Air Standard Efficiency for Diesel Engines Solution

STEP 0: Pre-Calculation Summary
Formula Used
Air Standard Efficiency = 100*(1-1/(Compression Ratio^(Heat Capacity Ratio-1))*(Cutoff Ratio^(Heat Capacity Ratio)-1)/(Heat Capacity Ratio*(Cutoff Ratio-1)))
ηair = 100*(1-1/(r^(γ-1))*(rc^(γ)-1)/(γ*(rc-1)))
This formula uses 4 Variables
Variables Used
Air Standard Efficiency - Air Standard Efficiency (in %) is the efficiency of the engine using air as the working medium. This efficiency is often called ideal efficiency.
Compression Ratio - Compression ratio is ratio between volume of cylinder and combustion chamber.
Heat Capacity Ratio - The Heat Capacity Ratio also known as the adiabatic index is the ratio of specific heats i.e. the ratio of the heat capacity at constant pressure to heat capacity at constant volume.
Cutoff Ratio - Cutoff Ratio is the ratio of the volume after combustion to the volume before combustion.
STEP 1: Convert Input(s) to Base Unit
Compression Ratio: 1.75 --> No Conversion Required
Heat Capacity Ratio: 1.4 --> No Conversion Required
Cutoff Ratio: 1.56 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ηair = 100*(1-1/(r^(γ-1))*(rc^(γ)-1)/(γ*(rc-1))) --> 100*(1-1/(1.75^(1.4-1))*(1.56^(1.4)-1)/(1.4*(1.56-1)))
Evaluating ... ...
ηair = 11.9299475409505
STEP 3: Convert Result to Output's Unit
11.9299475409505 --> No Conversion Required
FINAL ANSWER
11.9299475409505 11.92995 <-- Air Standard Efficiency
(Calculation completed in 00.004 seconds)

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18 Air-Standard Cycles Calculators

Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness
Go Thermal Efficiency of Stirling Cycle = 100*((Universal Gas Constant*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)))
Mean Effective Pressure in Dual Cycle
Go Mean Effective Pressure of Dual Cycle = Pressure at Start of Isentropic Compression*(Compression Ratio^Heat Capacity Ratio*((Explosion Ratio-1)+Heat Capacity Ratio*Explosion Ratio*(Cutoff Ratio-1))-Compression Ratio*(Explosion Ratio*Cutoff Ratio^Heat Capacity Ratio-1))/((Heat Capacity Ratio-1)*(Compression Ratio-1))
Work Output for Dual Cycle
Go Work Output of Engine = Pressure at Start of Isentropic Compression*Volume at Start of Isentropic Compression*(Compression Ratio^(Heat Capacity Ratio-1)*(Heat Capacity Ratio*Pressure Ratio*(Cutoff Ratio-1)+(Pressure Ratio-1))-(Pressure Ratio*Cutoff Ratio^(Heat Capacity Ratio)-1))/(Heat Capacity Ratio-1)
Work Output for Diesel Cycle
Go Work Output of Engine = Pressure at Start of Isentropic Compression*Volume at Start of Isentropic Compression*(Compression Ratio^(Heat Capacity Ratio-1)*(Heat Capacity Ratio*(Cutoff Ratio-1)-Compression Ratio^(1-Heat Capacity Ratio)*(Cutoff Ratio^(Heat Capacity Ratio)-1)))/(Heat Capacity Ratio-1)
Mean Effective Pressure in Diesel Cycle
Go Mean Effective Pressure in Diesel Cycle = Pressure at Start of Isentropic Compression*(Heat Capacity Ratio*Compression Ratio^Heat Capacity Ratio*(Cutoff Ratio-1)-Compression Ratio*(Cutoff 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))*((Explosion Ratio*Cutoff Ratio^Heat Capacity Ratio-1)/(Explosion Ratio-1+Explosion Ratio*Heat Capacity Ratio*(Cutoff Ratio-1))))
Mean Effective Pressure in Otto Cycle
Go Mean Effective Pressure = 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 Engine = 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)
Thermal Efficiency of Diesel Cycle
Go Thermal Efficiency of Diesel Cycle = 100*(1-1/Compression Ratio^(Heat Capacity Ratio-1)*(Cutoff Ratio^Heat Capacity Ratio-1)/(Heat Capacity Ratio*(Cutoff Ratio-1)))
Air Standard Efficiency for Diesel Engines
Go Air Standard Efficiency = 100*(1-1/(Compression Ratio^(Heat Capacity Ratio-1))*(Cutoff Ratio^(Heat Capacity Ratio)-1)/(Heat Capacity Ratio*(Cutoff 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 = 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

Air Standard Efficiency = 100*(1-1/(Compression Ratio^(Heat Capacity Ratio-1))*(Cutoff Ratio^(Heat Capacity Ratio)-1)/(Heat Capacity Ratio*(Cutoff Ratio-1)))
ηair = 100*(1-1/(r^(γ-1))*(rc^(γ)-1)/(γ*(rc-1)))

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 = 100*(1-1/(Compression Ratio^(Heat Capacity Ratio-1))*(Cutoff Ratio^(Heat Capacity Ratio)-1)/(Heat Capacity Ratio*(Cutoff Ratio-1))) to calculate the Air Standard Efficiency, 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 is denoted by ηair 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) & Cutoff Ratio (rc) and hit the calculate button. Here is how the Air Standard Efficiency for Diesel Engines calculation can be explained with given input values -> 11.92995 = 100*(1-1/(1.75^(1.4-1))*(1.56^(1.4)-1)/(1.4*(1.56-1))).

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 ηair = 100*(1-1/(r^(γ-1))*(rc^(γ)-1)/(γ*(rc-1))) or Air Standard Efficiency = 100*(1-1/(Compression Ratio^(Heat Capacity Ratio-1))*(Cutoff Ratio^(Heat Capacity Ratio)-1)/(Heat Capacity Ratio*(Cutoff Ratio-1))). Compression ratio is ratio between volume of cylinder and combustion chamber, The Heat Capacity Ratio also known as the adiabatic index is the ratio of specific heats i.e. the ratio of the heat capacity at constant pressure to heat capacity at constant volume & Cutoff Ratio is the ratio of the volume after combustion to the volume 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 = 100*(1-1/(Compression Ratio^(Heat Capacity Ratio-1))*(Cutoff Ratio^(Heat Capacity Ratio)-1)/(Heat Capacity Ratio*(Cutoff Ratio-1))). To calculate Air Standard Efficiency for Diesel Engines, you need Compression Ratio (r), Heat Capacity Ratio (γ) & Cutoff Ratio (rc). With our tool, you need to enter the respective value for Compression Ratio, Heat Capacity Ratio & Cutoff Ratio and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Air Standard Efficiency?
In this formula, Air Standard Efficiency uses Compression Ratio, Heat Capacity Ratio & Cutoff Ratio. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Air Standard Efficiency = 100*(1-1/(Compression Ratio^(Heat Capacity Ratio-1)))
  • Air Standard Efficiency = Indicated Thermal Efficiency/Relative Efficiency
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