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Static Density Equation using Stanton Number Formula

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The Static Density is the density of air at a given altitude and temperature, used to model the boundary layer in hypersonic flow conditions. Check FAQs

ρ e = \frac{q w}{St \cdot u e \cdot (h aw - h w)}

ρ_e - Static Density?q_w - Local Heat Transfer Rate?St - Stanton Number?u_e - Static Velocity?h_aw - Adiabatic Wall Enthalpy?h_w - Wall Enthalpy?

Static Density Equation using Stanton Number Example

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Here is how the Static Density Equation using Stanton Number equation looks like with Values.

Here is how the Static Density Equation using Stanton Number equation looks like with Units.

Here is how the Static Density Equation using Stanton Number equation looks like.

1217.5325 = \frac{12000}{0.4 \cdot 8.8 \cdot (102 - 99.2)}

1217.5325kg/m³ = \frac{12000W/m²}{0.4 \cdot 8.8m/s \cdot (102J/kg - 99.2J/kg)}

1217.5325 = \frac{12000}{0.4 \cdot 8.8 \cdot (102 - 99.2)}

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Static Density Equation using Stanton Number Solution

Follow our step by step solution on how to calculate Static Density Equation using Stanton Number?

FIRST Step Consider the formula

ρ e = \frac{q w}{St \cdot u e \cdot (h aw - h w)}

Next Step Substitute values of Variables

∴

ρ e = \frac{12000W/m²}{0.4 \cdot 8.8m/s \cdot (102J/kg - 99.2J/kg)}

Next Step Prepare to Evaluate

∴

ρ e = \frac{12000}{0.4 \cdot 8.8 \cdot (102 - 99.2)}

Next Step Evaluate

∴

ρ e = 1217.53246753247kg/m³

LAST Step Rounding Answer

∴

ρ e = 1217.5325kg/m³

Static Density Equation using Stanton Number Formula Elements

Variables

Static Density

The Static Density is the density of air at a given altitude and temperature, used to model the boundary layer in hypersonic flow conditions.

Symbol: ρ_e

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Static Density

Local Heat Transfer Rate

The Local Heat Transfer Rate is the amount of heat transferred per unit area per unit time from the surface to the fluid in a hypersonic boundary layer.

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 used to characterize heat transfer and frictional drag in the boundary layer of hypersonic flow.

Symbol: St

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Stanton Number

Static Velocity

The Static Velocity is the velocity of the fluid in the boundary layer at a given point, describing the flow characteristics near the surface.

Symbol: u_e

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Static Velocity

Adiabatic Wall Enthalpy

The Adiabatic Wall Enthalpy is the total enthalpy of a gas at the wall of a hypersonic vehicle, considering the heat transfer and friction effects.

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 total heat content of the wall boundary layer in a hypersonic flow, including both sensible and latent heat components.

Symbol: h_w

Measurement: Specific EnergyUnit: J/kg

Note: Value should be greater than 0.

Formulas to find Wall Enthalpy

Other formulas in Local Heat Transfer for Hypersonic Flow category

Go Nusselt Number for Hypersonic Vehicle

N u = \frac{q w \cdot x d}{k \cdot (T wall - Tw)}

Go Local Heat Transfer Rate using Nusselt's Number

q w = \frac{N u \cdot k \cdot (T wall - Tw)}{x d}

Go Thermal Conductivity at Edge of Boundary Layer Equation using Nusselt's Number

k = \frac{q w \cdot x d}{N u \cdot (T wall - Tw)}

Go Stanton Number for Hypersonic Vehicle

St = \frac{q w}{ρ e \cdot u e \cdot (h aw - h w)}

How to Evaluate Static Density Equation using Stanton Number?

Static Density Equation using Stanton Number evaluator uses Static Density = Local Heat Transfer Rate/(Stanton Number*Static Velocity*(Adiabatic Wall Enthalpy-Wall Enthalpy)) to evaluate the Static Density, Static Density Equation using Stanton Number formula is defined as a measure of the effective density of a fluid in a hypersonic boundary layer, which is essential in understanding the flow behavior and heat transfer characteristics in high-speed flows. Static Density is denoted by ρ_e symbol.

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

FAQs on Static Density Equation using Stanton Number

What is the formula to find Static Density Equation using Stanton Number?

The formula of Static Density Equation using Stanton Number is expressed as Static Density = Local Heat Transfer Rate/(Stanton Number*Static Velocity*(Adiabatic Wall Enthalpy-Wall Enthalpy)). Here is an example- 1217.532 = 12000/(0.4*8.8*(102-99.2)).

How to calculate Static Density Equation using Stanton Number?

With Local Heat Transfer Rate (q_w), Stanton Number (St), Static Velocity (u_e), Adiabatic Wall Enthalpy (h_aw) & Wall Enthalpy (h_w) we can find Static Density Equation using Stanton Number using the formula - Static Density = Local Heat Transfer Rate/(Stanton Number*Static Velocity*(Adiabatic Wall Enthalpy-Wall Enthalpy)).

Can the Static Density Equation using Stanton Number be negative?

No, the Static Density Equation using Stanton Number, measured in Density cannot be negative.

Which unit is used to measure Static Density Equation using Stanton Number?

Static Density Equation 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 Static Density Equation using Stanton Number can be measured.

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Static Density Equation using Stanton Number Formula

Static Density Equation using Stanton Number Example

Static Density Equation using Stanton Number Solution

Static Density Equation using Stanton Number Formula Elements

Other formulas in Local Heat Transfer for Hypersonic Flow category

How to Evaluate Static Density Equation using Stanton Number?

FAQs on Static Density Equation using Stanton Number

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