Thermal Efficiency of Jet Engines given Effective Speed Ratio Calculator

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✖Exit Velocity refers to the speed at which gases expand at the exit of nozzle of a engine.ⓘ Exit Velocity [V_e]			+10% -10%
✖Effective speed ratio is the ratio of aircraft forward speed to the aircraft jet velocity.ⓘ Effective Speed Ratio [α]			+10% -10%
✖Fuel air ratio is the ratio of mass flow rate of fuel to the mass flow rate of air.ⓘ Fuel Air Ratio [f]			+10% -10%
✖Fuel Calorific Value denotes the amount of heat energy released per unit mass of fuel upon complete combustion.ⓘ Fuel Calorific Value [Q]			+10% -10%

✖Thermal efficiency is a dimensionless performance measure of a device that uses thermal energy, such as an internal combustion engine, a steam turbine or a steam engine.ⓘ Thermal Efficiency of Jet Engines given Effective Speed Ratio [η_th]

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Formula

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Thermal Efficiency of Jet Engines given Effective Speed Ratio

Formula

`"η"_{"th"} = ("V"_{"e"}^2*(1-"α"^2))/(2*"f"*"Q")`

Example

`"0.062805"=(("248m/s")^2*(1-("0.4475")^2))/(2*"0.009"*"43510kJ/kg")`

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Thermal Efficiency of Jet Engines given Effective Speed Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Thermal Efficiency = (Exit Velocity^2*(1-Effective Speed Ratio^2))/(2*Fuel Air Ratio*Fuel Calorific Value)
η_th = (V_e^2*(1-α^2))/(2*f*Q)
This formula uses 5 Variables

Variables Used

Thermal Efficiency - Thermal efficiency is a dimensionless performance measure of a device that uses thermal energy, such as an internal combustion engine, a steam turbine or a steam engine.
Exit Velocity - (Measured in Meter per Second) - Exit Velocity refers to the speed at which gases expand at the exit of nozzle of a engine.
Effective Speed Ratio - Effective speed ratio is the ratio of aircraft forward speed to the aircraft jet velocity.
Fuel Air Ratio - Fuel air ratio is the ratio of mass flow rate of fuel to the mass flow rate of air.
Fuel Calorific Value - (Measured in Joule per Kilogram) - Fuel Calorific Value denotes the amount of heat energy released per unit mass of fuel upon complete combustion.

STEP 1: Convert Input(s) to Base Unit

Exit Velocity: 248 Meter per Second --> 248 Meter per Second No Conversion Required
Effective Speed Ratio: 0.4475 --> No Conversion Required
Fuel Air Ratio: 0.009 --> No Conversion Required
Fuel Calorific Value: 43510 Kilojoule per Kilogram --> 43510000 Joule per Kilogram (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

η_th = (V_e^2*(1-α^2))/(2*f*Q) --> (248^2*(1-0.4475^2))/(2*0.009*43510000)

Evaluating ... ...

η_th = 0.0628047697847238

STEP 3: Convert Result to Output's Unit

0.0628047697847238 --> No Conversion Required

FINAL ANSWER

0.0628047697847238 ≈ 0.062805 <-- Thermal Efficiency

(Calculation completed in 00.004 seconds)

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Home » Physics » Aeroengines » Jet Propulsion » Performance Parameters » Efficiency Metrics » Thermal Efficiency of Jet Engines given Effective Speed Ratio

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< 12 Efficiency Metrics Calculators

Net work output in simple gas turbine cycle

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

Change in Kinetic Energy of Jet Engine

Go Change in Kinetic Energy = (((Mass Flow Rate+Fuel Flow Rate)*Exit Velocity^2)-(Mass Flow Rate*Flight Speed^2 ))/2

Propulsive power

Go Propulsive Power = 1/2*((Mass Flow Rate+Fuel Flow Rate)*Exit Velocity^2-(Mass Flow Rate*Flight Speed^2))

Thermal Efficiency of Jet Engines given Effective Speed Ratio

Go Thermal Efficiency = (Exit Velocity^2*(1-Effective Speed Ratio^2))/(2*Fuel Air Ratio*Fuel Calorific Value)

Overall Efficiency given Specific Fuel Consumption

Go Overall Efficiency = Flight Speed/(Thrust-Specific Fuel Consumption*Fuel Calorific Value)

Overall Efficiency of Propulsive System

Go Overall Efficiency = Thermal Efficiency*Efficiency of Transmission*Propulsive Efficiency

Propulsive efficiency given aircraft velocity

Go Propulsive Efficiency = (2*Flight Speed)/(Exit Velocity+Flight Speed)

Transmission Efficiency given Output and Input of Transmission

Go Efficiency of Transmission = Transmission Output Power/Transmission Input Power

Propulsive Efficiency given Effective Speed Ratio

Go Propulsive Efficiency = (2*Effective Speed Ratio)/(1+Effective Speed Ratio)

Isentropic Efficiency of Expansion Machine

Go Turbine Efficiency = Actual Work/Isentropic Work Output

Propulsive efficiency

Go Propulsive Efficiency = Thrust Power/Propulsive Power

Effective speed ratio

Go Effective Speed Ratio = Flight Speed/Exit Velocity

Thermal Efficiency of Jet Engines given Effective Speed Ratio Formula

Thermal Efficiency = (Exit Velocity^2*(1-Effective Speed Ratio^2))/(2*Fuel Air Ratio*Fuel Calorific Value)
η_th = (V_e^2*(1-α^2))/(2*f*Q)

What is thermal efficiency?

Thermal efficiency is a dimensionless performance measure of a device that uses thermal energy, such as an internal combustion engine, a steam turbine or a steam engine, a boiler, furnace.

How to Calculate Thermal Efficiency of Jet Engines given Effective Speed Ratio?

Thermal Efficiency of Jet Engines given Effective Speed Ratio calculator uses Thermal Efficiency = (Exit Velocity^2*(1-Effective Speed Ratio^2))/(2*Fuel Air Ratio*Fuel Calorific Value) to calculate the Thermal Efficiency, The Thermal efficiency of jet engines given effective speed ratio formula is defined as the percentage of heat energy transformed into the work. This formula is used to calculate the thermal efficiency of jet engines when the effective speed ratio is given. Thermal Efficiency is denoted by η_th symbol.

How to calculate Thermal Efficiency of Jet Engines given Effective Speed Ratio using this online calculator? To use this online calculator for Thermal Efficiency of Jet Engines given Effective Speed Ratio, enter Exit Velocity (V_e), Effective Speed Ratio (α), Fuel Air Ratio (f) & Fuel Calorific Value (Q) and hit the calculate button. Here is how the Thermal Efficiency of Jet Engines given Effective Speed Ratio calculation can be explained with given input values -> 0.063327 = (248^2*(1-0.4475^2))/(2*0.009*43510000).

FAQ

What is Thermal Efficiency of Jet Engines given Effective Speed Ratio?

The Thermal efficiency of jet engines given effective speed ratio formula is defined as the percentage of heat energy transformed into the work. This formula is used to calculate the thermal efficiency of jet engines when the effective speed ratio is given and is represented as η_th = (V_e^2*(1-α^2))/(2*f*Q) or Thermal Efficiency = (Exit Velocity^2*(1-Effective Speed Ratio^2))/(2*Fuel Air Ratio*Fuel Calorific Value). Exit Velocity refers to the speed at which gases expand at the exit of nozzle of a engine, Effective speed ratio is the ratio of aircraft forward speed to the aircraft jet velocity, Fuel air ratio is the ratio of mass flow rate of fuel to the mass flow rate of air & Fuel Calorific Value denotes the amount of heat energy released per unit mass of fuel upon complete combustion.

How to calculate Thermal Efficiency of Jet Engines given Effective Speed Ratio?

The Thermal efficiency of jet engines given effective speed ratio formula is defined as the percentage of heat energy transformed into the work. This formula is used to calculate the thermal efficiency of jet engines when the effective speed ratio is given is calculated using Thermal Efficiency = (Exit Velocity^2*(1-Effective Speed Ratio^2))/(2*Fuel Air Ratio*Fuel Calorific Value). To calculate Thermal Efficiency of Jet Engines given Effective Speed Ratio, you need Exit Velocity (V_e), Effective Speed Ratio (α), Fuel Air Ratio (f) & Fuel Calorific Value (Q). With our tool, you need to enter the respective value for Exit Velocity, Effective Speed Ratio, Fuel Air Ratio & Fuel Calorific Value 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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