WOLFRAM SYSTEM MODELER
BaseModelNonconstantCrossSectionAreaGeneric pressure drop component with constant turbulent loss factor data and without an icon, for nonconstant cross section area 
SystemModel["Modelica.Fluid.Fittings.BaseClasses.QuadraticTurbulent.BaseModelNonconstantCrossSectionArea"]
This information is part of the Modelica Standard Library maintained by the Modelica Association.
This model computes the pressure loss of a pipe segment (orifice, bending etc.) with a minimum amount of data provided via parameter data. If available, data should be provided for both flow directions, i.e., flow from port_a to port_b and from port_b to port_a, as well as for the laminar and the turbulent region. It is also an option to provide the loss factor only for the turbulent region for a flow from port_a to port_b.
The following equations are used:
Δp = 0.5*ζ*ρ*v*v = 0.5*ζ/A^2 * (1/ρ) * m_flow*m_flow Re = v*D*ρ/μ
flow type  ζ =  flow region 
turbulent  zeta1 = const.  Re ≥ Re_turbulent, v ≥ 0 
zeta2 = const.  Re ≥ Re_turbulent, v < 0  
laminar  c0/Re  both flow directions, Re small; c0 = const. 
where
The laminar and the transition region is usually of not much technical interest because the operating point is mostly in the turbulent regime. For simplification and for numerical reasons, this whole region is described by two polynomials of third order, one polynomial for m_flow ≥ 0 and one for m_flow < 0. The polynomials start at Re = m_flow*4/(π*D_Re*μ), where D_Re is the smallest diameter between port_a and port_b. The common derivative of the two polynomials at Re = 0 is computed from the equation "c0/Re". Note, the pressure drop equation above in the laminar region is always defined with respect to the smallest diameter D_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:
dp_start 
Value: dp_nominal Type: AbsolutePressure (Pa) Description: Guess value of dp = port_a.p  port_b.p 

m_flow_small 
Value: if system.use_eps_Re then system.eps_m_flow * m_flow_nominal else system.m_flow_small Type: MassFlowRate (kg/s) Description: Small mass flow rate for regularization of zero flow 
show_T 
Value: true Type: Boolean Description: = true, if temperatures at port_a and port_b are computed 
show_V_flow 
Value: true Type: Boolean Description: = true, if volume flow rate at inflowing port is computed 
allowFlowReversal 
Value: system.allowFlowReversal Type: Boolean Description: = true to allow flow reversal, false restricts to design direction (m_flow >= 0) 
momentumDynamics 
Value: Types.Dynamics.SteadyState Type: Dynamics Description: Formulation of momentum balance 
m_flow_start 
Value: system.m_flow_start Type: MassFlowRate (kg/s) Description: Start value of mass flow rates 
data 
Value: Type: LossFactorData Description: Loss factor data 
m_flow_nominal 
Value: if system.use_eps_Re then system.m_flow_nominal else 1e2 * system.m_flow_small Type: MassFlowRate (kg/s) Description: Nominal mass flow rate 
use_Re 
Value: false Type: Boolean Description: = true, if turbulent region is defined by Re, otherwise by m_flow_small 
from_dp 
Value: false Type: Boolean Description: = true, use m_flow = f(dp) else dp = f(m_flow) 
show_Re 
Value: false Type: Boolean Description: = true, if Reynolds number is included for plotting 
show_totalPressures 
Value: false Type: Boolean Description: = true, if total pressures are included for plotting 
show_portVelocities 
Value: false Type: Boolean Description: = true, if port velocities are included for plotting 
pathLength 
Default Value: 0 Type: Length (m) Description: Length flow path 

port_a 
Type: FluidPort_a Description: Fluid connector a (positive design flow direction is from port_a to port_b) 


port_b 
Type: FluidPort_b Description: Fluid connector b (positive design flow direction is from port_a to port_b) 
state_a 
Type: ThermodynamicState Description: state for medium inflowing through port_a 


state_b 
Type: ThermodynamicState Description: state for medium inflowing through port_b 

system 
Type: System Description: System properties 

data 
Type: LossFactorData Description: Loss factor data 

state_nominal 
Type: ThermodynamicState Description: Medium state to compute nominal pressure drop 

state_b_des 
Type: ThermodynamicState Description: Thermodynamic state at port b for flow a > b 

state_a_nondes 
Type: ThermodynamicState Description: Thermodynamic state at port a for flow a < b 
Modelica.Fluid.Fittings Pressure drop in pipe due to suddenly expanding or reducing area (for both flow directions) 