Air Standard Efficiency for Diesel Engines Calculator

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✖Compression ratio is ratio of volume of cylinder to volume combustion chamber.ⓘ Compression Ratio [r]			+10% -10%
✖The Heat Capacity Ratio also known as the adiabatic index is the ratio of specific heat at constant pressure to specific heat at constant volume of air.ⓘ Heat Capacity Ratio [γ]			+10% -10%
✖Cut-off ratio is the ratio of the volume of combustion chamber after combustion to the volume of combustion chamber before combustion.ⓘ Cut-off Ratio [r_c]			+10% -10%

✖Air standard efficiency of diesel cycle is the ratio of work output to heat supplied by the engine. It is a parameter to determine the effectiveness of the engine.ⓘ Air Standard Efficiency for Diesel Engines [η_diesel]

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Formula

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Air Standard Efficiency for Diesel Engines

Formula

`"η"_{"diesel"} = 100*(1-1/("r"^("γ"-1))*("r"_{"c"}^("γ")-1)/("γ"*("r"_{"c"}-1)))`

Example

`"64.9039"=100*(1-1/(("20")^("1.4"-1))*(("1.95")^("1.4")-1)/("1.4"*("1.95"-1)))`

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Air Standard Efficiency for Diesel Engines Solution

STEP 0: Pre-Calculation Summary

Formula Used

Air Standard Efficiency of Diesel Cycle = 100*(1-1/(Compression Ratio^(Heat Capacity Ratio-1))*(Cut-off Ratio^(Heat Capacity Ratio)-1)/(Heat Capacity Ratio*(Cut-off Ratio-1)))
η_diesel = 100*(1-1/(r^(γ-1))*(r_c^(γ)-1)/(γ*(r_c-1)))
This formula uses 4 Variables

Variables Used

Air Standard Efficiency of Diesel Cycle - Air standard efficiency of diesel cycle is the ratio of work output to heat supplied by the engine. It is a parameter to determine the effectiveness of the engine.
Compression Ratio - Compression ratio is ratio of volume of cylinder to volume combustion chamber.
Heat Capacity Ratio - The Heat Capacity Ratio also known as the adiabatic index is the ratio of specific heat at constant pressure to specific heat at constant volume of air.
Cut-off Ratio - Cut-off ratio is the ratio of the volume of combustion chamber after combustion to the volume of combustion chamber before combustion.

STEP 1: Convert Input(s) to Base Unit

Compression Ratio: 20 --> No Conversion Required
Heat Capacity Ratio: 1.4 --> No Conversion Required
Cut-off Ratio: 1.95 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

η_diesel = 100*(1-1/(r^(γ-1))*(r_c^(γ)-1)/(γ*(r_c-1))) --> 100*(1-1/(20^(1.4-1))*(1.95^(1.4)-1)/(1.4*(1.95-1)))

Evaluating ... ...

η_diesel = 64.9039049927023

STEP 3: Convert Result to Output's Unit

64.9039049927023 --> No Conversion Required

FINAL ANSWER

64.9039049927023 ≈ 64.9039 <-- Air Standard Efficiency of Diesel Cycle

(Calculation completed in 00.004 seconds)

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Created by Aditya Prakash Gautam

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

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< 18 Air-Standard Cycles Calculators

Mean Effective Pressure in Dual Cycle

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))

Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness

Go Thermal Efficiency of Stirling Cycle = 100*(([R]*ln(Compression Ratio)*(Final Temperature-Initial Temperature))/(Universal Gas Constant*Final Temperature*ln(Compression Ratio)+Molar Specific Heat Capacity at Constant Volume*(1-Effectiveness of Heat Exchanger)*(Final Temperature-Initial Temperature)))

Work Output for Dual Cycle

Go 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)

Work Output for Diesel Cycle

Go 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)

Mean Effective Pressure in Diesel Cycle

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))

Thermal Efficiency of Dual Cycle

Go 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))))

Mean Effective Pressure in Otto Cycle

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)))

Thermal Efficiency of Atkinson Cycle

Go Thermal Efficiency of Atkinson Cycle = 100*(1-Heat Capacity Ratio*((Expansion Ratio-Compression Ratio)/(Expansion Ratio^(Heat Capacity Ratio)-Compression Ratio^(Heat Capacity Ratio))))

Work Output for Otto Cycle

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)

Air Standard Efficiency for Diesel Engines

Go Air Standard Efficiency of Diesel Cycle = 100*(1-1/(Compression Ratio^(Heat Capacity Ratio-1))*(Cut-off Ratio^(Heat Capacity Ratio)-1)/(Heat Capacity Ratio*(Cut-off Ratio-1)))

Thermal Efficiency of Diesel Cycle

Go Thermal Efficiency of Diesel Cycle = 100*(1-1/Compression Ratio^(Heat Capacity Ratio-1)*(Cut-off Ratio^Heat Capacity Ratio-1)/(Heat Capacity Ratio*(Cut-off Ratio-1)))

Thermal Efficiency of Lenoir Cycle

Go Thermal Efficiency of Lenoir Cycle = 100*(1-Heat Capacity Ratio*((Pressure Ratio^(1/Heat Capacity Ratio)-1)/(Pressure Ratio-1)))

Thermal Efficiency of Ericsson Cycle

Go Thermal Efficiency of Ericsson Cycle = (Higher Temperature-Lower Temperature)/(Higher Temperature)

Air Standard Efficiency for Petrol engines

Go Air Standard Efficiency of Otto Cycle = 100*(1-1/(Compression Ratio^(Heat Capacity Ratio-1)))

Relative Air-Fuel Ratio

Go Relative Air Fuel Ratio = Actual Air Fuel Ratio/Stoichiometric Air Fuel Ratio

Air Standard Efficiency given Relative Efficiency

Go Air Standard Efficiency = Indicated Thermal Efficiency/Relative Efficiency

Thermal Efficiency of Otto Cycle

Go OTE = 1-1/Compression Ratio^(Heat Capacity Ratio-1)

Actual Air Fuel Ratio

Go Actual Air Fuel Ratio = Mass of Air/Mass of Fuel

Air Standard Efficiency for Diesel Engines Formula

What is Air standard cycle ?

The air standard cycle is a thermodynamic power cycle that converts heat energy into mechanical power by considering air as a working fluid with constant specific heats (Cp & Cv). In this cycle, there is no internal energy generation by means of burning any fuel inside of the engine. The heat is extremely added by means of a heat exchanger & also it is rejected by using heat exchange to the sink. It works as a closed cycle with no mass transfer. Working fluid air is considered an ideal gas with constant specific heat.

How to Calculate Air Standard Efficiency for Diesel Engines?

Air Standard Efficiency for Diesel Engines calculator uses Air Standard Efficiency of Diesel Cycle = 100*(1-1/(Compression Ratio^(Heat Capacity Ratio-1))*(Cut-off Ratio^(Heat Capacity Ratio)-1)/(Heat Capacity Ratio*(Cut-off Ratio-1))) to calculate the Air Standard Efficiency of Diesel Cycle, The Air standard efficiency for Diesel engines formula is defined as the percentage of heat energy that is transformed into work in diesel engine following air standard cycle. Air Standard Efficiency of Diesel Cycle is denoted by η_diesel symbol.

How to calculate Air Standard Efficiency for Diesel Engines using this online calculator? To use this online calculator for Air Standard Efficiency for Diesel Engines, enter Compression Ratio (r), Heat Capacity Ratio (γ) & Cut-off Ratio (r_c) and hit the calculate button. Here is how the Air Standard Efficiency for Diesel Engines calculation can be explained with given input values -> 66.76226 = 100*(1-1/(20^(1.4-1))*(1.95^(1.4)-1)/(1.4*(1.95-1))).

FAQ

What is Air Standard Efficiency for Diesel Engines?

The Air standard efficiency for Diesel engines formula is defined as the percentage of heat energy that is transformed into work in diesel engine following air standard cycle and is represented as η_diesel = 100*(1-1/(r^(γ-1))*(r_c^(γ)-1)/(γ*(r_c-1))) or Air Standard Efficiency of Diesel Cycle = 100*(1-1/(Compression Ratio^(Heat Capacity Ratio-1))*(Cut-off Ratio^(Heat Capacity Ratio)-1)/(Heat Capacity Ratio*(Cut-off Ratio-1))). Compression ratio is ratio of volume of cylinder to volume combustion chamber, The Heat Capacity Ratio also known as the adiabatic index is the ratio of specific heat at constant pressure to specific heat at constant volume of air & Cut-off ratio is the ratio of the volume of combustion chamber after combustion to the volume of combustion chamber before combustion.

How to calculate Air Standard Efficiency for Diesel Engines?

The Air standard efficiency for Diesel engines formula is defined as the percentage of heat energy that is transformed into work in diesel engine following air standard cycle is calculated using Air Standard Efficiency of Diesel Cycle = 100*(1-1/(Compression Ratio^(Heat Capacity Ratio-1))*(Cut-off Ratio^(Heat Capacity Ratio)-1)/(Heat Capacity Ratio*(Cut-off Ratio-1))). To calculate Air Standard Efficiency for Diesel Engines, you need Compression Ratio (r), Heat Capacity Ratio (γ) & Cut-off Ratio (r_c). With our tool, you need to enter the respective value for Compression Ratio, Heat Capacity Ratio & Cut-off Ratio and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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