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Mean Effective Pressure in Dual Cycle Formula

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Mean effective pressure of dual cycle refers to a theoretical constant pressure that is applied on the piston throughout the cycle. MEP is calculated by using indicator diagram of the cycle. Check FAQs

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)}

P_d - Mean Effective Pressure of Dual Cycle?P₁ - Pressure at Start of Isentropic Compression?r - Compression Ratio?γ - Heat Capacity Ratio?R_p - Pressure Ratio in Dual Cycle?r_c - Cut-off Ratio?

Mean Effective Pressure in Dual Cycle Example

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Here is how the Mean Effective Pressure in Dual Cycle equation looks like with Values.

Here is how the Mean Effective Pressure in Dual Cycle equation looks like with Units.

Here is how the Mean Effective Pressure in Dual Cycle equation looks like.

4348.961 = 110 \cdot \frac{20^{1.4} \cdot ((3.35 - 1) + 1.4 \cdot 3.35 \cdot (1.95 - 1)) - 20 \cdot (3.35 \cdot {1.95}^{1.4} - 1)}{(1.4 - 1) \cdot (20 - 1)}

4348.961kPa = 110kPa \cdot \frac{20^{1.4} \cdot ((3.35 - 1) + 1.4 \cdot 3.35 \cdot (1.95 - 1)) - 20 \cdot (3.35 \cdot {1.95}^{1.4} - 1)}{(1.4 - 1) \cdot (20 - 1)}

4348.961 = 110 \cdot \frac{20^{1.4} \cdot ((3.35 - 1) + 1.4 \cdot 3.35 \cdot (1.95 - 1)) - 20 \cdot (3.35 \cdot {1.95}^{1.4} - 1)}{(1.4 - 1) \cdot (20 - 1)}

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Mean Effective Pressure in Dual Cycle Solution

Follow our step by step solution on how to calculate Mean Effective Pressure in Dual Cycle?

FIRST Step Consider the formula

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)}

Next Step Substitute values of Variables

∴

P d = 110kPa \cdot \frac{20^{1.4} \cdot ((3.35 - 1) + 1.4 \cdot 3.35 \cdot (1.95 - 1)) - 20 \cdot (3.35 \cdot {1.95}^{1.4} - 1)}{(1.4 - 1) \cdot (20 - 1)}

Next Step Convert Units

∴

P d = 110000Pa \cdot \frac{20^{1.4} \cdot ((3.35 - 1) + 1.4 \cdot 3.35 \cdot (1.95 - 1)) - 20 \cdot (3.35 \cdot {1.95}^{1.4} - 1)}{(1.4 - 1) \cdot (20 - 1)}

Next Step Prepare to Evaluate

∴

P d = 110000 \cdot \frac{20^{1.4} \cdot ((3.35 - 1) + 1.4 \cdot 3.35 \cdot (1.95 - 1)) - 20 \cdot (3.35 \cdot {1.95}^{1.4} - 1)}{(1.4 - 1) \cdot (20 - 1)}

Next Step Evaluate

∴

P d = 4348961.00762533Pa

Next Step Convert to Output's Unit

∴

P d = 4348.96100762533kPa

LAST Step Rounding Answer

∴

P d = 4348.961kPa

Mean Effective Pressure in Dual Cycle Formula Elements

Variables

Mean Effective Pressure of Dual Cycle

Mean effective pressure of dual cycle refers to a theoretical constant pressure that is applied on the piston throughout the cycle. MEP is calculated by using indicator diagram of the cycle.

Symbol: P_d

Measurement: PressureUnit: kPa

Note: Value should be greater than 0.

Formulas to find Mean Effective Pressure 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

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 in Dual Cycle

Pressure ratio in dual cycle 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 cycle.

Symbol: R_p

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Pressure Ratio in Dual 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.

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 Work Output for Otto Cycle

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

Go Work Output for Diesel Cycle

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}

How to Evaluate Mean Effective Pressure in Dual Cycle?

Mean Effective Pressure in Dual Cycle evaluator uses 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)) to evaluate the Mean Effective Pressure of Dual Cycle, Mean Effective Pressure in Dual Cycle is a vital parameter that reflects the dual cycle engine's ability to generate work output. Imagine a constant pressure acting on the engine piston throughout the entire cycle (intake, compression, combustion, exhaust) that would produce the same amount of work output as the actual varying pressure experienced in the real cycle. Mean effective pressure essentially represents that constant pressure. It is calculated based on the engine's geometry (displacement) and the indicator diagram, which depicts the pressure variations within the cylinder throughout the cycle. Mean Effective Pressure of Dual Cycle is denoted by P_d symbol.

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

FAQs on Mean Effective Pressure in Dual Cycle

What is the formula to find Mean Effective Pressure in Dual Cycle?

The formula of Mean Effective Pressure in Dual Cycle is expressed as 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)). Here is an example- 4.348961 = 110000*(20^1.4*((3.35-1)+1.4*3.35*(1.95-1))-20*(3.35*1.95^1.4-1))/((1.4-1)*(20-1)).

How to calculate Mean Effective Pressure in Dual Cycle?

With Pressure at Start of Isentropic Compression (P₁), Compression Ratio (r), Heat Capacity Ratio (γ), Pressure Ratio in Dual Cycle (R_p) & Cut-off Ratio (r_c) we can find Mean Effective Pressure in Dual Cycle using the formula - 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)).

Can the Mean Effective Pressure in Dual Cycle be negative?

No, the Mean Effective Pressure in Dual Cycle, measured in Pressure cannot be negative.

Which unit is used to measure Mean Effective Pressure in Dual Cycle?

Mean Effective Pressure in Dual Cycle is usually measured using the Kilopascal[kPa] for Pressure. Pascal[kPa], Bar[kPa], Pound Per Square Inch[kPa] are the few other units in which Mean Effective Pressure in Dual Cycle can be measured.

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Mean Effective Pressure in Dual Cycle Formula

Mean Effective Pressure in Dual Cycle Example

Mean Effective Pressure in Dual Cycle Solution

Mean Effective Pressure in Dual Cycle Formula Elements

Other formulas in Air Standard Cycles category

How to Evaluate Mean Effective Pressure in Dual Cycle?

FAQs on Mean Effective Pressure in Dual Cycle

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