Stagnation enthalpy

In <a href="/facts/Thermodynamics/q4hIx3yP">thermodynamics</a> and <a href="/facts/Fluid_mechanics/NIy4tRfE">fluid mechanics</a>, the stagnation enthalpy of a fluid is the <a href="/facts/Enthalpy/bBou8lCE">static enthalpy</a> of the fluid at a <a href="/facts/Stagnation_point/BKPkXJv2">stagnation point</a>. The stagnation enthalpy is also called total enthalpy. At a point where the flow does not stagnate, it corresponds to the static enthalpy of the fluid at that point assuming it was brought to rest from velocity 
 
 
 
 V
 
 
 {\displaystyle V}
 
 <a href="/facts/Isentropic_process/BYMe7V5P">isentropically</a>. That means all the <a href="/facts/Kinetic_energy/aJRxUd4p">kinetic energy</a> was converted to <a href="/facts/Internal_energy/IYdsoxhR">internal energy</a> without losses and is added to the local static enthalpy. When the <a href="/facts/Potential_energy/I03KLbmn">potential energy</a> of the fluid is negligible, the mass-specific stagnation enthalpy represents the total energy of a flowing fluid stream per unit mass.
Stagnation enthalpy, or total enthalpy, is the sum of the static enthalpy (associated with the <a href="/facts/Temperature/QyGe4gmj">temperature</a> and <a href="/facts/Static_pressure/ealK4UlR">static pressure</a> at that point) plus the enthalpy associated with the <a href="/facts/Dynamic_pressure/StNXM0sf">dynamic pressure</a>, or velocity. This can be expressed in a formula in various ways. Often it is expressed in specific quantities, where specific means mass-specific, to get an <a href="/facts/Intensive_and_extensive_properties/UcgSh8EG">intensive</a> quantity:

h
          
            0
          
        
        =
        h
        +
        
          
            
              V
              
                2
              
            
            2
          
        
      
    
    {\displaystyle h_{0}=h+{\frac {V^{2}}{2}}}

where:

h
          
            0
          
        
        =
      
    
    {\displaystyle h_{0}=}
  
 mass-specific total enthalpy, in [J/kg]

h
 =
 
 
 {\displaystyle h=}
 
 mass-specific <a href="/facts/Enthalpy/bBou8lCE">static enthalpy</a>, in [J/kg]

V
        =
      
    
    {\displaystyle V=}
  
 fluid velocity at the point of interest, in [m/s]

V
 
 2
 
 
 2
 
 
 =
 
 
 {\displaystyle {\frac {V^{2}}{2}}=}
 
 mass-specific <a href="/facts/Kinetic_energy/aJRxUd4p">kinetic energy</a>, in [J/kg]
The volume-specific version of this equation (in units of energy per volume, [J/m^3] is obtained by multiplying the equation with the fluid density 
 
 
 
 ρ
 
 
 {\displaystyle \rho }
 
:

h
          
            0
          
          
            ∗
          
        
        =
        
          h
          
            ∗
          
        
        +
        ρ
        
          
            
              V
              
                2
              
            
            2
          
        
      
    
    {\displaystyle h_{0}^{*}=h^{*}+\rho {\frac {V^{2}}{2}}}

where:

h
          
            0
          
          
            ∗
          
        
        =
      
    
    {\displaystyle h_{0}^{*}=}
  
 volume-specific total enthalpy, in [J/m^3]

h
 
 ∗
 
 
 =
 
 
 {\displaystyle h^{*}=}
 
 volume-specific <a href="/facts/Enthalpy/bBou8lCE">static enthalpy</a>, in [J/m^3]

V
        =
      
    
    {\displaystyle V=}
  
 fluid velocity at the point of interest, in [m/s]

ρ
        =
      
    
    {\displaystyle \rho =}
  
 fluid density at the point of interest, in [kg/m^3]

ρ
 
 
 
 V
 
 2
 
 
 2
 
 
 =
 
 
 {\displaystyle \rho {\frac {V^{2}}{2}}=}
 
 volume-specific <a href="/facts/Kinetic_energy/aJRxUd4p">kinetic energy</a>, in [J/m^3]
The non-specific version of this equation, that means <a href="/facts/Intensive_and_extensive_properties/UcgSh8EG">extensive</a> quantities are used, is:

H
          
            0
          
        
        =
        H
        +
        m
        
          
            
              V
              
                2
              
            
            2
          
        
      
    
    {\displaystyle H_{0}=H+m{\frac {V^{2}}{2}}}

where:

H
          
            0
          
        
        =
      
    
    {\displaystyle H_{0}=}
  
 total enthalpy, in [J]

H
 =
 
 
 {\displaystyle H=}
 
 <a href="/facts/Enthalpy/bBou8lCE">static enthalpy</a>, in [J]

m
        =
      
    
    {\displaystyle m=}
  
 fluid mass, in [kg]

V
        =
      
    
    {\displaystyle V=}
  
 fluid velocity at the point of interest, in [m/s]

m
 
 
 
 V
 
 2
 
 
 2
 
 
 =
 
 
 {\displaystyle m{\frac {V^{2}}{2}}=}
 
 <a href="/facts/Kinetic_energy/aJRxUd4p">kinetic energy</a>, in [J]
The suffix ‘0’ usually denotes the stagnation condition and is used as such here.
Enthalpy is the energy <a href="/facts/Internal_Energy/IYdsoxhR">associated with the temperature</a> plus the energy associated with the pressure. The stagnation enthalpy adds a term associated with the kinetic energy of the fluid mass.
The total enthalpy for a real or ideal gas does not change across a shock. The total enthalpy can not be measured directly. Instead, the static enthalpy and the fluid velocity can be measured. Static enthalpy is often used in the energy equation for a fluid.

Stagnation enthalpy open-in-new

Stagnation enthalpy