Pressure loss calculation with FVOL "dependent on mass and volume flow"

This applies to all components for which the pressure loss calculation can be set to "dependent on mass and volume flow" via a switch FVOL.

Ebsilon starts from the Bernoulli equation for the pressure loss Δp (as found in various textbooks - here e.g. Piping Technology by Walter Wagner from Vogel Verlag) :

Δp = lambda * (L/d_i) *rho*c²/2

Thereby:

• lambda the pipe coefficient, which is assumed to be constant for different loads in the following.
• L is the pipe length.
• di the pipe inner diameter.
• rho the density of the fluid
• c the velocity

Attentionally, a "c" is used because the "v" is used for the specific volume.

Adding rho*A² to the numerator and denominator gives

Δp = lambda * (L/d_i) * (rho² * A² * c²) / (rho * A² *2)

Since rho*A*c is equal to the mass flow m, and the density rho is the reciprocal of the specific volume v, we can write

Δp = lambda * (L/d_i) * (v * m²) / (A² *2)

Dividing the whole by the nominal values v_0 and m_0, we get for the partial load factor :

Δp/Δp_0 = ( v/v_0 ) * ( m/m_0 )²    (where the constants have been truncated away)

Since v*m is equal to the volumetric flow vm, one can also write

Δp/Δp_0 = ( vm/vm_0 ) * ( m/m_0 )

which is why this mode of calculation is also called "dependent on mass and volume flow".