Coefficient of Pressure with Slenderness Ratio Solution

STEP 0: Pre-Calculation Summary
Formula Used
Pressure Coefficient = 2/Specific Heat Ratio*Mach Number^2*(Non Dimensionalized Pressure*Specific Heat Ratio*Mach Number^2*Slenderness Ratio^2-1)
Cp = 2/γ*M^2*(p-*γ*M^2*λ^2-1)
This formula uses 5 Variables
Variables Used
Pressure Coefficient - Pressure coefficient defines the value of local pressure at a point in terms of free stream pressure and dynamic pressure.
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.
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.
Slenderness Ratio - The Slenderness Ratio is the ratio of the length of a column and the least radius of gyration of its cross section.
STEP 1: Convert Input(s) to Base Unit
Specific Heat Ratio: 1.1 --> No Conversion Required
Mach Number: 5.4 --> No Conversion Required
Non Dimensionalized Pressure: 0.81 --> No Conversion Required
Slenderness Ratio: 0.2 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Cp = 2/γ*M^2*(p-*γ*M^2*λ^2-1) --> 2/1.1*5.4^2*(0.81*1.1*5.4^2*0.2^2-1)
Evaluating ... ...
Cp = 2.0816210618182
STEP 3: Convert Result to Output's Unit
2.0816210618182 --> No Conversion Required
FINAL ANSWER
2.0816210618182 2.081621 <-- Pressure Coefficient
(Calculation completed in 00.004 seconds)

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Created by Sanjay Krishna
Amrita School of Engineering (ASE), Vallikavu
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12 Hypersonic Small Disturbance Equations Calculators

Inverse of Density for Hypersonic Flow using Mach Number
Go Inverse of Density = (2+(Specific Heat Ratio-1)*Mach Number^2*sin(Deflection Angle)^2)/(2+(Specific Heat Ratio+1)*Mach Number^2*sin(Deflection Angle)^2)
Coefficient of Pressure with Slenderness Ratio and Similarity Constant
Go Pressure Coefficient = (2*Slenderness Ratio^2)/(Specific Heat Ratio*Hypersonic Similarity Parameter^2)*(Specific Heat Ratio*Hypersonic Similarity Parameter^2*Non Dimensionalized Pressure-1)
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)))
Rasmussen Closed Form Expression for Shock Wave Angle
Go Wave Angle Similarity Parameter = Hypersonic Similarity Parameter*sqrt((Specific Heat Ratio+1)/2+1/Hypersonic Similarity Parameter^2)
Doty and Rasmussen- Normal Force Coefficient
Go Coefficient of Force = 2*Normal Force/(Density of Fluid*Freestream Velocity Normal^2*Area)
Constant G used for Finding Location of Perturbed Shock
Go Perturbed Shock Location Constant = Perturbed Shock Location Constant at Normal Force/Perturbed Shock Location Constant at Drag Force
Similarity Constant Equation using Wave Angle
Go Wave Angle Similarity Parameter = Mach Number*Wave Angle*180/pi
Change in Velocity for Hypersonic Flow in X Direction
Go Change in Velocity for Hypersonic Flow = Fluid Velocity-Freestream Velocity Normal
Distance from Tip of Leading Edge to Base
Go Distance from X-Axis = Freestream Velocity for Blast Wave*Total Time Taken
Similarity Constant Equation with Slenderness Ratio
Go Hypersonic Similarity Parameter = Mach Number*Slenderness Ratio
Inverse of Density for Hypersonic Flow
Go Inverse of Density = 1/(Density*Wave Angle)

Coefficient of Pressure with Slenderness Ratio Formula

Pressure Coefficient = 2/Specific Heat Ratio*Mach Number^2*(Non Dimensionalized Pressure*Specific Heat Ratio*Mach Number^2*Slenderness Ratio^2-1)
Cp = 2/γ*M^2*(p-*γ*M^2*λ^2-1)

What is pressure coefficient?

The pressure coefficient is a dimensionless number which describes the relative pressures throughout a flow field in fluid dynamics. The pressure coefficient is used in aerodynamics and hydrodynamics.

How to Calculate Coefficient of Pressure with Slenderness Ratio?

Coefficient of Pressure with Slenderness Ratio calculator uses Pressure Coefficient = 2/Specific Heat Ratio*Mach Number^2*(Non Dimensionalized Pressure*Specific Heat Ratio*Mach Number^2*Slenderness Ratio^2-1) to calculate the Pressure Coefficient, The Coefficient of pressure with slenderness ratio formula is defined as the interrelation between the specific heat ratio, non dimensional pressure, Mach infinity and slenderness ratio. Pressure Coefficient is denoted by Cp symbol.

How to calculate Coefficient of Pressure with Slenderness Ratio using this online calculator? To use this online calculator for Coefficient of Pressure with Slenderness Ratio, enter Specific Heat Ratio (γ), Mach Number (M), Non Dimensionalized Pressure (p-) & Slenderness Ratio (λ) and hit the calculate button. Here is how the Coefficient of Pressure with Slenderness Ratio calculation can be explained with given input values -> 2.081621 = 2/1.1*5.4^2*(0.81*1.1*5.4^2*0.2^2-1).

FAQ

What is Coefficient of Pressure with Slenderness Ratio?
The Coefficient of pressure with slenderness ratio formula is defined as the interrelation between the specific heat ratio, non dimensional pressure, Mach infinity and slenderness ratio and is represented as Cp = 2/γ*M^2*(p-*γ*M^2*λ^2-1) or Pressure Coefficient = 2/Specific Heat Ratio*Mach Number^2*(Non Dimensionalized Pressure*Specific Heat Ratio*Mach Number^2*Slenderness Ratio^2-1). 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, Non Dimensionalized Pressure is the technique which can ease the analysis of the problem at hand and reduce the number of free parameters & The Slenderness Ratio is the ratio of the length of a column and the least radius of gyration of its cross section.
How to calculate Coefficient of Pressure with Slenderness Ratio?
The Coefficient of pressure with slenderness ratio formula is defined as the interrelation between the specific heat ratio, non dimensional pressure, Mach infinity and slenderness ratio is calculated using Pressure Coefficient = 2/Specific Heat Ratio*Mach Number^2*(Non Dimensionalized Pressure*Specific Heat Ratio*Mach Number^2*Slenderness Ratio^2-1). To calculate Coefficient of Pressure with Slenderness Ratio, you need Specific Heat Ratio (γ), Mach Number (M), Non Dimensionalized Pressure (p-) & Slenderness Ratio (λ). With our tool, you need to enter the respective value for Specific Heat Ratio, Mach Number, Non Dimensionalized Pressure & Slenderness 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 Pressure Coefficient?
In this formula, Pressure Coefficient uses Specific Heat Ratio, Mach Number, Non Dimensionalized Pressure & Slenderness Ratio. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Pressure Coefficient = (2*Slenderness Ratio^2)/(Specific Heat Ratio*Hypersonic Similarity Parameter^2)*(Specific Heat Ratio*Hypersonic Similarity Parameter^2*Non Dimensionalized Pressure-1)
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