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Freestream Density over Flat Plate using Stanton Number Formula

GoFreestream Density over Flat under Freestream Flow Conditions Formula

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The Freestream Density is the mass per unit volume of air in the flow field surrounding a hypersonic vehicle, crucial for understanding aerodynamic performance. Check FAQs

ρ ∞ = \frac{q w}{St \cdot V ∞ \cdot (h aw - h w)}

ρ_∞ - Freestream Density?q_w - Local Heat Transfer Rate?St - Stanton Number?V_∞ - Freestream Velocity?h_aw - Adiabatic Wall Enthalpy?h_w - Wall Enthalpy?

Freestream Density over Flat Plate using Stanton Number Example

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Here is how the Freestream Density over Flat Plate using Stanton Number equation looks like with Values.

Here is how the Freestream Density over Flat Plate using Stanton Number equation looks like with Units.

Here is how the Freestream Density over Flat Plate using Stanton Number equation looks like.

2.1 = \frac{12000}{2 \cdot 100 \cdot (127.7714 - 99.2)}

2.1kg/m³ = \frac{12000W/m²}{2 \cdot 100m/s \cdot (127.7714J/kg - 99.2J/kg)}

2.1 = \frac{12000}{2 \cdot 100 \cdot (127.7714 - 99.2)}

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Freestream Density over Flat Plate using Stanton Number Solution

Follow our step by step solution on how to calculate Freestream Density over Flat Plate using Stanton Number?

FIRST Step Consider the formula

ρ ∞ = \frac{q w}{St \cdot V ∞ \cdot (h aw - h w)}

Next Step Substitute values of Variables

∴

ρ ∞ = \frac{12000W/m²}{2 \cdot 100m/s \cdot (127.7714J/kg - 99.2J/kg)}

Next Step Prepare to Evaluate

∴

ρ ∞ = \frac{12000}{2 \cdot 100 \cdot (127.7714 - 99.2)}

Next Step Evaluate

∴

ρ ∞ = 2.1000021000021kg/m³

LAST Step Rounding Answer

∴

ρ ∞ = 2.1kg/m³

Freestream Density over Flat Plate using Stanton Number Formula Elements

Variables

Freestream Density

The Freestream Density is the mass per unit volume of air in the flow field surrounding a hypersonic vehicle, crucial for understanding aerodynamic performance.

Symbol: ρ_∞

Measurement: DensityUnit: kg/m³

Note: Value can be positive or negative.

Formulas to find Freestream Density

Local Heat Transfer Rate

The Local Heat Transfer Rate is the measure of heat energy transfer per unit area in hypersonic vehicles, crucial for understanding thermal management and material performance.

Symbol: q_w

Measurement: Heat Flux DensityUnit: W/m²

Note: Value should be greater than 0.

Formulas to find Local Heat Transfer Rate

Stanton Number

The Stanton Number is a dimensionless quantity that characterizes the heat transfer between a fluid and a surface, particularly in the context of hypersonic vehicles.

Symbol: St

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Stanton Number

Freestream Velocity

The Freestream Velocity is the speed of fluid flow far away from any influence of objects, crucial for analyzing hypersonic vehicle performance and aerodynamic characteristics.

Symbol: V_∞

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Freestream Velocity

Adiabatic Wall Enthalpy

The Adiabatic Wall Enthalpy is the heat content of a system under adiabatic conditions, relevant for understanding thermal dynamics in hypersonic vehicles.

Symbol: h_aw

Measurement: Specific EnergyUnit: J/kg

Note: Value should be greater than 0.

Formulas to find Adiabatic Wall Enthalpy

Wall Enthalpy

The Wall Enthalpy is the measure of energy transfer at the surface of hypersonic vehicles, reflecting the thermal conditions experienced during high-speed flight.

Symbol: h_w

Measurement: Specific EnergyUnit: J/kg

Note: Value should be greater than 0.

Formulas to find Wall Enthalpy

Other Formulas to find Freestream Density

Go Freestream Density over Flat under Freestream Flow Conditions

ρ ∞ = \frac{F D}{0.5 \cdot C D \cdot {V ∞}^{2} \cdot S}

Other formulas in Approximate Results Applied to Hypersonic Vehicles category

Go Freestream Stanton Number for Flat Plate

St = \frac{q w}{ρ ∞ \cdot V ∞ \cdot (h aw - h w)}

Go Local Heat Transfer over Flat Plate using Stanton Number

q w = St \cdot ρ ∞ \cdot V ∞ \cdot (h aw - h w)

Go Freestream Velocity over Flat Plate using Stanton Number

V ∞ = \frac{q w}{St \cdot ρ ∞ \cdot (h aw - h w)}

Go Adiabatic Wall Enthalpy over Flat Plate using Stanton Number

h aw = \frac{q w}{ρ ∞ \cdot V ∞ \cdot St} + h w

How to Evaluate Freestream Density over Flat Plate using Stanton Number?

Freestream Density over Flat Plate using Stanton Number evaluator uses Freestream Density = Local Heat Transfer Rate/(Stanton Number*Freestream Velocity*(Adiabatic Wall Enthalpy-Wall Enthalpy)) to evaluate the Freestream Density, Freestream Density over Flat Plate using Stanton Number formula is defined as a measure of the air density in the freestream flow over a flat plate, which is essential in understanding the heat transfer and frictional characteristics of the plate in viscous flow conditions. Freestream Density is denoted by ρ_∞ symbol.

How to evaluate Freestream Density over Flat Plate using Stanton Number using this online evaluator? To use this online evaluator for Freestream Density over Flat Plate using Stanton Number, enter Local Heat Transfer Rate (q_w), Stanton Number (St), Freestream Velocity (V_∞), Adiabatic Wall Enthalpy (h_aw) & Wall Enthalpy (h_w) and hit the calculate button.

FAQs on Freestream Density over Flat Plate using Stanton Number

What is the formula to find Freestream Density over Flat Plate using Stanton Number?

The formula of Freestream Density over Flat Plate using Stanton Number is expressed as Freestream Density = Local Heat Transfer Rate/(Stanton Number*Freestream Velocity*(Adiabatic Wall Enthalpy-Wall Enthalpy)). Here is an example- 21.42857 = 12000/(2*100*(127.7714-99.2)).

How to calculate Freestream Density over Flat Plate using Stanton Number?

With Local Heat Transfer Rate (q_w), Stanton Number (St), Freestream Velocity (V_∞), Adiabatic Wall Enthalpy (h_aw) & Wall Enthalpy (h_w) we can find Freestream Density over Flat Plate using Stanton Number using the formula - Freestream Density = Local Heat Transfer Rate/(Stanton Number*Freestream Velocity*(Adiabatic Wall Enthalpy-Wall Enthalpy)).

What are the other ways to Calculate Freestream Density?

Here are the different ways to Calculate Freestream Density-

Freestream Density=Drag Force/(0.5*Drag Coefficient*Freestream Velocity^2*Reference Area)

Can the Freestream Density over Flat Plate using Stanton Number be negative?

Yes, the Freestream Density over Flat Plate using Stanton Number, measured in Density can be negative.

Which unit is used to measure Freestream Density over Flat Plate using Stanton Number?

Freestream Density over Flat Plate using Stanton Number is usually measured using the Kilogram per Cubic Meter[kg/m³] for Density. Kilogram per Cubic Centimeter[kg/m³], Gram per Cubic Meter[kg/m³], Gram per Cubic Centimeter[kg/m³] are the few other units in which Freestream Density over Flat Plate using Stanton Number can be measured.

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Freestream Density over Flat Plate using Stanton Number Formula

​GoFreestream Density over Flat under Freestream Flow Conditions Formula

Freestream Density over Flat Plate using Stanton Number Example

Freestream Density over Flat Plate using Stanton Number Solution

Freestream Density over Flat Plate using Stanton Number Formula Elements

Other Formulas to find Freestream Density

Other formulas in Approximate Results Applied to Hypersonic Vehicles category

How to Evaluate Freestream Density over Flat Plate using Stanton Number?

FAQs on Freestream Density over Flat Plate using Stanton Number

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GoFreestream Density over Flat under Freestream Flow Conditions Formula