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Compute mass flow rate from constant loss factor and pressure drop (m_flow = f(dp)). If the Reynolds-number Re ≥ data.Re_turbulent, the flow is treated as a turbulent flow with constant loss factor zeta. If the Reynolds-number Re < data.Re_turbulent, the flow is laminar and/or in a transition region between laminar and turbulent. This region is approximated by two polynomials of third order, one polynomial for m_flow ≥ 0 and one for m_flow < 0. The common derivative of the two polynomials at Re = 0 is computed from the equation "data.c0/Re".

If no data for c0 is available, the derivative at Re = 0 is computed in such a way, that the second derivatives of the two polynomials are identical at Re = 0. The polynomials are constructed, such that they smoothly touch the characteristic curves in the turbulent regions. The whole characteristic is therefore continuous and has a finite, continuous first derivative everywhere. In some cases, the constructed polynomials would "vibrate". This is avoided by reducing the derivative at Re=0 in such a way that the polynomials are guaranteed to be monotonically increasing. The used sufficient criteria for monotonicity follows from:

Fritsch F.N. and Carlson R.E. (1980):

Monotone piecewise cubic interpolation. SIAM J. Numerc. Anal., Vol. 17, No. 2, April 1980, pp. 238-246

m_flow = massFlowRate_dp_and_Re(dp, rho_a, rho_b, mu_a, mu_b, data)

dp	Type: Pressure (Pa) Description: Pressure drop (dp = port_a.p - port_b.p)
rho_a	Type: Density (kg/m³) Description: Density at port_a
rho_b	Type: Density (kg/m³) Description: Density at port_b
mu_a	Type: DynamicViscosity (Pa⋅s) Description: Dynamic viscosity at port_a
mu_b	Type: DynamicViscosity (Pa⋅s) Description: Dynamic viscosity at port_b
data	Type: LossFactorData Description: Constant loss factors for both flow directions

m_flow	Type: MassFlowRate (kg/s) Description: Mass flow rate from port_a to port_b