Enthalpy Difference using Hugoniot Equation Calculator

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Compressible Flow

Fundamentals of Inviscid and Incompressible Flow

Three-Dimensional Incompressible Flow

Two-Dimensional Incompressible Flow

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Normal Shock Wave

Governing Equations and Sound Wave

Oblique Shock and Expansion Waves

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Normal Shock Relations

Downstream Shock Waves

Property Change Across Shock Waves

Upstream Shock Waves

✖Static Pressure Behind Normal Shock denotes the pressure of a fluid after passing through a normal shock wave.ⓘ Static pressure Behind Normal shock [P₂]			+10% -10%
✖Static Pressure Ahead of Normal Shock is the pressure in the upstream direction of shock.ⓘ Static Pressure Ahead of Normal Shock [P₁]			+10% -10%
✖Density Ahead of Normal Shock refers to the density of a fluid before encountering a normal shock wave.ⓘ Density Ahead of Normal Shock [ρ₁]			+10% -10%
✖Density Behind Normal Shock represents the density of a fluid after passing through a normal shock wave.ⓘ Density Behind Normal Shock [ρ₂]			+10% -10%

✖Enthalpy Change is the thermodynamic quantity equivalent to the total difference between the heat content of a system.ⓘ Enthalpy Difference using Hugoniot Equation [ΔH]

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Formula

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Enthalpy Difference using Hugoniot Equation

Formula

`"ΔH" = 0.5*("P"_{"2"}-"P"_{"1"})*(("ρ"_{"1"}+"ρ"_{"2"})/("ρ"_{"2"}*"ρ"_{"1"})) `

Example

`"8.188946J/kg"=0.5*("110Pa"-"65.374Pa")*(("5.4kg/m³"+"5.5kg/m³")/("5.5kg/m³"*"5.4kg/m³")) `

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Enthalpy Difference using Hugoniot Equation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Enthalpy Change = 0.5*(Static pressure Behind Normal shock-Static Pressure Ahead of Normal Shock)*((Density Ahead of Normal Shock+Density Behind Normal Shock)/(Density Behind Normal Shock*Density Ahead of Normal Shock))
ΔH = 0.5*(P₂-P₁)*((ρ₁+ρ₂)/(ρ₂*ρ₁))
This formula uses 5 Variables

Variables Used

Enthalpy Change - (Measured in Joule per Kilogram) - Enthalpy Change is the thermodynamic quantity equivalent to the total difference between the heat content of a system.
Static pressure Behind Normal shock - (Measured in Pascal) - Static Pressure Behind Normal Shock denotes the pressure of a fluid after passing through a normal shock wave.
Static Pressure Ahead of Normal Shock - (Measured in Pascal) - Static Pressure Ahead of Normal Shock is the pressure in the upstream direction of shock.
Density Ahead of Normal Shock - (Measured in Kilogram per Cubic Meter) - Density Ahead of Normal Shock refers to the density of a fluid before encountering a normal shock wave.
Density Behind Normal Shock - (Measured in Kilogram per Cubic Meter) - Density Behind Normal Shock represents the density of a fluid after passing through a normal shock wave.

STEP 1: Convert Input(s) to Base Unit

Static pressure Behind Normal shock: 110 Pascal --> 110 Pascal No Conversion Required
Static Pressure Ahead of Normal Shock: 65.374 Pascal --> 65.374 Pascal No Conversion Required
Density Ahead of Normal Shock: 5.4 Kilogram per Cubic Meter --> 5.4 Kilogram per Cubic Meter No Conversion Required
Density Behind Normal Shock: 5.5 Kilogram per Cubic Meter --> 5.5 Kilogram per Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ΔH = 0.5*(P₂-P₁)*((ρ₁+ρ₂)/(ρ₂*ρ₁)) --> 0.5*(110-65.374)*((5.4+5.5)/(5.5*5.4))

Evaluating ... ...

ΔH = 8.18894612794613

STEP 3: Convert Result to Output's Unit

8.18894612794613 Joule per Kilogram --> No Conversion Required

FINAL ANSWER

8.18894612794613 ≈ 8.188946 Joule per Kilogram <-- Enthalpy Change

(Calculation completed in 00.004 seconds)

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Created by Prasana Kannan

Sri sivasubramaniyanadar college of engineering (ssn college of engineering), Chennai

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Verified by Kaki Varun Krishna

Mahatma Gandhi Institute of Technology (MGIT), Hyderabad

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< 7 Normal Shock Relations Calculators

Enthalpy Difference using Hugoniot Equation

Go Enthalpy Change = 0.5*(Static pressure Behind Normal shock-Static Pressure Ahead of Normal Shock)*((Density Ahead of Normal Shock+Density Behind Normal Shock)/(Density Behind Normal Shock*Density Ahead of Normal Shock))

Relation between Mach Number and Characteristic Mach Number

Go Characteristic Mach Number = ((Specific Heat Ratio+1)/(Specific Heat Ratio-1+2/(Mach Number^2)))^0.5

Critical Speed of Sound from Prandtl Relation

Go Critical Speed of Sound = sqrt(Velocity Downstream of Shock*Velocity Upstream of Shock)

Downstream Velocity using Prandtl Relation

Go Velocity Downstream of Shock = (Critical Speed of Sound^2)/Velocity Upstream of Shock

Upstream Velocity using Prandtl Relation

Go Velocity Upstream of Shock = (Critical Speed of Sound^2)/Velocity Downstream of Shock

Mach Number given Impact and Static Pressure

Go Mach Number = (5*((Impact Pressure/Static Pressure+1)^(2/7)-1))^(0.5)

Characteristic Mach Number

Go Characteristic Mach Number = Fluid Velocity/Critical Speed of Sound

Enthalpy Difference using Hugoniot Equation Formula

What does Enthalpy mean?

Enthalpy, a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume.

What is a one-dimensional flow? How do you know if a flow is compressible?

A one-dimensional flow is one that involves zero transverse components of flow. The magnitude of the compressibility effect can be judged by the flow velocity. For air, when the flow velocity is 100 m/s or less, the air is treated as an incompressible fluid, and when the velocity is greater than 100 m/s, the air is treated as compressible fluid.

How to Calculate Enthalpy Difference using Hugoniot Equation?

Enthalpy Difference using Hugoniot Equation calculator uses Enthalpy Change = 0.5*(Static pressure Behind Normal shock-Static Pressure Ahead of Normal Shock)*((Density Ahead of Normal Shock+Density Behind Normal Shock)/(Density Behind Normal Shock*Density Ahead of Normal Shock)) to calculate the Enthalpy Change, The Enthalpy Difference using Hugoniot Equation calculates the change in enthalpy across a normal shock wave employing the Hugoniot equation. This formula considers parameters such as the static pressures and densities ahead and behind the shock. It provides insight into the alteration in enthalpy resulting from the shock wave passage, aiding in the analysis of compressible flow phenomena. Enthalpy Change is denoted by ΔH symbol.

How to calculate Enthalpy Difference using Hugoniot Equation using this online calculator? To use this online calculator for Enthalpy Difference using Hugoniot Equation, enter Static pressure Behind Normal shock (P₂), Static Pressure Ahead of Normal Shock (P₁), Density Ahead of Normal Shock (ρ₁) & Density Behind Normal Shock (ρ₂) and hit the calculate button. Here is how the Enthalpy Difference using Hugoniot Equation calculation can be explained with given input values -> 8.188946 = 0.5*(110-65.374)*((5.4+5.5)/(5.5*5.4)) .

FAQ

What is Enthalpy Difference using Hugoniot Equation?

The Enthalpy Difference using Hugoniot Equation calculates the change in enthalpy across a normal shock wave employing the Hugoniot equation. This formula considers parameters such as the static pressures and densities ahead and behind the shock. It provides insight into the alteration in enthalpy resulting from the shock wave passage, aiding in the analysis of compressible flow phenomena and is represented as ΔH = 0.5*(P₂-P₁)*((ρ₁+ρ₂)/(ρ₂*ρ₁)) or Enthalpy Change = 0.5*(Static pressure Behind Normal shock-Static Pressure Ahead of Normal Shock)*((Density Ahead of Normal Shock+Density Behind Normal Shock)/(Density Behind Normal Shock*Density Ahead of Normal Shock)). Static Pressure Behind Normal Shock denotes the pressure of a fluid after passing through a normal shock wave, Static Pressure Ahead of Normal Shock is the pressure in the upstream direction of shock, Density Ahead of Normal Shock refers to the density of a fluid before encountering a normal shock wave & Density Behind Normal Shock represents the density of a fluid after passing through a normal shock wave.

How to calculate Enthalpy Difference using Hugoniot Equation?

The Enthalpy Difference using Hugoniot Equation calculates the change in enthalpy across a normal shock wave employing the Hugoniot equation. This formula considers parameters such as the static pressures and densities ahead and behind the shock. It provides insight into the alteration in enthalpy resulting from the shock wave passage, aiding in the analysis of compressible flow phenomena is calculated using Enthalpy Change = 0.5*(Static pressure Behind Normal shock-Static Pressure Ahead of Normal Shock)*((Density Ahead of Normal Shock+Density Behind Normal Shock)/(Density Behind Normal Shock*Density Ahead of Normal Shock)). To calculate Enthalpy Difference using Hugoniot Equation, you need Static pressure Behind Normal shock (P₂), Static Pressure Ahead of Normal Shock (P₁), Density Ahead of Normal Shock (ρ₁) & Density Behind Normal Shock (ρ₂). With our tool, you need to enter the respective value for Static pressure Behind Normal shock, Static Pressure Ahead of Normal Shock, Density Ahead of Normal Shock & Density Behind Normal Shock 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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