Minimum Temperature Ratio Calculator

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

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< Compressor Calculators

Tip Velocity of Impeller given Mean Diameter

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

Mean Diameter of Impeller

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

Degree of Reaction for Compressor

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

Isentropic Efficiency of Compression Machine

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

Minimum Temperature Ratio Formula

LaTeX Go

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 is a parameter used in the analysis of compression systems, indicating the minimum temperature ratio achieved during compression. This formula computes the temperature ratio by accounting for the pressure ratio, adiabatic index, isentropic efficiency of compression, and turbine efficiency. 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 is a parameter used in the analysis of compression systems, indicating the minimum temperature ratio achieved during compression. This formula computes the temperature ratio by accounting for the pressure ratio, adiabatic index, isentropic efficiency of compression, and turbine efficiency 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 is a parameter used in the analysis of compression systems, indicating the minimum temperature ratio achieved during compression. This formula computes the temperature ratio by accounting for the pressure ratio, adiabatic index, isentropic efficiency of compression, and turbine efficiency 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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