Dynamic pressure given gas constant Calculator

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Introduction and Governing Equations

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Preliminary Aerodynamics

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Atmosphere and Gas Properties

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✖Ambient air density is the mass per unit volume of Earth's atmosphere.ⓘ Ambient air density [ρ]			+10% -10%
✖Mach Number is a dimensionless quantity defined as ratio of speed of object to speed on sound.ⓘ Mach Number [M_r]			+10% -10%
✖Specific heat of air is the heat required to raise the temperature of a air by one degree to that required to raise the temperature of an equal mass of water one degree.ⓘ Specific Heat of Air [cp]			+10% -10%
✖Gas Constant is a general constant in the equation of state of gases that is equal in the case of an ideal gas to product of pressure and volume of one mole divided by the absolute temperature.ⓘ Gas Constant [R]			+10% -10%
✖Temperature is the degree or intensity of heat present in a substance or object.ⓘ Temperature [T]			+10% -10%

✖Dynamic Pressure is simply a convenient name for the quantity which represents the decrease in the pressure due to the velocity of the fluid.ⓘ Dynamic pressure given gas constant [q]

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Formula

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Dynamic pressure given gas constant

Formula

`"q" = 1/2*"ρ"*"M"_{"r"}^2*"cp"*"R"*"T"`

Example

`"70.51347Pa"=1/2*"1.225kg/m³"*("7.67")^2*"0.003J/(kg*K)"*"4.1J/(kg*K)"*"159.1K"`

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Dynamic pressure given gas constant Solution

STEP 0: Pre-Calculation Summary

Formula Used

Dynamic Pressure = 1/2*Ambient air density*Mach Number^2*Specific Heat of Air*Gas Constant*Temperature
q = 1/2*ρ*M_r^2*cp*R*T
This formula uses 6 Variables

Variables Used

Dynamic Pressure - (Measured in Pascal) - Dynamic Pressure is simply a convenient name for the quantity which represents the decrease in the pressure due to the velocity of the fluid.
Ambient air density - (Measured in Kilogram per Cubic Meter) - Ambient air density is the mass per unit volume of Earth's atmosphere.
Mach Number - Mach Number is a dimensionless quantity defined as ratio of speed of object to speed on sound.
Specific Heat of Air - (Measured in Joule per Kilogram per K) - Specific heat of air is the heat required to raise the temperature of a air by one degree to that required to raise the temperature of an equal mass of water one degree.
Gas Constant - (Measured in Joule per Kilogram per K) - Gas Constant is a general constant in the equation of state of gases that is equal in the case of an ideal gas to product of pressure and volume of one mole divided by the absolute temperature.
Temperature - (Measured in Kelvin) - Temperature is the degree or intensity of heat present in a substance or object.

STEP 1: Convert Input(s) to Base Unit

Ambient air density: 1.225 Kilogram per Cubic Meter --> 1.225 Kilogram per Cubic Meter No Conversion Required
Mach Number: 7.67 --> No Conversion Required
Specific Heat of Air: 0.003 Joule per Kilogram per K --> 0.003 Joule per Kilogram per K No Conversion Required
Gas Constant: 4.1 Joule per Kilogram per K --> 4.1 Joule per Kilogram per K No Conversion Required
Temperature: 159.1 Kelvin --> 159.1 Kelvin No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

q = 1/2*ρ*M_r^2*cp*R*T --> 1/2*1.225*7.67^2*0.003*4.1*159.1

Evaluating ... ...

q = 70.5134740571625

STEP 3: Convert Result to Output's Unit

70.5134740571625 Pascal --> No Conversion Required

FINAL ANSWER

70.5134740571625 ≈ 70.51347 Pascal <-- Dynamic Pressure

(Calculation completed in 00.004 seconds)

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National Institute of Technology, Hamirpur (NITH), Himachal Pradesh

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< 17 Preliminary Aerodynamics Calculators

Power required at sea-level conditions

Go Power required at sea-level = sqrt((2*Weight of body^3*Drag Coefficient^2)/([Std-Air-Density-Sea]*Reference Area*Lift Coefficient^3))

Mach Number-2

Go Mach number 2 = sqrt(((((Heat Capacity Ratio-1)*Mach Number^(2)+2))/(2*Heat Capacity Ratio*Mach Number^(2)-(Heat Capacity Ratio-1))))

Power required at Altitude

Go Power required at an altitude = sqrt((2*Weight of body^3*Drag Coefficient^2)/(Density*Reference Area*Lift Coefficient^3))

Velocity at Sea-level given Lift Coefficient

Go Velocity at sea-level = sqrt((2*Weight of body)/([Std-Air-Density-Sea]*Reference Area*Lift Coefficient))

Dynamic pressure given gas constant

Go Dynamic Pressure = 1/2*Ambient air density*Mach Number^2*Specific Heat of Air*Gas Constant*Temperature

Velocity at Altitude

Go Velocity at an altitude = sqrt(2*Weight of body/(Density*Reference Area*Lift Coefficient))

Power required at Altitude given Power at sea-level

Go Power required at an altitude = Power required at sea-level*sqrt([Std-Air-Density-Sea]/Density)

Velocity at Altitude given Velocity at Sea-Level

Go Velocity at an altitude = Velocity at sea-level*sqrt([Std-Air-Density-Sea]/Density)

Dynamic pressure given induced drag

Go Dynamic Pressure = Lift Force^2/(pi*Induced Drag*Lateral plane span^2)

Dynamic pressure given mach number

Go Dynamic Pressure = 1/2*Ambient air density*(Mach Number*Sonic speed)^2

Dynamic pressure given normal pressure

Go Dynamic Pressure = 1/2*Specific Heat of Air*Pressure*Mach Number^2

Flight speed given dynamic pressure

Go Flight speed = sqrt((2*Dynamic Pressure)/Ambient air density)

Dynamic pressure aircraft

Go Dynamic Pressure = 1/2*Ambient air density*Flight speed^2

Dynamic pressure given lift coefficient

Go Dynamic Pressure = Lift Force/Lift Coefficient

Dynamic pressure given drag coefficient

Go Dynamic Pressure = Drag Force/Drag Coefficient

Aerodynamic force

Go Aerodynamic Force = Drag Force+Lift Force

Mach number of moving object

Go Mach Number = Velocity/Speed of Sound

Dynamic pressure given gas constant Formula

Dynamic Pressure = 1/2*Ambient air density*Mach Number^2*Specific Heat of Air*Gas Constant*Temperature
q = 1/2*ρ*M_r^2*cp*R*T

What is dynamic pressure?

In fluid dynamics, dynamic pressure is the quantity defined by: {\displaystyle q={\frac {1}{2}}\rho \, u^{2}} where: q is the dynamic pressure in pascals, ρ is the fluid mass density, and u is the flow speed in m/s. It can be thought of as the fluid's kinetic energy per unit volume.

How to Calculate Dynamic pressure given gas constant?

Dynamic pressure given gas constant calculator uses Dynamic Pressure = 1/2*Ambient air density*Mach Number^2*Specific Heat of Air*Gas Constant*Temperature to calculate the Dynamic Pressure, The Dynamic pressure given gas constant formula is defined as pressure experianced by the the object in an air density with given gas constant and specific heat of air and temperature. Dynamic Pressure is denoted by q symbol.

How to calculate Dynamic pressure given gas constant using this online calculator? To use this online calculator for Dynamic pressure given gas constant, enter Ambient air density (ρ), Mach Number (M_r), Specific Heat of Air (cp), Gas Constant (R) & Temperature (T) and hit the calculate button. Here is how the Dynamic pressure given gas constant calculation can be explained with given input values -> 70.46915 = 1/2*1.225*7.67^2*0.003*4.1*159.1.

FAQ

What is Dynamic pressure given gas constant?

The Dynamic pressure given gas constant formula is defined as pressure experianced by the the object in an air density with given gas constant and specific heat of air and temperature and is represented as q = 1/2*ρ*M_r^2*cp*R*T or Dynamic Pressure = 1/2*Ambient air density*Mach Number^2*Specific Heat of Air*Gas Constant*Temperature. Ambient air density is the mass per unit volume of Earth's atmosphere, Mach Number is a dimensionless quantity defined as ratio of speed of object to speed on sound, Specific heat of air is the heat required to raise the temperature of a air by one degree to that required to raise the temperature of an equal mass of water one degree, Gas Constant is a general constant in the equation of state of gases that is equal in the case of an ideal gas to product of pressure and volume of one mole divided by the absolute temperature & Temperature is the degree or intensity of heat present in a substance or object.

How to calculate Dynamic pressure given gas constant?

The Dynamic pressure given gas constant formula is defined as pressure experianced by the the object in an air density with given gas constant and specific heat of air and temperature is calculated using Dynamic Pressure = 1/2*Ambient air density*Mach Number^2*Specific Heat of Air*Gas Constant*Temperature. To calculate Dynamic pressure given gas constant, you need Ambient air density (ρ), Mach Number (M_r), Specific Heat of Air (cp), Gas Constant (R) & Temperature (T). With our tool, you need to enter the respective value for Ambient air density, Mach Number, Specific Heat of Air, Gas Constant & Temperature 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 Dynamic Pressure?

In this formula, Dynamic Pressure uses Ambient air density, Mach Number, Specific Heat of Air, Gas Constant & Temperature. We can use 6 other way(s) to calculate the same, which is/are as follows -

Dynamic Pressure = Lift Force/Lift Coefficient
Dynamic Pressure = Drag Force/Drag Coefficient
Dynamic Pressure = 1/2*Ambient air density*Flight speed^2
Dynamic Pressure = 1/2*Ambient air density*(Mach Number*Sonic speed)^2
Dynamic Pressure = 1/2*Specific Heat of Air*Pressure*Mach Number^2
Dynamic Pressure = Lift Force^2/(pi*Induced Drag*Lateral plane span^2)

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