Power Required to Maintain Pressure inside Cabin including Ram Work Calculator

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Air Refrigeration Systems

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✖Mass of air is both a property of air and a measure of its resistance to acceleration when a net force is applied.ⓘ Mass of Air [ma]			+10% -10%
✖Specific Heat Capacity at Constant Pressure means the amount of heat that is required to raise the temperature of a unit mass of gas by 1 degree at constant pressure.ⓘ Specific Heat Capacity at Constant Pressure [C_p]			+10% -10%
✖Ambient Air Temperature is the temperature where the ramming process starts.ⓘ Ambient Air Temperature [T_a]			+10% -10%
✖Compressor efficiency is the ratio of input kinetic energy to the work done.ⓘ Compressor Efficiency [CE]			+10% -10%
✖Cabin Pressure is the pressure inside the aircraft.ⓘ Cabin Pressure [p_c]			+10% -10%
✖Atmospheric pressure, also known as barometric pressure, is the pressure within the atmosphere of Earth.ⓘ Atmospheric Pressure [P_atm]			+10% -10%
✖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.ⓘ Heat Capacity Ratio [γ]			+10% -10%

✖Input Power is the power, which is required by the appliance at its input i.e., from the plug point.ⓘ Power Required to Maintain Pressure inside Cabin including Ram Work [P_in]

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Formula

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Power Required to Maintain Pressure inside Cabin including Ram Work

Formula

`"P"_{"in"} = (("ma"*"C"_{"p"}*"T"_{"a"})/("CE"))*(("p"_{"c"}/"P"_{"atm"})^(("γ"-1)/"γ")-1)`

Example

`"57938.19kJ/min"=(("120kg/min"*"1.005kJ/kg*K"*"300K")/("0.3"))*(("400000Pa"/"101325Pa")^(("1.4"-1)/"1.4")-1)`

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Power Required to Maintain Pressure inside Cabin including Ram Work Solution

STEP 0: Pre-Calculation Summary

Formula Used

Input Power = ((Mass of Air*Specific Heat Capacity at Constant Pressure*Ambient Air Temperature)/(Compressor Efficiency))*((Cabin Pressure/Atmospheric Pressure)^((Heat Capacity Ratio-1)/Heat Capacity Ratio)-1)
P_in = ((ma*C_p*T_a)/(CE))*((p_c/P_atm)^((γ-1)/γ)-1)
This formula uses 8 Variables

Variables Used

Input Power - (Measured in Watt) - Input Power is the power, which is required by the appliance at its input i.e., from the plug point.
Mass of Air - (Measured in Kilogram per Second) - Mass of air is both a property of air and a measure of its resistance to acceleration when a net force is applied.
Specific Heat Capacity at Constant Pressure - (Measured in Joule per Kilogram per K) - Specific Heat Capacity at Constant Pressure means the amount of heat that is required to raise the temperature of a unit mass of gas by 1 degree at constant pressure.
Ambient Air Temperature - (Measured in Kelvin) - Ambient Air Temperature is the temperature where the ramming process starts.
Compressor Efficiency - Compressor efficiency is the ratio of input kinetic energy to the work done.
Cabin Pressure - (Measured in Pascal) - Cabin Pressure is the pressure inside the aircraft.
Atmospheric Pressure - (Measured in Pascal) - Atmospheric pressure, also known as barometric pressure, is the pressure within the atmosphere of Earth.
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.

STEP 1: Convert Input(s) to Base Unit

Mass of Air: 120 Kilogram per Minute --> 2 Kilogram per Second (Check conversion here)
Specific Heat Capacity at Constant Pressure: 1.005 Kilojoule per Kilogram per K --> 1005 Joule per Kilogram per K (Check conversion here)
Ambient Air Temperature: 300 Kelvin --> 300 Kelvin No Conversion Required
Compressor Efficiency: 0.3 --> No Conversion Required
Cabin Pressure: 400000 Pascal --> 400000 Pascal No Conversion Required
Atmospheric Pressure: 101325 Pascal --> 101325 Pascal No Conversion Required
Heat Capacity Ratio: 1.4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_in = ((ma*C_p*T_a)/(CE))*((p_c/P_atm)^((γ-1)/γ)-1) --> ((2*1005*300)/(0.3))*((400000/101325)^((1.4-1)/1.4)-1)

Evaluating ... ...

P_in = 965636.518631636

STEP 3: Convert Result to Output's Unit

965636.518631636 Watt -->57938.191117898 Kilojoule per Minute (Check conversion here)

FINAL ANSWER

57938.191117898 ≈ 57938.19 Kilojoule per Minute <-- Input Power

(Calculation completed in 00.004 seconds)

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Home » Physics » Refrigeration and Air Conditioning » Air Refrigeration Systems » Power Required to Maintain Pressure inside Cabin including Ram Work

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K J Somaiya College of Engineering (K J Somaiya), Mumbai

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< 17 Air Refrigeration Systems Calculators

Power required to maintain pressure inside cabin excluding ram work

Go Input Power = ((Mass of Air*Specific Heat Capacity at Constant Pressure*Actual temperature of Rammed Air)/(Compressor Efficiency))*((Cabin Pressure/Pressure of Rammed Air)^((Heat Capacity Ratio-1)/Heat Capacity Ratio)-1)

Power Required to Maintain Pressure inside Cabin including Ram Work

Go Input Power = ((Mass of Air*Specific Heat Capacity at Constant Pressure*Ambient Air Temperature)/(Compressor Efficiency))*((Cabin Pressure/Atmospheric Pressure)^((Heat Capacity Ratio-1)/Heat Capacity Ratio)-1)

C.O.P. of simple air evaporative cycle

Go Actual Coefficient of Performance = (210*Tonnage of Refrigeration in TR)/(Mass of Air*Specific Heat Capacity at Constant Pressure*(Actual End Temp of Isentropic Compression-Actual temperature of Rammed Air))

C.O.P. of simple air cycle

Go Actual Coefficient of Performance = (Inside temperature of cabin-Actual temperature at end of isentropic expansion)/(Actual End Temp of Isentropic Compression-Actual temperature of Rammed Air)

Mass of air to produce Q tonnes of refrigeration given exit temperature of cooling turbine

Go Mass of Air = (210*Tonnage of Refrigeration in TR)/(Specific Heat Capacity at Constant Pressure*(Temperature at End of Isentropic Expansion-Actual exit Temperature of cooling turbine))

Mass of air to produce Q tonnes of refrigeration

Go Mass of Air = (210*Tonnage of Refrigeration in TR)/(Specific Heat Capacity at Constant Pressure*(Inside temperature of cabin-Actual temperature at end of isentropic expansion))

Expansion Work

Go Work Done per min = Mass of Air*Specific Heat Capacity at Constant Pressure*(Temperature at the end of cooling process-Actual temperature at end of isentropic expansion)

Refrigeration Effect Produced

Go Refrigeration Effect Produced = Mass of Air*Specific Heat Capacity at Constant Pressure*(Inside temperature of cabin-Actual temperature at end of isentropic expansion)

Heat rejected during cooling process

Go Heat Rejected = Mass of Air*Specific Heat Capacity at Constant Pressure*(Actual End Temp of Isentropic Compression-Temperature at the end of cooling process)

Compression Work

Go Work Done per min = Mass of Air*Specific Heat Capacity at Constant Pressure*(Actual End Temp of Isentropic Compression-Actual temperature of Rammed Air)

Power Required for Refrigeration System

Go Input Power = (Mass of Air*Specific Heat Capacity at Constant Pressure*(Actual End Temp of Isentropic Compression-Actual temperature of Rammed Air))/60

Temperature Ratio at Start and End of Ramming Process

Go Temperature Ratio = 1+(Velocity^2*(Heat Capacity Ratio-1))/(2*Heat Capacity Ratio*[R]*Initial Temperature)

Ram Efficiency

Go Ram Efficiency = (Stagnation Pressure of System-Initial Pressure of System)/(Final Pressure of System-Initial Pressure of System)

Local Sonic or Acoustic Velocity at Ambient Air Conditions

Go Sonic Velocity = (Heat Capacity Ratio*[R]*Initial Temperature/Molecular Weight)^0.5

Initial Mass of Evaporant Required to be Carried for given Flight Time

Go Mass = (Rate of Heat Removal*Time in Minutes)/Latent Heat of Vaporization

COP of Air Cycle for given Input Power and Tonnage of Refrigeration

Go Actual Coefficient of Performance = (210*Tonnage of Refrigeration in TR)/(Input Power*60)

COP of Air Cycle given Input Power

Go Actual Coefficient of Performance = (210*Tonnage of Refrigeration in TR)/(Input Power*60)

Power Required to Maintain Pressure inside Cabin including Ram Work Formula

How is cabin pressure maintained in an aircraft?

To solve the problems, pressurization systems constantly pump fresh, outside air into the fuselage. To control the interior pressure, and allow old, stinky air to exit, there is a motorized door called an outflow valve located near the tail of the aircraft. ... Larger aircraft often have two outflow valves.

How to Calculate Power Required to Maintain Pressure inside Cabin including Ram Work?

Power Required to Maintain Pressure inside Cabin including Ram Work calculator uses Input Power = ((Mass of Air*Specific Heat Capacity at Constant Pressure*Ambient Air Temperature)/(Compressor Efficiency))*((Cabin Pressure/Atmospheric Pressure)^((Heat Capacity Ratio-1)/Heat Capacity Ratio)-1) to calculate the Input Power, Power Required to Maintain Pressure inside Cabin including Ram Work is inversely proportional to the compressor efficiency and directly proportional to the ratio of cabin pressure and atmospheric pressure. Input Power is denoted by P_in symbol.

How to calculate Power Required to Maintain Pressure inside Cabin including Ram Work using this online calculator? To use this online calculator for Power Required to Maintain Pressure inside Cabin including Ram Work, enter Mass of Air (ma), Specific Heat Capacity at Constant Pressure (C_p), Ambient Air Temperature (T_a), Compressor Efficiency (CE), Cabin Pressure (p_c), Atmospheric Pressure (P_atm) & Heat Capacity Ratio (γ) and hit the calculate button. Here is how the Power Required to Maintain Pressure inside Cabin including Ram Work calculation can be explained with given input values -> 3476.291 = ((2*1005*300)/(0.3))*((400000/101325)^((1.4-1)/1.4)-1).

FAQ

What is Power Required to Maintain Pressure inside Cabin including Ram Work?

Power Required to Maintain Pressure inside Cabin including Ram Work is inversely proportional to the compressor efficiency and directly proportional to the ratio of cabin pressure and atmospheric pressure and is represented as P_in = ((ma*C_p*T_a)/(CE))*((p_c/P_atm)^((γ-1)/γ)-1) or Input Power = ((Mass of Air*Specific Heat Capacity at Constant Pressure*Ambient Air Temperature)/(Compressor Efficiency))*((Cabin Pressure/Atmospheric Pressure)^((Heat Capacity Ratio-1)/Heat Capacity Ratio)-1). Mass of air is both a property of air and a measure of its resistance to acceleration when a net force is applied, Specific Heat Capacity at Constant Pressure means the amount of heat that is required to raise the temperature of a unit mass of gas by 1 degree at constant pressure, Ambient Air Temperature is the temperature where the ramming process starts, Compressor efficiency is the ratio of input kinetic energy to the work done, Cabin Pressure is the pressure inside the aircraft, Atmospheric pressure, also known as barometric pressure, is the pressure within the atmosphere of Earth & 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.

How to calculate Power Required to Maintain Pressure inside Cabin including Ram Work?

Power Required to Maintain Pressure inside Cabin including Ram Work is inversely proportional to the compressor efficiency and directly proportional to the ratio of cabin pressure and atmospheric pressure is calculated using Input Power = ((Mass of Air*Specific Heat Capacity at Constant Pressure*Ambient Air Temperature)/(Compressor Efficiency))*((Cabin Pressure/Atmospheric Pressure)^((Heat Capacity Ratio-1)/Heat Capacity Ratio)-1). To calculate Power Required to Maintain Pressure inside Cabin including Ram Work, you need Mass of Air (ma), Specific Heat Capacity at Constant Pressure (C_p), Ambient Air Temperature (T_a), Compressor Efficiency (CE), Cabin Pressure (p_c), Atmospheric Pressure (P_atm) & Heat Capacity Ratio (γ). With our tool, you need to enter the respective value for Mass of Air, Specific Heat Capacity at Constant Pressure, Ambient Air Temperature, Compressor Efficiency, Cabin Pressure, Atmospheric Pressure & Heat Capacity 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 Input Power?

In this formula, Input Power uses Mass of Air, Specific Heat Capacity at Constant Pressure, Ambient Air Temperature, Compressor Efficiency, Cabin Pressure, Atmospheric Pressure & Heat Capacity Ratio. We can use 2 other way(s) to calculate the same, which is/are as follows -

Input Power = (Mass of Air*Specific Heat Capacity at Constant Pressure*(Actual End Temp of Isentropic Compression-Actual temperature of Rammed Air))/60
Input Power = ((Mass of Air*Specific Heat Capacity at Constant Pressure*Actual temperature of Rammed Air)/(Compressor Efficiency))*((Cabin Pressure/Pressure of Rammed Air)^((Heat Capacity Ratio-1)/Heat Capacity Ratio)-1)

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