Engineering

The main purpose of using a nozzle is to accelerate the velocity of a flowing fluid using pressure. In this article we will discuss about Isentropic Efficiency of Nozzle.

Isentropic efficiency of nozzle is the ratio actual kinetic energy at nozzle exit and isentropic kinetic energy at nozzle exit for the same inlet and exit pressures.

A fluid accelerates in a nozzle as it is moving from high pressure to low pressure with an increase in kinetic energy. Frictional losses inside the nozzle decreases fluid KE and raise the temperature of the fluid, increasing its entropy.

Nozzles are operated under adiabatic condition but the ideal process for a nozzle is the isentropic process. To have a comparison between actual work done and work under isentropic conditions of a device, a parameter called Isentropic Efficiency is used.

What Is Isentropic Efficiency of Nozzle?

The isentropic process involves no irreversibilities and serves as the ideal process for adiabatic devices.

Turbines, compressors and nozzles works under adiabatic conditions. Since they are not truly isentropic, they are considered as isentropic for calculation point of view. Isentropic efficiency is the parameter for a nozzle, turbine or compressor which defines how efficiently these devices approximate a corresponding isentropic device.

Nearer to an idealized isentropic process, improved will be the performance of the nozzle.

IsentropicEfficiency of nozzle is generally greater than 95%. So losses due to irreversibilities are very small in case of a well designed nozzle.

What is a Nozzle?

Nozzles are most widely used steady flow device in steam turbines, gas turbines and rockets.

Nozzle is a device often a pipe or a tube of varying cross sectional area used to control the direction of flow as well as exit velocity, mass, shape and pressure of the flow. Inside a nozzle pressure energy is converted into kinetic energy or we can say the fluid velocity increases with an expense of pressure energy.

Depending on required velocity and mach number of the fluid, Nozzles can be categorised like Convergent type, Divergent type and Convergent-Divergent type. Nozzle can be used for both subsonic and supersonic flows.

In the above figure, a de Laval nozzle, showing approximate flow velocity increasing from green to red in the direction of flow

Isentropic Efficiency of Nozzle Formula

Isentropic Efficiency represents the performance index of a nozzle. A comparison of nozzle’s performance relative to an isentropic process.

Isentropic Efficiency of Nozzle can be defined as the ratio of actual enthalpy drop to isentropic enthalpy drop between the same pressures.

Isentropic Efficiency of Nozzle=Actual enthalpy drop/Isentropic enthalpy drop

Isentropic Efficiency formula is the measure of the deviation of actual processes from the corresponding idealized ones. The ratio of actual work done by a nozzle to work done by the nozzle under isentropic condition is called Isentropic Nozzle Efficiency.

Isentropic Efficiency of a nozzle η_N= Actual Kinetic Energy at Nozzle Exit/ Isentropic Kinetic Energy at Nozzle Exit.

Theoretically the process inside the nozzle is considered as isentropic but due to frictional losses the process is irreversible.

Process 1-2:Isentropic Process

Process1- 2{}’:Actual Process

Efficiency of nozzle,

For Process 1-2, applying SFEE,

 Or,

For Process 1- 2′, applying SFEE,

Or,

Now from Eq(1) substituting the values of h1 – h2 and h1 – h2` ,we get

Equation(1) and (4) are the formulas to calculate the Isentropic Efficiency of Nozzle.

How to Find Isentropic Efficiency of Nozzle?

A Nozzle reduces the pressure of the flow and at the same time speed up the flow to create a thrust.

Some amount of heat loss takes place from the steam due to the friction with the surface of the nozzle. Frictional effect also increases the dryness fraction of steam, because energy lost in friction is transferred into heat which tends to dry or super heat the steam.

In case of fluid dynamics, stagnation point denotes a point where local velocity of a fluid remains zero and isentropic stagnation state represents a state when a flow of fluid goes through reversible adiabatic deceleration to zero velocity.

Both actual and isentropic states are used for gases.

The actual stagnation state is obtained for actual deceleration to zero velocity, irreversibility may be also associated. For this reason stagnation property is sometimes reversed for actual state properties, and the term total property is applied for isentropic stagnation states.

Both isentropic and actual stagnation states have same enthalpy, same temperature(for ideal gas) but may be pressure is more in case of isentropic stagnation state in comparison to actual stagnation state.

In case of a nozzle the inlet velocity is negligible in comparison to exit velocity of  a flow.

From the energy balance,

Isentropic Efficiency of Nozzle=Actual enthalpy drop/Isentropic enthalpy drop

Where h₁ =specific enthalpy of the gas at the entrance

h_2a =specific enthalpy of gas at the exit for the actual process

h_2s = specific enthalpy of gas at the exit for the isentropic  process

Isentropic Efficiency Nozzle Example

Example: Steam enters a nozzle at 1.4 MPa  250⁰ C and negligible velocity and expands to 115 KPa and a quality of 97% dry. Determine the exit velocity of the steam.

Solution: Given data , Initial Pressure, P₁=1.4MPa

 =14 bar

Initial Temperature, T₁=250⁰ C

Final Pressure,P₂=115 KPa= 1.15 x 10⁵ Pa=1.15 bar

Quality of steam at exit, x₂=0.97

Exit Velocity, V₂=?

Neglecting initial velocity, Exit Velocity,

Considering initial velocity,

h₁=Enthalpy at initial condition i.e. at 1.14 MPa i.e at 14 bar 250⁰C, from steam tables,

h₁=2927.6 KJ/Kg

h₂=Enthalpy at exit condition i.e. at 115 KPa i.e at 1.15 bar x₂=0.97, from steam tables

h_f2=434.2 KJ/kg

h_fg2=2247.4 KJ/kg

Hence the exit velocity of steam,

In this article “Thermal equilibrium example” will be discuss with detailed explanations. Thermal equilibrium example is very important concept to understand the changing of state for a substance.

11+ Thermal Equilibrium Example is encounter in below,

• Refrigerator
• Oven
• Melting of a ice cube
• Freezing of water
• Drying of wet hair
• Drying of wet clothes
• Cooling of a cup of tea
• Melting of ice-cream
• Freezing of ice- cream
• Cooling of a hot rod
• Making of tea

Refrigerator:-

Refrigerator is a device which is appropriate example of thermal expansion. When a food item is stored in the refrigerator that time the item will start to goes down its temperature and the temperature of the refrigerator and the temperature of food item will be same and the process of temperature changing for the food item will be stop.

Refrigerator is a home appliance and commercial appliance. The refrigerator carry a compartment with thermal insulator and also a heat pump through which heat easily can transfer from its midst to its external surrounding. For this process the inside temperature of the refrigerator will be lower than the temperature of the room.

Oven:-

Oven is a device which is also an appropriate example of thermal expansion. When a food item is placed in an oven and heat is applied on it that time the item will start to goes up its temperature. When the temperature of the oven and the temperature of food item will be same that time the process of temperature changing between the oven and the food item will be stop.

An oven is use for cooking purpose and also heats the food item to a wished temperature.

Types of oven:

Types of oven is listed below,

1. Electric oven
2. Gas oven
3. Earth oven
4. Masonry oven
5. Toaster oven
6. Ceramic oven
7. Wall oven
8. Steam oven
9. Microwave oven

Melting of a ice cube:-

Another example of thermal expansion is melting of an ice cube. When an ice cube placed on a normal temperature its try to reaching at the room temperature and melting point will be increases at this particular time ice cube start to changing its state from solid to liquid.

Freezing of water:-

Another example of thermal expansion is freezing of water. When water is placed on a lower temperature its try to reaching at the lower temperature from the normal temperature at this particular time water starts to change its state from liquid to solid.

Drying of wet hair:-

Drying of wet hair is another regular example of thermal expansion. When we dry our wet hair in normal room temperature that time our wet hair reach at the room temperature and hair will be dry.

Drying of wet clothes:-

Drying of wet clothes is another regular example of thermal expansion. When we dry our wet clothes in normal room temperature that time our wet clothes reach at the room temperature and cloth will be dry.

Cooling of a cup of tea:-

Cooling of a cup of tea is another regular example of thermal expansion. When a cup of tea is placed on a normal room temperature that time a cup of tea try to reaching at the room temperature and boiling point will be decreases. A cup of tea starts to change its temperature and became cool.

Melting of ice-cream:-

Another example of thermal expansion is melting of ice cream. When ice cream is placed on a normal room temperature that time its try to reaching at the room temperature and melting point will be increases and freezing point will be decreases. The ice cream starts to change its state from solid to liquid.

Freezing of ice- cream:-

Another example of thermal expansion is freezing of ice cream. When ice cream is placed on a refrigerator that time ice cream try to reaching at the refrigerant temperature and melting point will be decreases and freezing point will be increases. For this particular reason the ice cream starts to change its state from liquid to solid.

Cooling of a hot rod:-

Cooling of a hot rod is another example of thermal expansion. When a rod has higher temperature after doing any operation it became hotter. When a hotter rod is placed in a normal room temperature that time the rod try to reach at the room temperature. The rod starts to decreases its temperature and became cool.

Making of tea:-

When we make tea that time with hot water milk is added at that time the temperature of milk is low and the temperature of water is cold but when hot water and cold milk is added to each the mixture comes in a normal temperature. So, making of tea is also another example of thermal expansion.

Frequent asked questions:-

Question: –

Write the formula for thermal equilibrium.

Solution: – When two different matters stay in same temperature that’s mean the two different matters maintain thermal equilibrium.

The formula for thermal equilibrium is,

Where,

Q = Total energy of the specific matter of the body which is expressed in Joule

m = Mass of the specific matter of the body which is expressed in grams

C_e = Specific heat of the specific matter of the body which is expressed in joule per Kelvin per kilogram

Δ t = (Final temperature – Starting temperature) of the specific matter of the body which is expressed in Kelvin

Question: –

In a house a bowl is present which is decorated with beautiful stones. The bowl is made with aluminium. The weight of the bowl is 15 gram and temperature is about 39 degree centigrade. Now in the aluminium bowl water is placed. At this condition the temperature of the water will be 20 degree centigrade and weight of the water is about 32 gram.

Find the exact temperature where the temperature of the aluminium and the temperature of the water will be same.

Solution: –

We know that,

Where,

Q = Total energy of the specific matter of the body

m = Mass of the specific matter of the body

C_e = Specific heat of the specific matter of the body

Δt= (Final temperature – Starting temperature) of the specific matter of the body

For aluminium,

Given data are,

m_A =  15 gram

C_eA = 0.215 calorie per gram degree centigrade

Δ t_A = (T_f – T_iA) degree centigrade = (T_f – 39) degree centigrade

For water,

Q_W = m_W * C_eW *Δt_W………….. eqn (1)

Given data are,

m_W = 32 gram

C_eW = 1 calorie per gram degree centigrade

Δt_W = (T_f – T_iW) degree centigrade = (T_f – 20) degree centigrade

Now, from………….. eqn (1) and ………….. eqn (2) we can write,

Putting the value from eqn (1) and eqn (2),

(Put the value for C_eW = 1 calorie per gram degree centigrade)

T_f= 21.7 degree centigrade

In a house a bowl is present which is decorated with beautiful stones. The bowl is made with aluminium. The weight of the bowl is 15 gram and temperature is about 39 degree centigrade. Now in the aluminium bowl water is placed. At this condition the temperature of the water will be 20 degree centigrade and weight of the water is about 32 gram

The exact temperature where the temperature of the aluminium and the temperature of the water will be same is 21.7 degree centigrade

Question: –

Explain types of thermodynamic equilibrium.

Solution: – A system is called thermodynamic equilibrium when mechanical equilibrium, thermal equilibrium and chemical equilibrium are same.

Thermodynamic equilibrium three types, they are,

• Mechanical equilibrium
• Thermal equilibrium
• Chemical equilibrium

Mechanical equilibrium:-

A system is called mechanical equilibrium when pressure will be no changed in any condition and also no changes in acting of unbalanced force.

Thermal equilibrium:-

A system is called thermal equilibrium when temperature will be no changed in any condition inside the system of the matter.

Chemical equilibrium:-

A system is called chemical equilibrium when chemical reaction no present inside the system and also any type of composition changes is not present of the matter.

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