cannot flow one area to another area among them Styrofoam is. The electrons of the Styrofoam could not carry electrons just because of the electrons which are present in the Styrofoam they are engage to make chemical bonds to each other for this reasons the electrons are not free to take part in the conduction of heat, for this reason heat could not flow through Styrofoam material.

In this article the “Vapor compression refrigeration cycle” topic and vapor compression refrigeration cycle related facts are going to summarize to briefly that a clear concept can we get from it effortlessly.

In vapor compression refrigeration cycle a refrigerant which is stays in fluid is used within a system which stays in as closed and proposed to going in four methods such as compression, then cooling with condensation, after that that expansion and lastly heating with evaporation.

What is vapor compression refrigeration cycle?

In the system of air conditioning the vapor compression refrigeration cycle is commonly used. The fluid which is works as medium in the vapor compression refrigeration cycle is states in vapor state.

Vapor compression refrigeration cycle can be explain in this way lowering the inside temperature of a closed system than the normal temperature and helps to reject the excess amount of heat from the area of the closed system and after doing this process finally transfer the excess amount of heat in environment.

The compression refrigeration cycle of vapor is used in many purposes like, for domestic purposes, commercial purposes, industrial services and automobile sectors.

In vapor compression cycle the refrigerants which are used commonly they are, NH­_3, R – 12, and R- 11. In the vapor compression cycle of a refrigeration system which components are used they are listed below,

• Refrigerant compressor
• Liquid compressor
• Liquid receiver
• Evaporator valve

Expansion valve These Evaporator valve and Expansion valve both are called as refrigerant control valve.

Vapor compression refrigeration cycle diagram:

The Vapor compression cycle contain liquid refrigerant which act as a medium of the vapor compression refrigeration cycle. The refrigerant changes state of phase during the process for two times.

A simple type of vapor compression refrigeration cycle diagram if we observe then can found main four components.

They are components are,

• Compressor
• Condenser
• Receiver
• Expansion valve
• Evaporator

Compressor:-

The refrigerant when it is vapour state that time it carry lower temperature and lower pressure than the regular one and enters to the compressor of the vapor compression refrigeration cycle from the evaporator of the system. After enter to the evaporator the vapour became carry higher temperature as well as higher pressure. The refrigerant vapor of the system which carries higher temperature and higher pressure is entering to the condenser with the help of discharge valve.

Condenser:-

In the condenser when the refrigerant vapors of the system which carries higher temperature and higher pressure is enter that time the vapor of the refrigerant became condensed and cooled for the coils are present in the pipe inside the air conditioning system.

When the refrigerant is go through the condenser that time latent heat is emitted in the surrounding of the condensing medium which consider as water or air.

Read more about Hydrocyclone Separator

Receiver:-

The liquid refrigerant which is in condensed state of phase is stored in a container from the condenser. The container where liquid refrigerant is stores is known as receiver. After go through the condenser liquid refrigerant is comes to the evaporator by the evaporator valve.

Expansion valve:-

Another name for the expansion valve is throttle valve. The function of expansion valve is to give permission to liquid refrigerant go through with high temperature and high pressure where the liquid refrigerant could reduce its pressure and temperature.

Evaporator:-

In the evaporator of any cooling system contain pipes or coils where the liquid refrigerant has low temperature and low pressure. In evaporator liquid refrigerant is evaporated and transfer into vapor refrigerant where the temperature and pressure is both are stays in low.

In the beginning of the process the liquid refrigerant change its state of phase liquid to vapor and after that the liquid refrigerant change state of phase from vapor state to liquid.

Vapor compression refrigeration cycle T-S and P-V diagram:

For any cooling system the cycle process of vapor compression can be figure out with the help of Pressure – Volume diagram and Temperature –Specific entropy diagram.

• Pressure – Volume diagram
• Temperature –Specific entropy diagram

Pressure – Volume diagram

Temperature –Specific entropy diagram

If we observe the Pressure – Volume diagram and Temperature –Specific entropy diagram then can figure out refrigerant vapor is entr to the compressor in dry saturation situation. After that the saturated and dry refrigerant vapor is enter to the compressor of the refrigeration system at the point 1 where the vapor refrigeration is compress in isentropically process. Now the vapor refrigerant is go from 1 point to 2 point at this particular time pressure is increases from pressure of evaporator to pressure of condenser.

Now at the point 2 saturated refrigerant vapor is enter to the condenser. In condenser heat is emitted at the fixed pressure. For emission of heat normally temperature of the system is decreases and at the same time change of phase is happened. Latent heat is rejected and reaches to liquid refrigerant at saturation temperature at the point of 3.

Then the liquid refrigerant is passes by the expansion valve. In this situation liquid refrigerant decreases its pressure and throttle upbringing the enthalpy constant.

How vapour compression refrigeration system works?

The Vapor compression cycle is a method which is most commonly used in various fields because its cost of charge is very low and the construction of the vapor compression cycle is quite easy to establish.

The cycle process of vapor compression in refrigeration system is working based on reverse Rankine cycle. The Vapor compression cycle process is proceeding in four steps. They are listed below,

• Compression
• Condensation
• Throttling
• Evaporation

In this below section the four steps are discusses,

Compression (Reversible adiabatic compression):

 The refrigerant of vapor compression cycle at low temperature and pressure stretched from evaporator to compressor where the refrigerant is compressed isentropically. The pressure is rises from p₁ to p₂ and temperature is rises from T₁ to T ₂.  The total workdone per kg of refrigerant happened during isentropic compression can be express as,

w = h₂ – h₁

Where,

h₁ = Amount of enthalpy of vapor compression cycle in temperature T₁, at the step of suction of compressor

h₂  = Amount of enthalpy of vapor compression cycle in temperature T₂, at the step of discharge of compressor.

Condensation (Constant pressure heat rejection):

The refrigerant of vapor compression cycle is passes through from compressor to condenser at high temperature and pressure. At constant pressure and temperature the refrigerant is completely condensed. The refrigerant changes its state from vapor to liquid.

Throttling (Reversible adiabatic expansion):

At high temperature and high pressure the refrigerant of vapor compression cycle is expanded through the process of throttling. That time the expansion valve is stays in low temperature and pressure. A little amount of liquid refrigerant is evaporating by the help of expansion valve and a huge amount of liquid refrigerant is vaporised by the help of evaporator.

Evaporation (Constant pressure heat addition):

The refrigerant mixture of vapor and liquid is completely evaporated and changed itself into vapor refrigerant. During this evaporation process the refrigerant is absorb latent heat which state is cool. The amount of latent heat absorption by the refrigerant in vapor cycle is known as Refrigerating effect.

Performance of vapour compression cycle in the refrigeration system:

The vapour compression cycle in the refrigeration system is working at evaporator in the law of Steady Flow Energy Equation,

h₄ + Q_e = h₁ + 0

Q_e = h₁ – h₄

The vapour compression cycle in the refrigeration system is working at condenser in the law of Steady Flow Energy Equation,

h₂ + Q_c = h₃ + 0

Q_c = h₃ – h₂

The vapour compression cycle in the refrigeration system is working at expansion valve in the law of Steady Flow Energy Equation,

h₃ + Q = h₄ + W

We know, value of Q and W is 0

So, we can write,

h₃ = h₄

Performance of vapour compression cycle in the refrigeration system is,

Vapor compression refrigeration cycle steps:

Vapor absorption cycle process is done by four steps.

• Compression process
• Condensation process
• Expansion process
• Vaporization process

Compression process:

In first of the Vapor absorption cycle process compression process is done. In this process vapor stays at very low pressure and temperature.  The vapor is enters to the compressor when it is compressed subsequently and isentropically. After this both temperature and pressure are increases.

Condensation process:

After completing the process in compressor vapor enter to condenser. The vapor is condensed in the high pressure and goes to the receiver tank.

Expansion process:

After completing the process in condenser vapour enter to expansion valve from receiver tank. The throttling process is done in the low pressure and low temperature.

Vaporization process:

After completing the process in expansion valve vapour enter to evaporator. In the evaporator the vapour is extracts heat and circulating fluid in the surrounding environment and in lower pressure vapour is vaporized.

If without throttling expansion is takes place then the level of temperature will be drop in very low temperature and undergoes sensible heat, latent heat to particularly reach to stage of evaporation.

Increasing Vapor compression refrigeration cycle efficiency:

Increasing Vapor compression refrigeration cycle efficiency in a system is listed below,

1. Optimize setting
2. Size of the compressors to match loads as nearly as possible
3. Install VFDs on screw compressor
4. Install VFDs on motor of the compressor
5. Use integrated automation system
6. Use floating head pressure to maintain ideal temperature.

Actual vapor compression refrigeration cycle:

Actual vapor compression cycle refrigeration cycle is not same process as the theoretical vapor compression refrigeration cycle. In the actual vapor compression cycle loss and unavoidable vapor is present.  The refrigerant leaves the evaporator in the state of superheat.

Frequent Asked Questions:-

Question: – Mention the characteristics for good refrigerant.

Solution: – Refrigerant is actually a medium which carry heat during the process of the vapor compression refrigeration cycle. In the refrigeration system heat is absorb from a lower temperature system and after that heat is rejected so system can absorb higher temperature.

The characteristics for good refrigerant is listed below,

1. Refrigerant should have high critical temperature
2. Refrigerant should have low boiling point
3. Non toxic
4. Non flammable
5. Non explosive
6. High latent heat of vaporization
7. Non corrosiveness for the metals uses in the system of vapor compression refrigeration cycle
8. Low specific heat of liquidity refrigerant
9. Low specific heat of vaporized refrigerant
10. Easy to identified leaks by taking smell or suitable indicator
11. Easy to liquefy at moderate temperature and pressure.

Question: – Describe the major difference between Carnot cycle and Rankine cycle.

Solution: – The major difference between Carnot cycle and Rankine cycle is discuss below,

Thermal insulators reduce heat transfer. Examples include aerogel (R-value up to 10.3 per inch), vacuum insulated panels (R-value 45), fiberglass (R-value 2.2-2.7 per inch), polystyrene (R-value 3.6-5), and mineral wool (R-value 3.0-3.3). Each material’s effectiveness varies with thickness and application.Lets discuss few of thermal insulator in detail

9+ Thermal Insulator Examples are listed below,

• Water
• Plastic
• Paper
• Glass
• Styrofoam
• Dry air
• Dry cotton
• Oil
• Rubber

Thermal Insulator Examples:-

Water:-

Water is an example of thermal insulator. The electrons which are present in the water they are engage to make chemical bonds for this reasons the electrons are not free to take part in the conduction of heat, for this reason heat could not flow through it. So, water works as a thermal insulator.

Plastic:-

Plastic is a perfect example of thermal insulator. The electrons which are present in the plastic they are engage to make chemical bonds to each other for this reasons the electrons are not free to take part in the conduction of heat, for this reason heat could not flow through plastic. So, plastic is not good heat conductor it is good insulator.

The plastics types which perfect example of thermal insulator are polyester films, Mylar, Melinex.

Paper:-

Paper is an example of thermal insulator. Dry papers electrons could not carry electrons just because of the electrons which are present in the dry papers they are engage to make chemical bonds to each other for this reasons the electrons are not free to take part in the conduction of heat, for this reason heat could not flow through paper.

Glass:-

Glassis an also example of thermal insulator. Thermal insulator means from where heat cannot flow one area to another area. The electrons of the glass could not carry electrons just because of the electrons which are present in the glass they are engage to make chemical bonds to each other for this reasons the electrons are not free to take part in the conduction of heat, for this reason heat could not flow through glass material.

Styrofoam:-

Styrofoam is another example of thermal insulator. Thermal insulator material means from where heat cannot flow one area to another area among them Styrofoam is. The electrons of the Styrofoam could not carry electrons just because of the electrons which are present in the Styrofoam they are engage to make chemical bonds to each other for this reasons the electrons are not free to take part in the conduction of heat, for this reason heat could not flow through Styrofoam material.

Dry air:-

Dry air is an example of thermal insulator. Density of the dry air is a vital factor which is affects a matters insulation capability.  Density is a physical parameter which depends upon the spacing of the intermolecular of the particles in a matter. For because of dry air is a gaseous matter it can spread particle configure resist heat convection to some degree.

Dry air electrons could not carry electrons just because of the electrons which are present in the dry air they are engage to make chemical bonds to each other for this reasons the electrons are not free to take part in the conduction of heat.

Dry cotton:-

Dry cotton is an example of thermal insulator. From the dry cotton heat cannot flow but from wet cotton heat can flow. Means dry cotton works at insulator and wet cotton works as heat conductor.

The electrons of the dry cotton could not carry electrons just because of the electrons which are present in the dry cotton they are engage to make chemical bonds to each other for this reasons the electrons are not free to take part in the conduction of heat in a system, for this reason heat could not flow through dry cotton material.

Oil:-

Oil is another example of thermal insulator. The electrons of the oil could not carry electrons just because of the electrons which are present in the oil they are engage to make chemical bonds to each other for this reasons the electrons are not free to take part in the conduction of heat, for this reason heat could not flow through oil material.

The viscosity of the oil is also reason for thermal insulation. The relation between the viscosity and thermal conductivity is when the thermal conductivity is increases

Rubber:-

Rubber is an example of thermal insulator. The electrons of rubbers are same like another type of thermal insulators. The electrons of the rubber not free to carry electrons just because of the electrons which are present in the rubber they are engage to make chemical bonds to each other for this reasons the electrons are not free to take part in the conduction of heat, for this reason heat could not flow through rubber made materials.

Frequent Asked Questions:-

Question: – Write the major difference points between the thermal conductor and thermal insulator.

Solution: – The major difference points between the thermal conductor and thermal insulator is discuss below,

Question: – Give two examples of Insulation Material.

Solution: – The two examples of Insulation Material are,

• Glasswool insulation material
• Cellulose insulation materials

Glasswool insulation material:-

Fiber glass insulation material is used almost everywhere. Fiber glass insulation material uses in residential and also in many commercial purposes, industrial applications. The fiber glass insulation material has extremely good quality glass fiber and ubiquitous insulation material. In industries many industrialist produce medium to high density fiber glass insulation material which are higher than the R values than the regular ones.

Benefit using of Fiber glass insulation material:-

1. Eco friendly
2. High thermal performance
3. Light weight

Cellulose insulation materials:-

Cellulose insulation material is used in new buildings and old buildings, ceilings of the cathedral and walls for building cavities. Cellulose insulation material is made with recycled products mainly newspapers are used to make it. Near about 82 percentages to 85 percentages recycled products are used to make this process. In new type of construction cellulose insulation material is used as damp sprayed or dry sprayed.

Benefit using of Cellulose insulation material:-

1. Eco friendly
2. Economical
3. Light weight
4. Cost is not too high
5. Non combustible
6. Easy to install
7. Maintenance is very less

Read more about Is Water An Insulator?

In this article “Drag coefficient of sphere” will be discuss and drag coefficient of sphere related detailed facts will be also explain. Drag coefficient of sphere is very important factor for a matter.

Drag coefficient of sphere derive as, the ratio between the surface area of the sphere of the similar volume for the matter of the body comparative to the surface area for the matter of the body. Drag coefficient of sphere is a physical parameter which is deeply depends upon the shape and size of the matter.

What is the drag coefficient of a sphere?

The drag coefficient of a sphere is depending upon the geometry of the matter and viscosity of the liquid substance through which the matter can flow.

Drag coefficient of sphere derive as, any sphere shaped matter is move in a motion through a liquid substance is facing the physical parameter of drag. The total amount of force is applied in same direction where shear stress force and pressure acted on the plane of the matter.

How to calculate drag coefficient of a sphere?

Drag pressure coefficient for a sphere shaped matter can calculated using this formula,

Where,

c_d = Drag pressure coefficient for a sphere shaped matter

F_d = Drag force for a sphere shaped matter expressed in Newton

A = Plan form area for a for a sphere shaped matter expressed in square meter

ρ = Density of a sphere shaped matter express in kilogram per cubic meter

v = Viscosity a sphere shaped matter express in meter per second

Using the eqn (1) putting the values of mass density, flow speed, drag force and area we can get the value of drag coefficient of a sphere.

For sphere matter the area can be calculated as, A = π r² ……..eqn (2)

The eqn (2) is applicable for the surface area. Because surface area formula is, A = 4 πr²

Drag coefficient of sphere formula:

The formula of the coefficient of pressure drag is given below,

Where,

F_d = Drag force express in Newton

c_d = Drag coefficient

ρ = Density of a liquid substance express in kilogram per cubic meter

 v = Flow velocity of a liquid substance express in meter per second

A =Reference area for a particular body shape substance expressed in square meter

The pressure drag for sphere shape matter coefficient is dependent some several facts such as size and shape means geometry of the sphere body and viscosity of the liquid substance through which sphere shape matter can flow.

Drag coefficient of a sphere vs. Reynolds number:

The Drag coefficient of a sphere is decreases with the Reynolds number and drag coefficient becomes almost a constant (C_D = 0.4) for a Reynolds number between 10³ and 2×10⁵. As the Reynolds number increases (Re > 2×10⁵), the boundary layer becomes thinner in the front of the sphere and begins its transition to turbulent.

When a system is design which is flow in a motion through a liquid substance that time drag is best for measurement for the system or calculate drag by a simulation. Drag coefficient is frequently helpful revert the data back for a particular analytical model.

The only problem is arising during this process that is one model is not appropriate to derive all type of flow of motion in liquid substance in the region of transition and for both regimes.

Instead of particular practice is use to measure and simulated data to calculate models in each and every flow type regime and after that follow where the models are intersect for calculate the region of transition.

Now we are going to discuss the examples and the C_f expression is consider for both pressure drag and skin friction drag.

• Laminar Example
• Turbulent Example

Laminar Example:-

Drag coefficient of a sphere vs. Reynolds number for laminar flow can be written as,

Drag coefficient of a sphere vs. Reynolds number for laminar flow equation is perfectly goes with a wide range of Reynolds numbers in a closed system of geometries. Drag coefficient of a sphere vs. Reynolds number for laminar flow equation is not appropriate for low drag Reynolds number that could be less than 36 especially for incompressible or very near to incompressible flow.

In the incompressible or very near to incompressible flow we can observe drag coefficient is close to linear function of the velocity.

Turbulent Example:-

Drag coefficient of a sphere vs. Reynolds number for turbulent can be written as,

Drag coefficient of a sphere vs. Reynolds number for turbulent flow equation is perfectly goes with a one simple range of Reynolds numbers in a closed system of geometries.

Drag force coefficient of sphere:

The most studies case of the drag force coefficient is for sphere shaped matter of the body.

When a sphere shaped body in solid state interact with the fluid that time drag force coefficient is produced on the sphere shaped solid matter. Drag force coefficient of sphere matter is not produced by any type of force field.

Frequent Asked Questions:-

Question: –

Write about Skin Friction drag Coefficient.

Solution: –. Skin Friction drag coefficient is physical parameter which is dimensionless skin shear stress. It is mainly dimensionless because of the dynamic pressure is applied on the matter by the free stream.

Skin Friction drag coefficient formula is,

Where,

C_f = Skin friction coefficient

T_w= Skin shear stress which is applied in the surface plane of the body

v_∞ = Free stream speed for velocity of the body

ρ_∞ = Free stream speed for density of the body

1/2ρ_∞ v²_∞ ≡  q_∞ = Free stream dynamic pressure for the body of the matter

Relation with the Reynolds number and the Skin Friction drag coefficient is indirectly proportional to each other. Means if Reynolds number is increases then skin Friction drag coefficient decreases and if the Reynolds number is decreases then skin Friction drag coefficient is increases.

Laminar flow:-

Where,

Re_x = ρ vx/μ Represent the Reynolds number

x = Represent the distance particularly from point of the reference at which the layers of boundary is started.

Transitional flow:-

Where,

y = Represent the distance from the wall

u = The speed for the fluid which is flow in a motion and given as y

K₁ = Karman Constant

The value of Karman Constant is lower than the 0.41 and Karman Constant is the value for transitional boundary layer and turbulent boundary layer

K₂= Van Driest constant

K₃= Pressure parameter

p = Pressure

x = The coordinate along a surface where a boundary layers forms

Turbulent flow:-

Question: –

Riva drives her car daily Kolkata to Durgapur. When Riva drives her car that time the speed of the car is about 90 kilometres per hour and that time the drag coefficient is 0.35. The cross sectional area for the car is 6 square meter.

Now determine the amount of drag force.

Solution: – Given data are,

Velocity of the car = 90 kilometres per hour

Drag coefficient of the car = 0.35

Cross sectional area of the car = 6 square meter

Density of the fluid of the car = 1.2 kilogram per cubic meter

We all are know that the velocity of the air is, 1.2 kilogram per cubic meter

Now, applied Drag force formula,

Where,

D = Pressure drag force

C_d= Pressure drag coefficient

ρ = Density

 v = Velocity

 A = Reference area

D = 0.35 * 1.2 * 8100 * 6 /2 * 3600

D = 2.8 Newton

Riva drives her car daily Kolkata to Durgapur. When Riva drives her car that time the speed of the car is about 90 kilometres per hour and that time the drag coefficient is 0.35. The cross sectional area for the car is 6 square meter.

The amount of drag force 2.8 Newton

Question: –

A plane is daily moves Mumbai to Katakana. When the plane moves that time the speed of the plane is about 750 kilometres per hour and that time the drag coefficient is 0.30. The cross sectional area for the car is 115 square meter.

Now determine the amount of drag force for the plane.

Solution: – Given data are,

Velocity of the plane = 750 kilometres per hour

Drag coefficient of the plane = 0.30

Cross sectional area of the plane = 115 square meter

Density of the fluid of the plane = 1.2 kilogram per cubic meter

We all are know that the velocity of the air is, 1.2 kilogram per cubic meter

Now, applied Drag force formula,

D = C_d * ρ * A/2

Where,

D = Pressure drag force

C_d = Pressure drag coefficient

ρ = Density

 v = Velocity

 A = Reference area

D = 3234 Newton

A plane is daily moves Mumbai to Katakana. When the plane moves that time the speed of the plane is about 750 kilometres per hour and that time the drag coefficient is 0.30. The cross sectional area for the car is 115 square meter.

The amount of drag force for the plane is 3234 Newton

Question: –

What is the relationship between drag and Reynolds number?

Solution: – The relationship between drag and Reynolds number is directly proportional to each other. Means if the drag is increases then Reynolds number is also increases and if the drag is deceases then Reynolds number is also decreases.

When Reynolds number is increases that time the viscous forces decreases relative to the internal forces so the point of separation moves in upward direction towards the equator.

In modern generation a wide “Types of insulation material” are very easily available. In these article types of insulation material is prate and also types of insulation material relate facts are derived.

7+ Types of Insulation Material are listed below,

• Glasswool insulation material
• Earthwool insulation material
• Rockwool insulation material
• Polyester insulation material
• Spray foam insulation material
• Reflective insulation material
• Insulation rigid insulation material

Example of 7+ Types of insulation material and their explanations:-

Glasswool insulation material:-

Glasswool insulation material is used almost everywhere starting from residential glasswool insulation material is used in many commercial purposes and also in industrial applications. The glasswool insulation material has extremely good quality glass fibre and ubiquitous insulation material.

Glasswool insulation material is used in many form of insulation such as loose fill, blanket and also in duct insulation and rigid board. Glasswool insulation material is made with molten glass which is blown or spun into fibres. In most manufacturing industries for made this use 40 percent to 60 percent recycled glass material.

Benefit using of Glasswool insulation material:-

• Light weight
• Flexible and resilient
• Non combustible
• Saves lots of energy
• Easy to installation and also easy to handle
• High thermal performance

Earthwool insulation material:-

Earthwool insulation material is generally made with Knauf insulation. Earthwool insulation material is made with a technology which name is ECOSE technology. This type of insulation material most use in residential, industrial and also in commercial.

Benefit using of Earth insulation material:-

• Non combustible
• No smell is present in it
• Long life
• Acoustic product available
• High thermal performance
• Eco friendly
• Low irritant product material

Rockwool insulation material:-

Rockwool insulation material is an artificial man made insulation material. In rockwool insulation material natural insulation minerals are used such as basalt or diabase. Near about 75 percent recycled materials are used in it. This material can withstand temperature of higher 1000 degree centigrade.

Benefit using of Rookwool insulation material:-

• Fire resistance
• High in durable
• Non combustible
• Long life
• High thermal performance
• High acoustic rating
• Not affected by water

Polyester insulation material:-

Polyester insulation material is a transparent thermoplastic and it has no colour.  Polyester insulation material is mainly used for making beadboard insulation, loose fill insulation and concrete block insulation carrying small beads of polyester. Thermal resistance of polyester insulation material depend on its density.

In this material near about 50 percentages of recycled products are uses such as bottles of drinking. This type of material is made with heat any type of chemical binder not used in it.

Benefit using of Polyester insulation material:-

• Non flammable
• Non toxic
• Irritant is not appear to touch this polyester insulation material
• Long life
• Non allergenic particles

Spray foam insulation material:-

Spray foam insulation material is an expensive material comparative to other insulation materials. For installation and maintenance trained people are used for this reason this insulation material became more expensive.

Benefit using of Spray foam insulation material:-

• Eco friendly
• Long life
• Seal of the spray foam insulation material is airtight
• Reduce energy bill
• Help mould growth

Reflective insulation material:-

In the reflective insulation aluminium metal is used which also a reflective type material. Reflective foils are helps to increases the value of the thermal insulation by reflecting the heat to entering into the houses and buildings. The reflective insulation materials uses in for both commercial and residential applications.

Benefit using of Reflective insulation material:-

• Cost is not too high
• Non combustible
• Easy to install
• Maintenance is very less
• Non degradable
• Lightweight and thin
• Hot climate cannot affect reflective insulation material

Insulation rigid insulation material:-

In the insulation rigid insulation process insulated materials are used such as Kraft paper, aluminium foil and white vinyl sheeting. The materials are used they all are vapour barrio and air barrier. A facing protects is used in insulation rigid insulation process thus insulation can hold together.

Benefit using of Insulated rigid insulation material:-

• Hot climate cannot affect
• Vapor and air does not affect on it
• High thermal performance

Types of insulation material for wall:

The Types of insulation material for wall is listed below,

1. Nu Wool insulation material
2. Open cell spray insulation material
3. Foil faced insulation material
4. Flash and batt insulation material
5. Foam board insulation material
6. Fiberglass insulation material
7. Wet applied cellulose insulation material

Types of insulation material for transformer:

The Types of insulation material for transformer is listed below,

1. Pressboard
2. Insulating tape
3. Insulating paper
4. Insulating oil
5. Wood based laminates

Types of insulation materials of cables:

The types of insulation materials of cables is listed below,

1. Nylon
2. Polyurethane
3. Plastic insulation
4. Glass
5. Teflon
6. Paper

Types of insulation materials in buildings:

The insulation materials which are used in buildings listed below,

• Fiber glass insulation materials
• Cellulose insulation materials
• Mineral wool insulation materials
• Insulation facings insulation materials
• Perlite insulation materials

Fiber glass insulation materials:-

Fiber glass insulation material is used almost everywhere. Fiber glass insulation material uses in residential and also in many commercial purposes, industrial applications. The fiber glass insulation material has extremely good quality glass fibre and ubiquitous insulation material. In industries many industrialist produce medium to high density fiber glass insulation material which are higher than the R values than the regular ones.

Benefit using of Fiber glass insulation material:-

• Eco friendly
• High thermal performance
• Light weight

Cellulose insulation materials:-

Cellulose insulation material is used in new buildings and old buildings, ceilings of the cathedral and walls for building cavities. Cellulose insulation material is made with recycled products mainly newspapers are used to make it. Near about 82 percentages to 85 percentages recycled products are used to make this process. In new type of construction cellulose insulation material is used as damp sprayed or dry sprayed.

Benefit using of Cellulose insulation material:-

• Eco friendly
• Economical
• Light weight
• Cost is not too high
• Non combustible
• Easy to install
• Maintenance is very less

Mineral wool insulation materials:-

Mineral wool insulation material is made with recycled products mainly industrial products are used to make it. Near about 76 percentages recycled products are used to make this process. Rock wool and slag wool both are manmade products. Rock wool mainly made with natural product such as basalt and slag wool made with blast furnace slag.

Benefit using of Mineral wool insulation material:-

• Eco friendly
• Economical
• Light weight
• High thermal performance

Insulation facings insulation materials:-

Insulation facings insulation manufacturing process facings are fastened. The facing of the insulation a material protect the surface of the insulation and helps to hold the insulation together. Common material with are used in insulation manufacturing process are aluminium foil, kraft paper and white vinyl sheeting. Vapor barrier and air barrier does not affect on it at all.

Benefit using of Insulation of facings insulation material:-

• Hot climate cannot affect
• Vapor and air does not affect on it
• High thermal performance
• Eco friendly

Perlite insulation materials:-

The perlite insulation materials uses in very old type buildings. The material of perlite insulation is use as attic insulation. The perlite insulation carry small size and bulky pellets made with heating rock pellets.

Benefit using of Perlite insulation material:-

• Low cost in install
• Low maintenance
• Light weight
• Easy to install
• Eco friendly