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Coefficient of pressure with slenderness ratio Solution

STEP 0: Pre-Calculation Summary
Formula Used
pressure_coeff = 2*(Slenderness Ratio^2)*(Non-dimensionalized Pressure-(1/(Specific Heat Ratio*(Mach Number^2)*(Slenderness Ratio^2))))
Cp = 2*(λ^2)*(p--(1/(γ*(M^2)*(λ^2))))
This formula uses 4 Variables
Variables Used
Slenderness Ratio- The Slenderness ratio is the ratio of the length of a column and the least radius of gyration of its cross section.
Non-dimensionalized Pressure- Non-dimensionalized Pressure is the technique can ease the analysis of the problem at hand, and reduce the number of free parameters
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
STEP 1: Convert Input(s) to Base Unit
Slenderness Ratio: 50 --> No Conversion Required
Non-dimensionalized Pressure: 1 --> No Conversion Required
Specific Heat Ratio: 1.6 --> No Conversion Required
Mach Number: 1 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Cp = 2*(λ^2)*(p--(1/(γ*(M^2)*(λ^2)))) --> 2*(50^2)*(1-(1/(1.6*(1^2)*(50^2))))
Evaluating ... ...
Cp = 4998.75
STEP 3: Convert Result to Output's Unit
4998.75 --> No Conversion Required
FINAL ANSWER
4998.75 <-- Pressure coefficient
(Calculation completed in 00.031 seconds)

11 Other formulas that you can solve using the same Inputs

Allowable Compression Stress when Slenderness Ratio is less than Cc
allowable_compression_stress = (1-((Slenderness Ratio^2)/(2*Value of Cc^2)))/((5/3)+(3*Slenderness Ratio/(8*Value of Cc))-((Slenderness Ratio^3)/(8*(Value of Cc^3))))*minimum specified yield stress of steel Go
Ratio of stagnation and static pressure
stagnation_to_static_pressure = (1+(((Specific Heat Ratio-1)/2)*(Mach Number^2)))^(Specific Heat Ratio/(Specific Heat Ratio-1)) Go
Mach number
mach_no = Fluid Velocity/(sqrt(Specific Heat Ratio*Universal Gas Constant*Final Temp.)) Go
Ratio of Stagnation and Static Density
stagnation_to_static_density = (1+(((Specific Heat Ratio-1)/2)*(Mach Number^2)))^(1/(Specific Heat Ratio-1)) Go
Deflection angle
deflection_angle = (2/(Specific Heat Ratio-1))*((1/Mach Number ahead of shock)-(1/Mach Number behind shock)) Go
Relation between Characteristic Mach number and Mach number
characteristic_mach_number = ((Specific heat ratio+1)/((Specific heat ratio-1)+(2/(Mach Number^2))))^0.5 Go
Speed of Sound
speed_sound = sqrt(Specific Heat Ratio*[R-Dry-Air]*Temperature of Gas) Go
Cross-Sectional Area when Critical Buckling Load for Pin Ended Columns is Given
cross_sectional_area = Critical Buckling Load*(Slenderness Ratio^2)/((pi^2)*Young's Modulus) Go
Allowable Compression Stress when Slenderness Ratio is Greater than Cc
allowable_compression_stress = (12*(pi^2)*elastic modulus of steel)/(23*(Slenderness Ratio^2)) Go
Ratio of Stagnation and Static Temperature
stagnation_to_static_temp = 1+(((Specific Heat Ratio-1)/2)*(Mach Number^2)) Go
Mach Angle
mach_angle = asin(1/Mach Number) Go

11 Other formulas that calculate the same Output

Coefficient of pressure with slenderness ratio
pressure_coeff = (2/Specific Heat Ratio*Mach Number^2)*(Non-dimensionalized Pressure*Specific Heat Ratio*(Mach Number^2)*(Slenderness Ratio^2)-1) Go
Coefficient of pressure with similarity parameters
pressure_coeff = (2*(Flow Deflection angle)^2)*(((Specific Heat Ratio+1)/4)+sqrt((((Specific Heat Ratio+1)/4)^2)+(1/(Hypersonic similarity parameter)^2))) Go
Exact relation for pressure coefficient behind an oblique shock wave
pressure_coeff = (4/(Specific Heat Ratio+1))*(((sin(Wave angle))^2)-(1/Mach Number^2)) Go
Pressure coefficient for slender bodies of revolution
pressure_coeff = 2*(Angle of Deflection^2)+(Curvature of the surface*Distance of Point from Centroidal Axis) Go
Pressure coefficient for slender 2-D bodies
pressure_coeff = 2*((deflection angle^2)+(Curvature of the surface*Distance of Point from Centroidal Axis)) Go
Modified Newtonian Law
pressure_coeff = The maximum pressure coefficient*(sin(deflection angle))^2 Go
Exact relation for pressure coefficient behind an oblique shock wave when Mach no. tends to infinite
pressure_coeff = (4/(Specific Heat Ratio+1))*(sin(Wave angle))^2 Go
Supersonic expression for pressure coefficient on a surface with local deflection angle θ
pressure_coeff = (2*deflection angle)/(sqrt(Mach Number^2-1)) Go
Non-dimensional pressure coefficient
pressure_coeff = Change in static pressure/Dynamic Pressure Go
Newtonian sine-squared law for pressure coefficient
pressure_coeff = 2*(sin(deflection angle))^2 Go
Coefficient of pressure derived from oblique shock theory
pressure_coeff = 2*(sin(Wave angle))^2 Go

Coefficient of pressure with slenderness ratio Formula

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

what is slenderness ratio?

Slenderness ratio is the ratio of length to diameter of the body, Since the configuration under consideration is slender.

How to Calculate Coefficient of pressure with slenderness ratio?

Coefficient of pressure with slenderness ratio calculator uses pressure_coeff = 2*(Slenderness Ratio^2)*(Non-dimensionalized Pressure-(1/(Specific Heat Ratio*(Mach Number^2)*(Slenderness Ratio^2)))) to calculate the Pressure coefficient, The Coefficient of pressure with slenderness ratio formula is defined as interrelation between non dimensional pressure, slenderness ratio, and specific heat ratio. Pressure coefficient and 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 Slenderness Ratio (λ), Non-dimensionalized Pressure (p-), Specific Heat Ratio (γ) and Mach Number (M) and hit the calculate button. Here is how the Coefficient of pressure with slenderness ratio calculation can be explained with given input values -> 4998.75 = 2*(50^2)*(1-(1/(1.6*(1^2)*(50^2)))).

FAQ

What is Coefficient of pressure with slenderness ratio?
The Coefficient of pressure with slenderness ratio formula is defined as interrelation between non dimensional pressure, slenderness ratio, and specific heat ratio and is represented as Cp = 2*(λ^2)*(p--(1/(γ*(M^2)*(λ^2)))) or pressure_coeff = 2*(Slenderness Ratio^2)*(Non-dimensionalized Pressure-(1/(Specific Heat Ratio*(Mach Number^2)*(Slenderness Ratio^2)))). The Slenderness ratio is the ratio of the length of a column and the least radius of gyration of its cross section, Non-dimensionalized Pressure is the technique can ease the analysis of the problem at hand, and reduce the number of free parameters, 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 and Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.
How to calculate Coefficient of pressure with slenderness ratio?
The Coefficient of pressure with slenderness ratio formula is defined as interrelation between non dimensional pressure, slenderness ratio, and specific heat ratio is calculated using pressure_coeff = 2*(Slenderness Ratio^2)*(Non-dimensionalized Pressure-(1/(Specific Heat Ratio*(Mach Number^2)*(Slenderness Ratio^2)))). To calculate Coefficient of pressure with slenderness ratio, you need Slenderness Ratio (λ), Non-dimensionalized Pressure (p-), Specific Heat Ratio (γ) and Mach Number (M). With our tool, you need to enter the respective value for Slenderness Ratio, Non-dimensionalized Pressure, Specific Heat Ratio and Mach Number 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 Slenderness Ratio, Non-dimensionalized Pressure, Specific Heat Ratio and Mach Number. We can use 11 other way(s) to calculate the same, which is/are as follows -
  • pressure_coeff = Change in static pressure/Dynamic Pressure
  • pressure_coeff = (4/(Specific Heat Ratio+1))*(((sin(Wave angle))^2)-(1/Mach Number^2))
  • pressure_coeff = (4/(Specific Heat Ratio+1))*(sin(Wave angle))^2
  • pressure_coeff = (2*(Flow Deflection angle)^2)*(((Specific Heat Ratio+1)/4)+sqrt((((Specific Heat Ratio+1)/4)^2)+(1/(Hypersonic similarity parameter)^2)))
  • pressure_coeff = 2*(sin(deflection angle))^2
  • pressure_coeff = (2*deflection angle)/(sqrt(Mach Number^2-1))
  • pressure_coeff = The maximum pressure coefficient*(sin(deflection angle))^2
  • pressure_coeff = 2*((deflection angle^2)+(Curvature of the surface*Distance of Point from Centroidal Axis))
  • pressure_coeff = 2*(Angle of Deflection^2)+(Curvature of the surface*Distance of Point from Centroidal Axis)
  • pressure_coeff = 2*(sin(Wave angle))^2
  • pressure_coeff = (2/Specific Heat Ratio*Mach Number^2)*(Non-dimensionalized Pressure*Specific Heat Ratio*(Mach Number^2)*(Slenderness Ratio^2)-1)
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