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Thermal Efficiency of Jet Engines given Effective Speed Ratio Formula

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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. Check FAQs

η th = \frac{{V e}^{2} \cdot (1 - α^{2})}{2 \cdot f \cdot Q}

η_th - Thermal Efficiency?V_e - Exit Velocity?α - Effective Speed Ratio?f - Fuel Air Ratio?Q - Fuel Calorific Value?

Thermal Efficiency of Jet Engines given Effective Speed Ratio Example

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Here is how the Thermal Efficiency of Jet Engines given Effective Speed Ratio equation looks like with Values.

Here is how the Thermal Efficiency of Jet Engines given Effective Speed Ratio equation looks like with Units.

Here is how the Thermal Efficiency of Jet Engines given Effective Speed Ratio equation looks like.

0.0628 = \frac{248^{2} \cdot (1 - {0.4475}^{2})}{2 \cdot 0.009 \cdot 43510}

0.0628 = \frac{{248m/s}^{2} \cdot (1 - {0.4475}^{2})}{2 \cdot 0.009 \cdot 43510kJ/kg}

0.0628 = \frac{248^{2} \cdot (1 - {0.4475}^{2})}{2 \cdot 0.009 \cdot 43510}

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Thermal Efficiency of Jet Engines given Effective Speed Ratio Solution

Follow our step by step solution on how to calculate Thermal Efficiency of Jet Engines given Effective Speed Ratio?

FIRST Step Consider the formula

η th = \frac{{V e}^{2} \cdot (1 - α^{2})}{2 \cdot f \cdot Q}

Next Step Substitute values of Variables

∴

η th = \frac{{248m/s}^{2} \cdot (1 - {0.4475}^{2})}{2 \cdot 0.009 \cdot 43510kJ/kg}

Next Step Convert Units

∴

η th = \frac{{248m/s}^{2} \cdot (1 - {0.4475}^{2})}{2 \cdot 0.009 \cdot 4.4E+7J/kg}

Next Step Prepare to Evaluate

∴

η th = \frac{248^{2} \cdot (1 - {0.4475}^{2})}{2 \cdot 0.009 \cdot 4.4E+7}

Next Step Evaluate

∴

η th = 0.0628047697847238

LAST Step Rounding Answer

∴

η th = 0.0628

Thermal Efficiency of Jet Engines given Effective Speed Ratio Formula Elements

Variables

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.

Symbol: η_th

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Thermal Efficiency

Exit Velocity

Exit Velocity refers to the speed at which gases expand at the exit of nozzle of a engine.

Symbol: V_e

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Exit Velocity

Effective Speed Ratio

Effective Speed Ratio is the ratio of aircraft forward speed to the aircraft jet velocity.

Symbol: α

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Effective Speed Ratio

Fuel Air Ratio

Fuel Air Ratio is the ratio of mass flow rate of fuel to the mass flow rate of air.

Symbol: f

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Fuel Air Ratio

Fuel Calorific Value

Fuel Calorific Value denotes the amount of heat energy released per unit mass of fuel upon complete combustion.

Symbol: Q

Measurement: Specific EnergyUnit: kJ/kg

Note: Value should be greater than 0.

Formulas to find Fuel Calorific Value

Other formulas in Efficiency Metrics category

Go Isentropic Efficiency of Expansion Machine

η T = \frac{W actual}{W s,out}

Go Net work output in simple gas turbine cycle

W Net = C p \cdot ((T 3 - T 4) - (T 2 - T 1))

Go Propulsive power

P = \frac{1}{2} \cdot ((m a + m f) \cdot {V e}^{2} - (m a \cdot V^{2}))

Go Transmission Efficiency given Output and Input of Transmission

η transmission = \frac{P out}{P in}

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

Thermal Efficiency of Jet Engines given Effective Speed Ratio evaluator uses Thermal Efficiency = (Exit Velocity^2*(1-Effective Speed Ratio^2))/(2*Fuel Air Ratio*Fuel Calorific Value) to evaluate the Thermal Efficiency, Thermal Efficiency of Jet Engines given Effective Speed Ratio is a measure of the efficiency of a jet engine, which is a critical parameter in aerospace engineering, defined as the ratio of the useful work output to the total energy input, indicating how effectively the engine converts energy into thrust. Thermal Efficiency is denoted by η_th symbol.

How to evaluate Thermal Efficiency of Jet Engines given Effective Speed Ratio using this online evaluator? To use this online evaluator 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.

FAQs on Thermal Efficiency of Jet Engines given Effective Speed Ratio

What is the formula to find Thermal Efficiency of Jet Engines given Effective Speed Ratio?

The formula of Thermal Efficiency of Jet Engines given Effective Speed Ratio is expressed as Thermal Efficiency = (Exit Velocity^2*(1-Effective Speed Ratio^2))/(2*Fuel Air Ratio*Fuel Calorific Value). Here is an example- 0.062805 = (248^2*(1-0.4475^2))/(2*0.009*43510000).

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

With Exit Velocity (V_e), Effective Speed Ratio (α), Fuel Air Ratio (f) & Fuel Calorific Value (Q) we can find Thermal Efficiency of Jet Engines given Effective Speed Ratio using the formula - Thermal Efficiency = (Exit Velocity^2*(1-Effective Speed Ratio^2))/(2*Fuel Air Ratio*Fuel Calorific Value).

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Thermal Efficiency of Jet Engines given Effective Speed Ratio Formula

Thermal Efficiency of Jet Engines given Effective Speed Ratio Example

Thermal Efficiency of Jet Engines given Effective Speed Ratio Solution

Thermal Efficiency of Jet Engines given Effective Speed Ratio Formula Elements

Other formulas in Efficiency Metrics category

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

FAQs on Thermal Efficiency of Jet Engines given Effective Speed Ratio

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