Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number Solution

STEP 0: Pre-Calculation Summary
Formula Used
Enthalpy Behind Normal Shock = Enthalpy Ahead of Normal Shock*(1+((2*Specific Heat Ratio)/(Specific Heat Ratio+1))*(Mach Number Ahead of Normal Shock^2-1))/((Specific Heat Ratio+1)*(Mach Number Ahead of Normal Shock^2)/(2+(Specific Heat Ratio-1)*Mach Number Ahead of Normal Shock^2))
h2 = h1*(1+((2*γ)/(γ+1))*(M1^2-1))/((γ+1)*(M1^2)/(2+(γ-1)*M1^2))
This formula uses 4 Variables
Variables Used
Enthalpy Behind Normal Shock - (Measured in Joule per Kilogram) - Enthalpy Behind Normal Shock is the enthalpy of downstream of shock and it is defined as the sum of the system's internal energy and the product of its pressure and volume for per unit mass.
Enthalpy Ahead of Normal Shock - (Measured in Joule per Kilogram) - Enthalpy Ahead of Normal Shock is the enthalpy of upstream of shock and it is defined as the sum of the system's internal energy and the product of its pressure and volume for per unit mass.
Specific Heat Ratio - The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.
Mach Number Ahead of Normal Shock - Mach Number Ahead of Normal Shock represents the velocity of a fluid or airflow relative to the speed of sound before encountering a normal shock wave.
STEP 1: Convert Input(s) to Base Unit
Enthalpy Ahead of Normal Shock: 200.203 Joule per Kilogram --> 200.203 Joule per Kilogram No Conversion Required
Specific Heat Ratio: 1.4 --> No Conversion Required
Mach Number Ahead of Normal Shock: 1.49 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
h2 = h1*(1+((2*γ)/(γ+1))*(M1^2-1))/((γ+1)*(M1^2)/(2+(γ-1)*M1^2)) --> 200.203*(1+((2*1.4)/(1.4+1))*(1.49^2-1))/((1.4+1)*(1.49^2)/(2+(1.4-1)*1.49^2))
Evaluating ... ...
h2 = 262.980817074534
STEP 3: Convert Result to Output's Unit
262.980817074534 Joule per Kilogram --> No Conversion Required
FINAL ANSWER
262.980817074534 262.9808 Joule per Kilogram <-- Enthalpy Behind Normal Shock
(Calculation completed in 00.004 seconds)

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Created by Shikha Maurya
Indian Institute of Technology (IIT), Bombay
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15 Downstream Shock Waves Calculators

Stagnation Pressure behind Normal Shock by Rayleigh Pitot Tube formula
Go Stagnation Pressure Behind Normal Shock = Static Pressure Ahead of Normal Shock*((1-Specific Heat Ratio+2*Specific Heat Ratio*Mach Number Ahead of Normal Shock^2)/(Specific Heat Ratio+1))*(((Specific Heat Ratio+1)^2*Mach Number Ahead of Normal Shock^2)/(4*Specific Heat Ratio*Mach Number Ahead of Normal Shock^2-2*(Specific Heat Ratio-1)))^((Specific Heat Ratio)/(Specific Heat Ratio-1))
Static Temperature behind Normal Shock for given Upstream Temperature and Mach Number
Go Temperature Behind Normal Shock = Temperature Ahead of Normal Shock*((1+((2*Specific Heat Ratio)/(Specific Heat Ratio+1))*(Mach Number Ahead of Normal Shock^2-1))/((Specific Heat Ratio+1)*(Mach Number Ahead of Normal Shock^2)/(2+(Specific Heat Ratio-1)*Mach Number Ahead of Normal Shock^2)))
Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number
Go Enthalpy Behind Normal Shock = Enthalpy Ahead of Normal Shock*(1+((2*Specific Heat Ratio)/(Specific Heat Ratio+1))*(Mach Number Ahead of Normal Shock^2-1))/((Specific Heat Ratio+1)*(Mach Number Ahead of Normal Shock^2)/(2+(Specific Heat Ratio-1)*Mach Number Ahead of Normal Shock^2))
Mach Number behind Shock
Go Mach Number Behind Normal Shock = ((2+Specific Heat Ratio*Mach Number Ahead of Normal Shock^2-Mach Number Ahead of Normal Shock^2)/(2*Specific Heat Ratio*Mach Number Ahead of Normal Shock^2-Specific Heat Ratio+1))^(1/2)
Velocity behind Normal Shock by Normal Shock Momentum Equation
Go Velocity Downstream of Shock = sqrt((Static Pressure Ahead of Normal Shock-Static pressure Behind Normal shock+Density Ahead of Normal Shock*Velocity Upstream of Shock^2)/Density Behind Normal Shock)
Density behind Normal Shock using Normal Shock Momentum Equation
Go Density Behind Normal Shock = (Static Pressure Ahead of Normal Shock+Density Ahead of Normal Shock*Velocity Upstream of Shock^2-Static pressure Behind Normal shock)/(Velocity Downstream of Shock^2)
Static Pressure behind Normal Shock using Normal Shock Momentum Equation
Go Static pressure Behind Normal shock = Static Pressure Ahead of Normal Shock+Density Ahead of Normal Shock*Velocity Upstream of Shock^2-Density Behind Normal Shock*Velocity Downstream of Shock^2
Density behind Normal Shock given Upstream Density and Mach Number
Go Density Behind Normal Shock = Density Ahead of Normal Shock*(((Specific Heat Ratio+1)*Mach Number^2)/(2+(Specific Heat Ratio-1)*Mach Number^2))
Static Pressure behind Normal Shock for given Upstream Pressure and Mach Number
Go Static pressure Behind Normal shock = Static Pressure Ahead of Normal Shock*(1+((2*Specific Heat Ratio)/(Specific Heat Ratio+1))*(Mach Number Ahead of Normal Shock^2-1))
Velocity behind Normal Shock from Normal Shock Energy Equation
Go Velocity Downstream of Shock = sqrt(2*(Enthalpy Ahead of Normal Shock+(Velocity Upstream of Shock^2)/2-Enthalpy Behind Normal Shock))
Velocity behind Normal Shock
Go Velocity Downstream of Shock = Velocity Upstream of Shock/((Specific Heat Ratio+1)/((Specific Heat Ratio-1)+2/(Mach Number^2)))
Enthalpy behind Normal Shock from Normal Shock Energy Equation
Go Enthalpy Behind Normal Shock = Enthalpy Ahead of Normal Shock+(Velocity Upstream of Shock^2-Velocity Downstream of Shock^2)/2
Flow Velocity Downstream of Shock Wave using Continuity Equation
Go Velocity Downstream of Shock = (Density Ahead of Normal Shock*Velocity Upstream of Shock)/Density Behind Normal Shock
Density Downstream of Shock Wave using Continuity Equation
Go Density Behind Normal Shock = (Density Ahead of Normal Shock*Velocity Upstream of Shock)/Velocity Downstream of Shock
Characteristic Mach Number behind Shock
Go Characteristic Mach Number Behind Shock = 1/Characteristic Mach Number Ahead of Shock

Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number Formula

Enthalpy Behind Normal Shock = Enthalpy Ahead of Normal Shock*(1+((2*Specific Heat Ratio)/(Specific Heat Ratio+1))*(Mach Number Ahead of Normal Shock^2-1))/((Specific Heat Ratio+1)*(Mach Number Ahead of Normal Shock^2)/(2+(Specific Heat Ratio-1)*Mach Number Ahead of Normal Shock^2))
h2 = h1*(1+((2*γ)/(γ+1))*(M1^2-1))/((γ+1)*(M1^2)/(2+(γ-1)*M1^2))

How to obtain static enthalpy ratio across normal shock?

Static enthalpy ratio across a normal shock is obtained as the ratio of static temperature ratio across the normal shock wave.

How to Calculate Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number?

Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number calculator uses Enthalpy Behind Normal Shock = Enthalpy Ahead of Normal Shock*(1+((2*Specific Heat Ratio)/(Specific Heat Ratio+1))*(Mach Number Ahead of Normal Shock^2-1))/((Specific Heat Ratio+1)*(Mach Number Ahead of Normal Shock^2)/(2+(Specific Heat Ratio-1)*Mach Number Ahead of Normal Shock^2)) to calculate the Enthalpy Behind Normal Shock, The Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number computes the enthalpy of a fluid behind a normal shock wave based on the enthalpy ahead of the shock and the Mach number of the flow. This formula accounts for the ratio of specific heats for the fluid and provides insights into the change in enthalpy resulting from the shock wave passage. Enthalpy Behind Normal Shock is denoted by h2 symbol.

How to calculate Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number using this online calculator? To use this online calculator for Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number, enter Enthalpy Ahead of Normal Shock (h1), Specific Heat Ratio (γ) & Mach Number Ahead of Normal Shock (M1) and hit the calculate button. Here is how the Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number calculation can be explained with given input values -> 200.3364 = 200.203*(1+((2*1.4)/(1.4+1))*(1.49^2-1))/((1.4+1)*(1.49^2)/(2+(1.4-1)*1.49^2)).

FAQ

What is Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number?
The Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number computes the enthalpy of a fluid behind a normal shock wave based on the enthalpy ahead of the shock and the Mach number of the flow. This formula accounts for the ratio of specific heats for the fluid and provides insights into the change in enthalpy resulting from the shock wave passage and is represented as h2 = h1*(1+((2*γ)/(γ+1))*(M1^2-1))/((γ+1)*(M1^2)/(2+(γ-1)*M1^2)) or Enthalpy Behind Normal Shock = Enthalpy Ahead of Normal Shock*(1+((2*Specific Heat Ratio)/(Specific Heat Ratio+1))*(Mach Number Ahead of Normal Shock^2-1))/((Specific Heat Ratio+1)*(Mach Number Ahead of Normal Shock^2)/(2+(Specific Heat Ratio-1)*Mach Number Ahead of Normal Shock^2)). Enthalpy Ahead of Normal Shock is the enthalpy of upstream of shock and it is defined as the sum of the system's internal energy and the product of its pressure and volume for per unit mass, The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume & Mach Number Ahead of Normal Shock represents the velocity of a fluid or airflow relative to the speed of sound before encountering a normal shock wave.
How to calculate Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number?
The Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number computes the enthalpy of a fluid behind a normal shock wave based on the enthalpy ahead of the shock and the Mach number of the flow. This formula accounts for the ratio of specific heats for the fluid and provides insights into the change in enthalpy resulting from the shock wave passage is calculated using Enthalpy Behind Normal Shock = Enthalpy Ahead of Normal Shock*(1+((2*Specific Heat Ratio)/(Specific Heat Ratio+1))*(Mach Number Ahead of Normal Shock^2-1))/((Specific Heat Ratio+1)*(Mach Number Ahead of Normal Shock^2)/(2+(Specific Heat Ratio-1)*Mach Number Ahead of Normal Shock^2)). To calculate Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number, you need Enthalpy Ahead of Normal Shock (h1), Specific Heat Ratio (γ) & Mach Number Ahead of Normal Shock (M1). With our tool, you need to enter the respective value for Enthalpy Ahead of Normal Shock, Specific Heat Ratio & Mach Number Ahead of Normal Shock 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 Enthalpy Behind Normal Shock?
In this formula, Enthalpy Behind Normal Shock uses Enthalpy Ahead of Normal Shock, Specific Heat Ratio & Mach Number Ahead of Normal Shock. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Enthalpy Behind Normal Shock = Enthalpy Ahead of Normal Shock+(Velocity Upstream of Shock^2-Velocity Downstream of Shock^2)/2
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