Total enthelpy concept question

[xzibition8612]

Homework Statement

Total enthalpy is defined such that:

h+(V^2)/2 = constant ... (1)

h0 is the stagnation enthalpy. Stagnation means V=0. Plug this V into the above, get

h=h0.

Hence h+(V^2)/2 = h0 ... (2)

My question is we already defined V=0, so how could there still be a V^2/2 term in (2)? The total enthalpy is defined as the sum of the static enthalpy plus the kinetic energy. But we've already defined V=0! So shouldn't there be no kinetic energy? I'm really confused on this.

Homework Equations

The Attempt at a Solution

 

[benny_91]

Homework Statement

Total enthalpy is defined such that:

h+(V^2)/2 = constant ... (1)

h0 is the stagnation enthalpy. Stagnation means V=0. Plug this V into the above, get

h=h0.

Hence h+(V^2)/2 = h0 ... (2)

My question is we already defined V=0, so how could there still be a V^2/2 term in (2)? The total enthalpy is defined as the sum of the static enthalpy plus the kinetic energy. But we've already defined V=0! So shouldn't there be no kinetic energy? I'm really confused on this.

Homework Equations

The Attempt at a Solution

Firstly you need to understand the definition of stagnation enthalpy. Stagnation enthalpy of a fluid is the enthalpy it attains when it is isentropically decelerated to zero velocity. We are not defining the velocity as zero. Here h is the enthalpy at initial state and h₀ is the enthalpy at the final stage when isentropic deceleration is over. If subscript 0 denotes the stagnation state of the fluid simple energy balance will give us the equation:
h+(V^2)/2 = h₀+(V₀^2/2)...(assuming all other variables of steady flow energy equation to be 0)
But V₀=0 since velocity is 0 at stagnation state
Substitute this and you get your equation.