Minimum Temperature Ratio Calculator

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Components of Gas Turbine

Jet Propulsion

Rocket Propulsion

Thermodynamics and Governing Equations

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✖Pressure Ratio is the ratio of pressures at entry and exit of compressor.ⓘ Pressure Ratio [P_r]			+10% -10%
✖The Heat Capacity Ratio also known as the adiabatic index is the ratio of specific heats i.e. the ratio of the heat capacity at constant pressure to heat capacity at constant volume.ⓘ Heat Capacity Ratio [γ]			+10% -10%
✖Isentropic Efficiency of compressor is the ratio of isentropic work of compressor to actual work of compressor.ⓘ Isentropic Efficiency of Compressor [η_C]			+10% -10%
✖Efficiency of Turbine is the ratio of work obtained from turbine to the heat supplied to turbine.ⓘ Efficiency of Turbine [η_T]			+10% -10%

✖Temperature Ratio is the ratio of temperature at entry and exit of compressor.ⓘ Minimum Temperature Ratio [T_r]

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Formula

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Minimum Temperature Ratio

Formula

`"T"_{"r"} = ("P"_{"r"}^(("γ"-1)/"γ"))/("η"_{"C"}*"η"_{"T"})`

Example

`"1.533919"=(("2.4")^(("1.4"-1)/"1.4"))/("0.92"*"0.91")`

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Minimum Temperature Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Temperature Ratio = (Pressure Ratio^((Heat Capacity Ratio-1)/Heat Capacity Ratio))/(Isentropic Efficiency of Compressor*Efficiency of Turbine)
T_r = (P_r^((γ-1)/γ))/(η_C*η_T)
This formula uses 5 Variables

Variables Used

Temperature Ratio - Temperature Ratio is the ratio of temperature at entry and exit of compressor.
Pressure Ratio - Pressure Ratio is the ratio of pressures at entry and exit of compressor.
Heat Capacity Ratio - The Heat Capacity Ratio also known as the adiabatic index is the ratio of specific heats i.e. the ratio of the heat capacity at constant pressure to heat capacity at constant volume.
Isentropic Efficiency of Compressor - Isentropic Efficiency of compressor is the ratio of isentropic work of compressor to actual work of compressor.
Efficiency of Turbine - Efficiency of Turbine is the ratio of work obtained from turbine to the heat supplied to turbine.

STEP 1: Convert Input(s) to Base Unit

Pressure Ratio: 2.4 --> No Conversion Required
Heat Capacity Ratio: 1.4 --> No Conversion Required
Isentropic Efficiency of Compressor: 0.92 --> No Conversion Required
Efficiency of Turbine: 0.91 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_r = (P_r^((γ-1)/γ))/(η_C*η_T) --> (2.4^((1.4-1)/1.4))/(0.92*0.91)

Evaluating ... ...

T_r = 1.53391948310279

STEP 3: Convert Result to Output's Unit

1.53391948310279 --> No Conversion Required

FINAL ANSWER

1.53391948310279 ≈ 1.533919 <-- Temperature Ratio

(Calculation completed in 00.004 seconds)

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Created by Chilvera Bhanu Teja

Institute of Aeronautical Engineering (IARE), Hyderabad

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Verified by Rajat Vishwakarma

University Institute of Technology RGPV (UIT - RGPV), Bhopal

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< 14 Compressor Calculators

Efficiency of compressor in actual gas turbine cycle

Go Isentropic Efficiency of Compressor = (Temperature at Compressor Exit-Temperature at Compressor Inlet)/(Actual Temperature at Compressor Exit-Temperature at Compressor Inlet)

Minimum Temperature Ratio

Go Temperature Ratio = (Pressure Ratio^((Heat Capacity Ratio-1)/Heat Capacity Ratio))/(Isentropic Efficiency of Compressor*Efficiency of Turbine)

Efficiency of Compressor given Enthalpy

Go Isentropic Efficiency of Compressor = (Ideal Enthalpy after Compression-Enthalpy at Compressor Inlet)/(Actual Enthalpy after Compression-Enthalpy at Compressor Inlet)

Work Required to Drive Compressor Including Mechanical Losses

Go Compressor Work = (1/Mechanical Efficiency)*Specific Heat Capacity at Constant Pressure*(Temperature at Compressor Exit-Temperature at Compressor Inlet)

Shaft Work in Compressible Flow Machines

Go Shaft Work = (Enthalpy at Compressor Inlet+Compressor Inlet Velocity^2/2)-(Enthalpy at Exit of Compressor+Compressor Exit Velocity^2/2)

Tip Velocity of Impeller given Hub Diameter

Go Tip Velocity = pi*RPM/60*sqrt((Impeller Tip Diameter^2+Impeller Hub Diameter^2)/2)

Compressor Work in Gas Turbine given Temperature

Go Compressor Work = Specific Heat Capacity at Constant Pressure*(Temperature at Compressor Exit-Temperature at Compressor Inlet)

Tip Velocity of Impeller given Mean Diameter

Go Tip Velocity = pi*(2*Mean Diameter of Impeller^2-Impeller Hub Diameter^2)^0.5*RPM/60

Mean Diameter of Impeller

Go Mean Diameter of Impeller = sqrt((Impeller Tip Diameter^2+Impeller Hub Diameter^2)/2)

Impeller Outlet Diameter

Go Impeller Tip Diameter = (60*Tip Velocity)/(pi*RPM)

Degree of Reaction for Compressor

Go Degree of Reaction = (Enthalpy Increase in Rotor)/(Enthalpy Increase in Stage)

Isentropic Efficiency of Compression Machine

Go Isentropic Efficiency of Compressor = Isentropic Work Input/Actual Work Input

Compressor work

Go Compressor Work = Enthalpy at Exit of Compressor-Enthalpy at Compressor Inlet

Shaft Work in Compressible Flow Machines neglecting Inlet and Exit Velocities

Go Shaft Work = Enthalpy at Compressor Inlet-Enthalpy at Exit of Compressor

Minimum Temperature Ratio Formula

Temperature Ratio = (Pressure Ratio^((Heat Capacity Ratio-1)/Heat Capacity Ratio))/(Isentropic Efficiency of Compressor*Efficiency of Turbine)
T_r = (P_r^((γ-1)/γ))/(η_C*η_T)

What is temperature?

Temperature refers to the hotness or coldness of a body. In specific terms, it is the way of determining the kinetic energy of particles within an object. Faster the movement of particles; more the temperature and vice versa.

How to Calculate Minimum Temperature Ratio?

Minimum Temperature Ratio calculator uses Temperature Ratio = (Pressure Ratio^((Heat Capacity Ratio-1)/Heat Capacity Ratio))/(Isentropic Efficiency of Compressor*Efficiency of Turbine) to calculate the Temperature Ratio, The Minimum temperature ratio formula is defined as the pressure ratio raised to power of the term ratio of adiabatic index substracted by unity to the adiabatic index and divided by the product of efficiency of compressor and efficiency of turbine. Temperature Ratio is denoted by T_r symbol.

How to calculate Minimum Temperature Ratio using this online calculator? To use this online calculator for Minimum Temperature Ratio, enter Pressure Ratio (P_r), Heat Capacity Ratio (γ), Isentropic Efficiency of Compressor (η_C) & Efficiency of Turbine (η_T) and hit the calculate button. Here is how the Minimum Temperature Ratio calculation can be explained with given input values -> 2.908056 = (2.4^((1.4-1)/1.4))/(0.92*efficiency_of_turbine).

FAQ

What is Minimum Temperature Ratio?

The Minimum temperature ratio formula is defined as the pressure ratio raised to power of the term ratio of adiabatic index substracted by unity to the adiabatic index and divided by the product of efficiency of compressor and efficiency of turbine and is represented as T_r = (P_r^((γ-1)/γ))/(η_C*η_T) or Temperature Ratio = (Pressure Ratio^((Heat Capacity Ratio-1)/Heat Capacity Ratio))/(Isentropic Efficiency of Compressor*Efficiency of Turbine). Pressure Ratio is the ratio of pressures at entry and exit of compressor, The Heat Capacity Ratio also known as the adiabatic index is the ratio of specific heats i.e. the ratio of the heat capacity at constant pressure to heat capacity at constant volume, Isentropic Efficiency of compressor is the ratio of isentropic work of compressor to actual work of compressor & Efficiency of Turbine is the ratio of work obtained from turbine to the heat supplied to turbine.

How to calculate Minimum Temperature Ratio?

The Minimum temperature ratio formula is defined as the pressure ratio raised to power of the term ratio of adiabatic index substracted by unity to the adiabatic index and divided by the product of efficiency of compressor and efficiency of turbine is calculated using Temperature Ratio = (Pressure Ratio^((Heat Capacity Ratio-1)/Heat Capacity Ratio))/(Isentropic Efficiency of Compressor*Efficiency of Turbine). To calculate Minimum Temperature Ratio, you need Pressure Ratio (P_r), Heat Capacity Ratio (γ), Isentropic Efficiency of Compressor (η_C) & Efficiency of Turbine (η_T). With our tool, you need to enter the respective value for Pressure Ratio, Heat Capacity Ratio, Isentropic Efficiency of Compressor & Efficiency of Turbine and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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