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Work Output for Dual Cycle Formula

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The work output of dual cycle is the net difference between the work done on the gas during compression and the work done by the gas during expansion. It is the area enclosed by p-v diagram. Check FAQs

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

W_D - Work Output of Dual Cycle?P₁ - Pressure at Start of Isentropic Compression?V₁ - Volume at Start of Isentropic Compression?r - Compression Ratio?γ - Heat Capacity Ratio?r_p - Pressure Ratio?r_c - Cut-off Ratio?

Work Output for Dual Cycle Example

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Here is how the Work Output for Dual Cycle equation looks like with Values.

Here is how the Work Output for Dual Cycle equation looks like with Units.

Here is how the Work Output for Dual Cycle equation looks like.

2676.2321 = 110 \cdot 0.65 \cdot \frac{20^{1.4 - 1} \cdot (1.4 \cdot 3.34 \cdot (1.95 - 1) + (3.34 - 1)) - (3.34 \cdot {1.95}^{1.4} - 1)}{1.4 - 1}

2676.2321KJ = 110kPa \cdot 0.65m³ \cdot \frac{20^{1.4 - 1} \cdot (1.4 \cdot 3.34 \cdot (1.95 - 1) + (3.34 - 1)) - (3.34 \cdot {1.95}^{1.4} - 1)}{1.4 - 1}

2676.2321 = 110 \cdot 0.65 \cdot \frac{20^{1.4 - 1} \cdot (1.4 \cdot 3.34 \cdot (1.95 - 1) + (3.34 - 1)) - (3.34 \cdot {1.95}^{1.4} - 1)}{1.4 - 1}

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Work Output for Dual Cycle Solution

Follow our step by step solution on how to calculate Work Output for Dual Cycle?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

W D = 110kPa \cdot 0.65m³ \cdot \frac{20^{1.4 - 1} \cdot (1.4 \cdot 3.34 \cdot (1.95 - 1) + (3.34 - 1)) - (3.34 \cdot {1.95}^{1.4} - 1)}{1.4 - 1}

Next Step Convert Units

∴

W D = 110000Pa \cdot 0.65m³ \cdot \frac{20^{1.4 - 1} \cdot (1.4 \cdot 3.34 \cdot (1.95 - 1) + (3.34 - 1)) - (3.34 \cdot {1.95}^{1.4} - 1)}{1.4 - 1}

Next Step Prepare to Evaluate

∴

W D = 110000 \cdot 0.65 \cdot \frac{20^{1.4 - 1} \cdot (1.4 \cdot 3.34 \cdot (1.95 - 1) + (3.34 - 1)) - (3.34 \cdot {1.95}^{1.4} - 1)}{1.4 - 1}

Next Step Evaluate

∴

W D = 2676232.10257339J

Next Step Convert to Output's Unit

∴

W D = 2676.23210257339KJ

LAST Step Rounding Answer

∴

W D = 2676.2321KJ

Work Output for Dual Cycle Formula Elements

Variables

Work Output of Dual Cycle

The work output of dual cycle is the net difference between the work done on the gas during compression and the work done by the gas during expansion. It is the area enclosed by p-v diagram.

Symbol: W_D

Measurement: EnergyUnit: KJ

Note: Value should be greater than 0.

Formulas to find Work Output of Dual Cycle

Pressure at Start of Isentropic Compression

Pressure at Start of Isentropic Compression refers to the pressure exerted by the charge inside the wall of the cylinder at the start of the reversible adiabatic compression process in IC engine.

Symbol: P₁

Measurement: PressureUnit: kPa

Note: Value should be greater than 0.

Formulas to find Pressure at Start of Isentropic Compression

Volume at Start of Isentropic Compression

Volume at Start of Isentropic Compression is the volume of the engine cylinder before reversible adiabatic process, keeping entropy as constant. It is essentially the swept volume of the cylinder.

Symbol: V₁

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume at Start of Isentropic Compression

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

Pressure ratio 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 engine cycle.

Symbol: r_p

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Pressure Ratio

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)}

How to Evaluate Work Output for Dual Cycle?

Work Output for Dual Cycle evaluator uses Work Output of Dual Cycle = Pressure at Start of Isentropic Compression*Volume at Start of Isentropic Compression*(Compression Ratio^(Heat Capacity Ratio-1)*(Heat Capacity Ratio*Pressure Ratio*(Cut-off Ratio-1)+(Pressure Ratio-1))-(Pressure Ratio*Cut-off Ratio^(Heat Capacity Ratio)-1))/(Heat Capacity Ratio-1) to evaluate the Work Output of Dual Cycle, Work Output for Dual Cycle refers to the net mechanical work obtained by the dual cycle engine during the combined power stroke. This work is calculated as the area enclosed by the pressure-volume (P-V) diagram of the dual cycle. It represents the usable energy extracted from the fuel by the engine. It is a crucial parameter for determining the efficiency of the engine. Work Output of Dual Cycle is denoted by W_D symbol.

How to evaluate Work Output for Dual Cycle using this online evaluator? To use this online evaluator for Work Output for Dual Cycle, enter Pressure at Start of Isentropic Compression (P₁), Volume at Start of Isentropic Compression (V₁), Compression Ratio (r), Heat Capacity Ratio (γ), Pressure Ratio (r_p) & Cut-off Ratio (r_c) and hit the calculate button.

FAQs on Work Output for Dual Cycle

What is the formula to find Work Output for Dual Cycle?

The formula of Work Output for Dual Cycle is expressed as Work Output of Dual Cycle = Pressure at Start of Isentropic Compression*Volume at Start of Isentropic Compression*(Compression Ratio^(Heat Capacity Ratio-1)*(Heat Capacity Ratio*Pressure Ratio*(Cut-off Ratio-1)+(Pressure Ratio-1))-(Pressure Ratio*Cut-off Ratio^(Heat Capacity Ratio)-1))/(Heat Capacity Ratio-1). Here is an example- 2.676232 = 110000*0.65*(20^(1.4-1)*(1.4*3.34*(1.95-1)+(3.34-1))-(3.34*1.95^(1.4)-1))/(1.4-1).

How to calculate Work Output for Dual Cycle?

With Pressure at Start of Isentropic Compression (P₁), Volume at Start of Isentropic Compression (V₁), Compression Ratio (r), Heat Capacity Ratio (γ), Pressure Ratio (r_p) & Cut-off Ratio (r_c) we can find Work Output for Dual Cycle using the formula - Work Output of Dual Cycle = Pressure at Start of Isentropic Compression*Volume at Start of Isentropic Compression*(Compression Ratio^(Heat Capacity Ratio-1)*(Heat Capacity Ratio*Pressure Ratio*(Cut-off Ratio-1)+(Pressure Ratio-1))-(Pressure Ratio*Cut-off Ratio^(Heat Capacity Ratio)-1))/(Heat Capacity Ratio-1).

Can the Work Output for Dual Cycle be negative?

No, the Work Output for Dual Cycle, measured in Energy cannot be negative.

Which unit is used to measure Work Output for Dual Cycle?

Work Output for Dual Cycle is usually measured using the Kilojoule[KJ] for Energy. Joule[KJ], Gigajoule[KJ], Megajoule[KJ] are the few other units in which Work Output for Dual Cycle can be measured.

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Work Output for Dual Cycle Formula

Work Output for Dual Cycle Example

Work Output for Dual Cycle Solution

Work Output for Dual Cycle Formula Elements

Other formulas in Air Standard Cycles category

How to Evaluate Work Output for Dual Cycle?

FAQs on Work Output for Dual Cycle

Variable Name