Non Dimensional Pressure Equation with Slenderness Ratio Calculator

✖Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.ⓘ Pressure [P]			+10% -10%
✖The Specific Heat Ratio of a gas is the ratio of the specific heat of the gas at a constant pressure to its specific heat at a constant volume.ⓘ Specific Heat Ratio [γ]			+10% -10%
✖Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.ⓘ Mach Number [M]			+10% -10%
✖The Slenderness Ratio is the ratio of the length of a column and the least radius of gyration of its cross section.ⓘ Slenderness Ratio [λ]			+10% -10%
✖Free Stream Pressure is the pressure of fluid that hasn't encountered any disturbance.ⓘ Free Stream Pressure [p_∞]			+10% -10%

✖Non Dimensionalized Pressure is the technique which can ease the analysis of the problem at hand and reduce the number of free parameters.ⓘ Non Dimensional Pressure Equation with Slenderness Ratio [p_-]

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Formula

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Non Dimensional Pressure Equation with Slenderness Ratio

Formula

p - = \frac{P}{γ \cdot M^{2} \cdot λ^{2} \cdot p ∞}

Example

1.07689 = \frac{80 Pa}{1.1 \cdot {5.4}^{2} \cdot {0.2}^{2} \cdot 57.9 Pa}

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Non Dimensional Pressure Equation with Slenderness Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Non Dimensionalized Pressure = Pressure/(Specific Heat Ratio*Mach Number^2*Slenderness Ratio^2*Free Stream Pressure)
p_- = P/(γ*M^2*λ^2*p_∞)
This formula uses 6 Variables

Variables Used

Non Dimensionalized Pressure - Non Dimensionalized Pressure is the technique which can ease the analysis of the problem at hand and reduce the number of free parameters.
Pressure - (Measured in Pascal) - Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.
Specific Heat Ratio - The Specific Heat Ratio of a gas is the ratio of the specific heat of the gas at a constant pressure to its specific heat at a constant volume.
Mach Number - Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.
Slenderness Ratio - The Slenderness Ratio is the ratio of the length of a column and the least radius of gyration of its cross section.
Free Stream Pressure - (Measured in Pascal) - Free Stream Pressure is the pressure of fluid that hasn't encountered any disturbance.

STEP 1: Convert Input(s) to Base Unit

Pressure: 80 Pascal --> 80 Pascal No Conversion Required
Specific Heat Ratio: 1.1 --> No Conversion Required
Mach Number: 5.4 --> No Conversion Required
Slenderness Ratio: 0.2 --> No Conversion Required
Free Stream Pressure: 57.9 Pascal --> 57.9 Pascal No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

p_- = P/(γ*M^2*λ^2*p_∞) --> 80/(1.1*5.4^2*0.2^2*57.9)

Evaluating ... ...

p_- = 1.0768897099096

STEP 3: Convert Result to Output's Unit

1.0768897099096 --> No Conversion Required

FINAL ANSWER

1.0768897099096 ≈ 1.07689 <-- Non Dimensionalized Pressure

(Calculation completed in 00.020 seconds)

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Created by Sanjay Krishna

Amrita School of Engineering (ASE), Vallikavu

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< Hypersonic Flow and Disturbances Calculators

Coefficient of Pressure with Slenderness Ratio

Go Pressure Coefficient = 2/Specific Heat Ratio*Mach Number^2*(Non Dimensionalized Pressure*Specific Heat Ratio*Mach Number^2*Slenderness Ratio^2-1)

Density Ratio with Similarity Constant having Slenderness Ratio

Go Density Ratio = ((Specific Heat Ratio+1)/(Specific Heat Ratio-1))*(1/(1+2/((Specific Heat Ratio-1)*Hypersonic Similarity Parameter^2)))

Change in Velocity for Hypersonic Flow in X Direction

Go Change in Velocity for Hypersonic Flow = Fluid Velocity-Freestream Velocity Normal

Similarity Constant Equation with Slenderness Ratio

Go Hypersonic Similarity Parameter = Mach Number*Slenderness Ratio

Non Dimensional Pressure Equation with Slenderness Ratio Formula

Non Dimensionalized Pressure = Pressure/(Specific Heat Ratio*Mach Number^2*Slenderness Ratio^2*Free Stream Pressure)
p_- = P/(γ*M^2*λ^2*p_∞)

What is slenderness ratio?

Since the configuration under consideration is slender, the slope at any point is of the
order of ratio of length to diameter of the body.

How to Calculate Non Dimensional Pressure Equation with Slenderness Ratio?

Non Dimensional Pressure Equation with Slenderness Ratio calculator uses Non Dimensionalized Pressure = Pressure/(Specific Heat Ratio*Mach Number^2*Slenderness Ratio^2*Free Stream Pressure) to calculate the Non Dimensionalized Pressure, The Non dimensional pressure equation with slenderness ratio formula is defined as the interrelation between the pressure of fluid, mach number, slenderness ratio and freestream pressure. Non Dimensionalized Pressure is denoted by p_- symbol.

How to calculate Non Dimensional Pressure Equation with Slenderness Ratio using this online calculator? To use this online calculator for Non Dimensional Pressure Equation with Slenderness Ratio, enter Pressure (P), Specific Heat Ratio (γ), Mach Number (M), Slenderness Ratio (λ) & Free Stream Pressure (p_∞) and hit the calculate button. Here is how the Non Dimensional Pressure Equation with Slenderness Ratio calculation can be explained with given input values -> 1.07689 = 80/(1.1*5.4^2*0.2^2*57.9).

FAQ

What is Non Dimensional Pressure Equation with Slenderness Ratio?

The Non dimensional pressure equation with slenderness ratio formula is defined as the interrelation between the pressure of fluid, mach number, slenderness ratio and freestream pressure and is represented as p_- = P/(γ*M^2*λ^2*p_∞) or Non Dimensionalized Pressure = Pressure/(Specific Heat Ratio*Mach Number^2*Slenderness Ratio^2*Free Stream Pressure). Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed, The Specific Heat Ratio of a gas is the ratio of the specific heat of the gas at a constant pressure to its specific heat at a constant volume, Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound, The Slenderness Ratio is the ratio of the length of a column and the least radius of gyration of its cross section & Free Stream Pressure is the pressure of fluid that hasn't encountered any disturbance.

How to calculate Non Dimensional Pressure Equation with Slenderness Ratio?

The Non dimensional pressure equation with slenderness ratio formula is defined as the interrelation between the pressure of fluid, mach number, slenderness ratio and freestream pressure is calculated using Non Dimensionalized Pressure = Pressure/(Specific Heat Ratio*Mach Number^2*Slenderness Ratio^2*Free Stream Pressure). To calculate Non Dimensional Pressure Equation with Slenderness Ratio, you need Pressure (P), Specific Heat Ratio (γ), Mach Number (M), Slenderness Ratio (λ) & Free Stream Pressure (p_∞). With our tool, you need to enter the respective value for Pressure, Specific Heat Ratio, Mach Number, Slenderness Ratio & Free Stream Pressure 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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