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Thermal Efficiency of Dual Cycle Formula

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The Thermal Efficiency of Dual Cycle represents the effectiveness of dual engine. It is measured by comparing how much work is done through out the system to the heat supplied to the system. Check FAQs

ε d = 100 \cdot (1 - \frac{1}{r^{γ - 1}} \cdot (\frac{R p \cdot {r c}^{γ} - 1}{R p - 1 + R p \cdot γ \cdot (r c - 1)}))

ε_d - Thermal Efficiency of Dual Cycle?r - Compression Ratio?γ - Heat Capacity Ratio?R_p - Pressure Ratio in Dual Cycle?r_c - Cut-off Ratio?

Thermal Efficiency of Dual Cycle Example

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Here is how the Thermal Efficiency of Dual Cycle equation looks like with Values.

Here is how the Thermal Efficiency of Dual Cycle equation looks like with Units.

Here is how the Thermal Efficiency of Dual Cycle equation looks like.

66.6046 = 100 \cdot (1 - \frac{1}{20^{1.4 - 1}} \cdot (\frac{3.35 \cdot {1.95}^{1.4} - 1}{3.35 - 1 + 3.35 \cdot 1.4 \cdot (1.95 - 1)}))

66.6046 = 100 \cdot (1 - \frac{1}{20^{1.4 - 1}} \cdot (\frac{3.35 \cdot {1.95}^{1.4} - 1}{3.35 - 1 + 3.35 \cdot 1.4 \cdot (1.95 - 1)}))

66.6046 = 100 \cdot (1 - \frac{1}{20^{1.4 - 1}} \cdot (\frac{3.35 \cdot {1.95}^{1.4} - 1}{3.35 - 1 + 3.35 \cdot 1.4 \cdot (1.95 - 1)}))

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Thermal Efficiency of Dual Cycle Solution

Follow our step by step solution on how to calculate Thermal Efficiency of Dual Cycle?

FIRST Step Consider the formula

ε d = 100 \cdot (1 - \frac{1}{r^{γ - 1}} \cdot (\frac{R p \cdot {r c}^{γ} - 1}{R p - 1 + R p \cdot γ \cdot (r c - 1)}))

Next Step Substitute values of Variables

∴

ε d = 100 \cdot (1 - \frac{1}{20^{1.4 - 1}} \cdot (\frac{3.35 \cdot {1.95}^{1.4} - 1}{3.35 - 1 + 3.35 \cdot 1.4 \cdot (1.95 - 1)}))

Next Step Prepare to Evaluate

∴

ε d = 100 \cdot (1 - \frac{1}{20^{1.4 - 1}} \cdot (\frac{3.35 \cdot {1.95}^{1.4} - 1}{3.35 - 1 + 3.35 \cdot 1.4 \cdot (1.95 - 1)}))

Next Step Evaluate

∴

ε d = 66.6046251914744

LAST Step Rounding Answer

∴

ε d = 66.6046

Thermal Efficiency of Dual Cycle Formula Elements

Variables

Thermal Efficiency of Dual Cycle

The Thermal Efficiency of Dual Cycle represents the effectiveness of dual engine. It is measured by comparing how much work is done through out the system to the heat supplied to the system.

Symbol: ε_d

Measurement: NAUnit: Unitless

Note: Value should be less than 100.

Formulas to find Thermal Efficiency of Dual Cycle

Compression Ratio

Compression ratio refers to how much the air-fuel mixture is squeezed in the cylinder before ignition. It's essentially the ratio between the volume of the cylinder at BDC to TDC.

Symbol: r

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Compression Ratio

Heat Capacity Ratio

The Heat Capacity Ratio or, adiabatic index quantifies the relationship between heat added at constant pressure and the resulting temperature increase compared to heat added at constant volume.

Symbol: γ

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Heat Capacity Ratio

Pressure Ratio in Dual Cycle

Pressure ratio in dual cycle is the ratio of the maximum pressure during combustion to the minimum pressure at the end of exhaust, reflecting compression and expansion characteristics of the cycle.

Symbol: R_p

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Pressure Ratio in Dual Cycle

Cut-off Ratio

Cut-off ratio is the ratio of the cylinder volume at the start of compression stroke to the volume at the end of expansion stroke. It's a measure of piston's compression of the charge before ignition.

Symbol: r_c

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Cut-off Ratio

Other formulas in Air Standard Cycles category

Go Mean Effective Pressure in Otto Cycle

P O = P 1 \cdot r \cdot (\frac{(r^{γ - 1} - 1) \cdot (r p - 1)}{(r - 1) \cdot (γ - 1)})

Go Mean Effective Pressure in Diesel Cycle

P D = P 1 \cdot \frac{γ \cdot r^{γ} \cdot (r c - 1) - r \cdot ({r c}^{γ} - 1)}{(γ - 1) \cdot (r - 1)}

Go Mean Effective Pressure in Dual Cycle

P d = P 1 \cdot \frac{r^{γ} \cdot ((R p - 1) + γ \cdot R p \cdot (r c - 1)) - r \cdot (R p \cdot {r c}^{γ} - 1)}{(γ - 1) \cdot (r - 1)}

Go Work Output for Otto Cycle

W o = P 1 \cdot V 1 \cdot \frac{(r p - 1) \cdot (r^{γ - 1} - 1)}{γ - 1}

How to Evaluate Thermal Efficiency of Dual Cycle?

Thermal Efficiency of Dual Cycle evaluator uses Thermal Efficiency of Dual Cycle = 100*(1-1/(Compression Ratio^(Heat Capacity Ratio-1))*((Pressure Ratio in Dual Cycle*Cut-off Ratio^Heat Capacity Ratio-1)/(Pressure Ratio in Dual Cycle-1+Pressure Ratio in Dual Cycle*Heat Capacity Ratio*(Cut-off Ratio-1)))) to evaluate the Thermal Efficiency of Dual Cycle, Thermal Efficiency of Dual Cycle refers to the ability to efficiently convert heat energy from burning fuel into usable work output of dual cycle engine. It aims to combine the benefits of both Diesel and Otto cycles, potentially achieving improved overall efficiency in certain operating conditions. Thermal Efficiency of Dual Cycle is denoted by ε_d symbol.

How to evaluate Thermal Efficiency of Dual Cycle using this online evaluator? To use this online evaluator for Thermal Efficiency of Dual Cycle, enter Compression Ratio (r), Heat Capacity Ratio (γ), Pressure Ratio in Dual Cycle (R_p) & Cut-off Ratio (r_c) and hit the calculate button.

FAQs on Thermal Efficiency of Dual Cycle

What is the formula to find Thermal Efficiency of Dual Cycle?

The formula of Thermal Efficiency of Dual Cycle is expressed as Thermal Efficiency of Dual Cycle = 100*(1-1/(Compression Ratio^(Heat Capacity Ratio-1))*((Pressure Ratio in Dual Cycle*Cut-off Ratio^Heat Capacity Ratio-1)/(Pressure Ratio in Dual Cycle-1+Pressure Ratio in Dual Cycle*Heat Capacity Ratio*(Cut-off Ratio-1)))). Here is an example- 66.60463 = 100*(1-1/(20^(1.4-1))*((3.35*1.95^1.4-1)/(3.35-1+3.35*1.4*(1.95-1)))).

How to calculate Thermal Efficiency of Dual Cycle?

With Compression Ratio (r), Heat Capacity Ratio (γ), Pressure Ratio in Dual Cycle (R_p) & Cut-off Ratio (r_c) we can find Thermal Efficiency of Dual Cycle using the formula - Thermal Efficiency of Dual Cycle = 100*(1-1/(Compression Ratio^(Heat Capacity Ratio-1))*((Pressure Ratio in Dual Cycle*Cut-off Ratio^Heat Capacity Ratio-1)/(Pressure Ratio in Dual Cycle-1+Pressure Ratio in Dual Cycle*Heat Capacity Ratio*(Cut-off Ratio-1)))).

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Thermal Efficiency of Dual Cycle Formula

Thermal Efficiency of Dual Cycle Example

Thermal Efficiency of Dual Cycle Solution

Thermal Efficiency of Dual Cycle Formula Elements

Other formulas in Air Standard Cycles category

How to Evaluate Thermal Efficiency of Dual Cycle?

FAQs on Thermal Efficiency of Dual Cycle

Variable Name