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Work Output for Diesel Cycle Formula

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Work output of diesel 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 c - 1) - r^{1 - γ} \cdot ({r c}^{γ} - 1))}{γ - 1}

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

Work Output for Diesel Cycle Example

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

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

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

511.4233 = 110 \cdot 0.65 \cdot \frac{20^{1.4 - 1} \cdot (1.4 \cdot (1.95 - 1) - 20^{1 - 1.4} \cdot ({1.95}^{1.4} - 1))}{1.4 - 1}

511.4233KJ = 110kPa \cdot 0.65m³ \cdot \frac{20^{1.4 - 1} \cdot (1.4 \cdot (1.95 - 1) - 20^{1 - 1.4} \cdot ({1.95}^{1.4} - 1))}{1.4 - 1}

511.4233 = 110 \cdot 0.65 \cdot \frac{20^{1.4 - 1} \cdot (1.4 \cdot (1.95 - 1) - 20^{1 - 1.4} \cdot ({1.95}^{1.4} - 1))}{1.4 - 1}

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Work Output for Diesel Cycle Solution

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

FIRST Step Consider the formula

W d = P 1 \cdot V 1 \cdot \frac{r^{γ - 1} \cdot (γ \cdot (r c - 1) - r^{1 - γ} \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 (1.95 - 1) - 20^{1 - 1.4} \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 (1.95 - 1) - 20^{1 - 1.4} \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 (1.95 - 1) - 20^{1 - 1.4} \cdot ({1.95}^{1.4} - 1))}{1.4 - 1}

Next Step Evaluate

∴

W d = 511423.307925302J

Next Step Convert to Output's Unit

∴

W d = 511.423307925302KJ

LAST Step Rounding Answer

∴

W d = 511.4233KJ

Work Output for Diesel Cycle Formula Elements

Variables

Work Output of Diesel Cycle

Work output of diesel 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 Diesel 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

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 Work Output for Diesel Cycle?

Work Output for Diesel Cycle evaluator uses Work Output of Diesel Cycle = Pressure at Start of Isentropic Compression*Volume at Start of Isentropic Compression*(Compression Ratio^(Heat Capacity Ratio-1)*(Heat Capacity Ratio*(Cut-off Ratio-1)-Compression Ratio^(1-Heat Capacity Ratio)*(Cut-off Ratio^(Heat Capacity Ratio)-1)))/(Heat Capacity Ratio-1) to evaluate the Work Output of Diesel Cycle, Work Output for Diesel Cycle refers to the net mechanical work obtained by the diesel engine during the power stroke. This work is calculated as the area enclosed by the pressure-volume (P-V) diagram of the diesel 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 Diesel Cycle is denoted by W_d symbol.

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

FAQs on Work Output for Diesel Cycle

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

The formula of Work Output for Diesel Cycle is expressed as Work Output of Diesel Cycle = Pressure at Start of Isentropic Compression*Volume at Start of Isentropic Compression*(Compression Ratio^(Heat Capacity Ratio-1)*(Heat Capacity Ratio*(Cut-off Ratio-1)-Compression Ratio^(1-Heat Capacity Ratio)*(Cut-off Ratio^(Heat Capacity Ratio)-1)))/(Heat Capacity Ratio-1). Here is an example- 0.511423 = 110000*0.65*(20^(1.4-1)*(1.4*(1.95-1)-20^(1-1.4)*(1.95^(1.4)-1)))/(1.4-1).

How to calculate Work Output for Diesel Cycle?

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

Can the Work Output for Diesel Cycle be negative?

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

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

Work Output for Diesel 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 Diesel Cycle can be measured.

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Work Output for Diesel Cycle Formula

Work Output for Diesel Cycle Example

Work Output for Diesel Cycle Solution

Work Output for Diesel Cycle Formula Elements

Other formulas in Air Standard Cycles category

How to Evaluate Work Output for Diesel Cycle?

FAQs on Work Output for Diesel Cycle

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