HCF of three numbers

Work Output for Dual Cycle Calculator

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✖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.ⓘ Pressure at Start of Isentropic Compression [P₁]			+10% -10%
✖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.ⓘ Volume at Start of Isentropic Compression [V₁]			+10% -10%
✖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.ⓘ Compression Ratio [r]			+10% -10%
✖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.ⓘ Heat Capacity Ratio [γ]			+10% -10%
✖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.ⓘ Pressure Ratio [r_p]			+10% -10%
✖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.ⓘ Cut-off Ratio [r_c]			+10% -10%

✖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.ⓘ Work Output for Dual Cycle [W_D]

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Work Output for Dual Cycle Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
W_D = P₁*V₁*(r^(γ-1)*(γ*r_p*(r_c-1)+(r_p-1))-(r_p*r_c^(γ)-1))/(γ-1)
This formula uses 7 Variables

Variables Used

Work Output of Dual Cycle - (Measured in Joule) - 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.
Pressure at Start of Isentropic Compression - (Measured in Pascal) - 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.
Volume at Start of Isentropic Compression - (Measured in Cubic Meter) - 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.
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.
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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Pressure at Start of Isentropic Compression: 110 Kilopascal --> 110000 Pascal (Check conversion here)
Volume at Start of Isentropic Compression: 0.65 Cubic Meter --> 0.65 Cubic Meter No Conversion Required
Compression Ratio: 20 --> No Conversion Required
Heat Capacity Ratio: 1.4 --> No Conversion Required
Pressure Ratio: 3.34 --> No Conversion Required
Cut-off Ratio: 1.95 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

W_D = P₁*V₁*(r^(γ-1)*(γ*r_p*(r_c-1)+(r_p-1))-(r_p*r_c^(γ)-1))/(γ-1) --> 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)

Evaluating ... ...

W_D = 2676232.10257339

STEP 3: Convert Result to Output's Unit

2676232.10257339 Joule -->2676.23210257339 Kilojoule (Check conversion here)

FINAL ANSWER

2676.23210257339 ≈ 2676.232 Kilojoule <-- Work Output of Dual Cycle

(Calculation completed in 00.004 seconds)

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Indian Institute of Technology (IIT (ISM) ), Dhanbad, Jharkhand

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< Air Standard Cycles Calculators

Mean Effective Pressure in Dual Cycle

LaTeX Go Mean Effective Pressure of Dual Cycle = Pressure at Start of Isentropic Compression*(Compression Ratio^Heat Capacity Ratio*((Pressure Ratio in Dual Cycle-1)+Heat Capacity Ratio*Pressure Ratio in Dual Cycle*(Cut-off Ratio-1))-Compression Ratio*(Pressure Ratio in Dual Cycle*Cut-off Ratio^Heat Capacity Ratio-1))/((Heat Capacity Ratio-1)*(Compression Ratio-1))

Mean Effective Pressure in Diesel Cycle

LaTeX Go Mean Effective Pressure of Diesel Cycle = Pressure at Start of Isentropic Compression*(Heat Capacity Ratio*Compression Ratio^Heat Capacity Ratio*(Cut-off Ratio-1)-Compression Ratio*(Cut-off Ratio^Heat Capacity Ratio-1))/((Heat Capacity Ratio-1)*(Compression Ratio-1))

Mean Effective Pressure in Otto Cycle

LaTeX Go Mean Effective Pressure of Otto Cycle = Pressure at Start of Isentropic Compression*Compression Ratio*(((Compression Ratio^(Heat Capacity Ratio-1)-1)*(Pressure Ratio-1))/((Compression Ratio-1)*(Heat Capacity Ratio-1)))

Work Output for Otto Cycle

LaTeX Go Work Output of Otto Cycle = Pressure at Start of Isentropic Compression*Volume at Start of Isentropic Compression*((Pressure Ratio-1)*(Compression Ratio^(Heat Capacity Ratio-1)-1))/(Heat Capacity Ratio-1)

Work Output for Dual Cycle Formula

LaTeX Go

What is Dual Cycle?

Dual cycle or Limited Pressure cycle is a thermodynamic cycle that combines the Otto cycle and the Diesel cycle. In the dual cycle, combustion occurs partly at constant volume and partly at constant pressure.
In a dual cycle, the system executing the cycle undergoes a series of five processes: two isentropic (reversible adiabatic) processes alternated with two isochoric processes and one isobaric process.

How to Calculate Work Output for Dual Cycle?

Work Output for Dual Cycle calculator 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 calculate 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 calculate Work Output for Dual Cycle using this online calculator? To use this online calculator 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. Here is how the Work Output for Dual Cycle calculation can be explained with given input values -> 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).

FAQ

What is Work Output for 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 and is represented as W_D = P₁*V₁*(r^(γ-1)*(γ*r_p*(r_c-1)+(r_p-1))-(r_p*r_c^(γ)-1))/(γ-1) or 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). 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, 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, 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, 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, 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 & 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.

How to calculate Work Output for Dual Cycle?

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