TubeBase
IconTubeBase
Models the pressure drop in a fluid-carrying tube considering friction and optional inertia.
This component calculates the pressure drop () across a tube as a function of the mass flow rate (m_flow
). The calculation includes frictional losses, represented by the sheer
variable, based on the Darcy-Weisbach equation. The friction factor () is determined from flow conditions, fluid properties (density and dynamic viscosity ), tube geometry (length length
, cross-sectional area area
, hydraulic diameter d_h
), and a shape_factor
. An additional head_factor
can scale these frictional losses. Fluid density and viscosity are obtained from the medium properties at port_a
. The hydraulic diameter is defined as:
The fluid velocity is:
\[\text{velocity} = \frac{\text{m_flow}}{\rho \cdot \text{area}}\]
The pressure drop due to friction (sheer
) is calculated as:
\[\text{sheer} = 0.5 \cdot \rho \cdot \text{velocity}^2 \cdot ff \cdot \text{head_factor} \cdot \frac{\text{length}}{d_h}\]
The total pressure drop () can optionally incorporate fluid inertia, adding a dynamic pressure component proportional to the rate of change of mass flow rate (der(m_flow)
):
\[\Delta p = \text{sheer} + \begin{cases} \frac{\text{length}}{\text{area}} \frac{d(\text{m_flow})}{dt} & \text{if add_inertia is true} \\ 0 & \text{if add_inertia is false} \end{cases}\]
Usage
TubeBase(area, length, perimeter, shape_factor, head_factor, add_inertia=false, d_h=4*area/perimeter, m_flow0)
Parameters:
Name | Description | Units | Default value |
---|---|---|---|
area | Cross-sectional area of the tube | m2 | |
length | Length of the tube | m | |
perimeter | Wetted perimeter of the tube's cross-section | m | |
shape_factor | Factor accounting for non-circular cross-section in friction calculation | – | |
head_factor | Multiplier for head losses (e.g., minor losses, bends) | – | |
add_inertia | Flag to include (if true) or exclude (if false) fluid inertial effects | – | false |
m_flow0 | Initial guess or value for the mass flow rate | kg/s |
Connectors
Variables
Name | Description | Units |
---|---|---|
Δp | Pressure difference across the component, defined as porta.p - portb.p | Pa |
m_flow | Overall mass flow rate through the component | kg/s |
rho | Density of the fluid | kg/m3 |
mu | Dynamic viscosity of the fluid | Pa.s |
velocity | Average velocity of the fluid in the tube | m/s |
sheer | Pressure drop component due to frictional shear | Pa |
ff | Darcy friction factor | – |
Behavior
Behavior of this component cannot be rendered because it includes path
variables.
Source
# Models the pressure drop in a fluid-carrying tube considering friction and optional inertia.
#
# This component calculates the pressure drop ($\Delta p$) across a tube as a function of the mass flow rate (`m_flow`).
# The calculation includes frictional losses, represented by the `sheer` variable, based on the Darcy-Weisbach equation.
# The friction factor ($ff$) is determined from flow conditions, fluid properties (density $\rho$ and dynamic viscosity $\mu$),
# tube geometry (length `length`, cross-sectional area `area`, hydraulic diameter `d_h`), and a `shape_factor`.
# An additional `head_factor` can scale these frictional losses. Fluid density and viscosity are obtained from the medium properties at `port_a`.
# The hydraulic diameter is defined as:
# ```math
# d_h = \frac{4 \cdot \text{area}}{\text{perimeter}}
# ```
# The fluid velocity is:
# ```math
# \text{velocity} = \frac{\text{m_flow}}{\rho \cdot \text{area}}
# ```
# The pressure drop due to friction (`sheer`) is calculated as:
# ```math
# \text{sheer} = 0.5 \cdot \rho \cdot \text{velocity}^2 \cdot ff \cdot \text{head_factor} \cdot \frac{\text{length}}{d_h}
# ```
# The total pressure drop ($\Delta p$) can optionally incorporate fluid inertia, adding a dynamic pressure component
# proportional to the rate of change of mass flow rate (`der(m_flow)`):
# ```math
# \Delta p = \text{sheer} + \begin{cases} \frac{\text{length}}{\text{area}} \frac{d(\text{m_flow})}{dt} & \text{if add_inertia is true} \\ 0 & \text{if add_inertia is false} \end{cases}
# ```
component TubeBase
extends TwoPorts
# Cross-sectional area of the tube
parameter area::Area
# Length of the tube
parameter length::Length
# Wetted perimeter of the tube's cross-section
parameter perimeter::Length
# Factor accounting for non-circular cross-section in friction calculation
parameter shape_factor::Real
# Multiplier for head losses (e.g., minor losses, bends)
parameter head_factor::Real
# Flag to include (if true) or exclude (if false) fluid inertial effects
parameter add_inertia::Boolean = false
# Calculated hydraulic diameter of the tube
final parameter d_h::Length = 4*area/perimeter
# Density of the fluid
variable rho::Density
# Dynamic viscosity of the fluid
variable mu::DynamicViscosity
# Average velocity of the fluid in the tube
variable velocity::Velocity
# Pressure drop component due to frictional shear
variable sheer::Pressure
# Darcy friction factor
variable ff::Real
# Initial guess or value for the mass flow rate
parameter m_flow0::MassFlowRate
relations
initial m_flow = m_flow0
rho = density(port_a.medium, port_a.p)
mu = viscosity(port_a.medium)
velocity = m_flow/(rho*area)
ff = friction_factor(m_flow, area, d_h, mu, shape_factor)
sheer = 0.5*rho*reg_pow(velocity, 2)*ff*head_factor*(length/d_h)
Δp = if add_inertia then sheer+(length/area)*der(m_flow) else sheer
m_flow = port_a.m_flow
end
Flattened Source
# Models the pressure drop in a fluid-carrying tube considering friction and optional inertia.
#
# This component calculates the pressure drop ($\Delta p$) across a tube as a function of the mass flow rate (`m_flow`).
# The calculation includes frictional losses, represented by the `sheer` variable, based on the Darcy-Weisbach equation.
# The friction factor ($ff$) is determined from flow conditions, fluid properties (density $\rho$ and dynamic viscosity $\mu$),
# tube geometry (length `length`, cross-sectional area `area`, hydraulic diameter `d_h`), and a `shape_factor`.
# An additional `head_factor` can scale these frictional losses. Fluid density and viscosity are obtained from the medium properties at `port_a`.
# The hydraulic diameter is defined as:
# ```math
# d_h = \frac{4 \cdot \text{area}}{\text{perimeter}}
# ```
# The fluid velocity is:
# ```math
# \text{velocity} = \frac{\text{m_flow}}{\rho \cdot \text{area}}
# ```
# The pressure drop due to friction (`sheer`) is calculated as:
# ```math
# \text{sheer} = 0.5 \cdot \rho \cdot \text{velocity}^2 \cdot ff \cdot \text{head_factor} \cdot \frac{\text{length}}{d_h}
# ```
# The total pressure drop ($\Delta p$) can optionally incorporate fluid inertia, adding a dynamic pressure component
# proportional to the rate of change of mass flow rate (`der(m_flow)`):
# ```math
# \Delta p = \text{sheer} + \begin{cases} \frac{\text{length}}{\text{area}} \frac{d(\text{m_flow})}{dt} & \text{if add_inertia is true} \\ 0 & \text{if add_inertia is false} \end{cases}
# ```
component TubeBase
# The first fluid port of the component
port_a = Port()
# The second fluid port of the component
port_b = Port()
# Pressure difference across the component, defined as port_a.p - port_b.p
variable Δp::AbsolutePressure
# Overall mass flow rate through the component
variable m_flow::MassFlowRate
# Cross-sectional area of the tube
parameter area::Area
# Length of the tube
parameter length::Length
# Wetted perimeter of the tube's cross-section
parameter perimeter::Length
# Factor accounting for non-circular cross-section in friction calculation
parameter shape_factor::Real
# Multiplier for head losses (e.g., minor losses, bends)
parameter head_factor::Real
# Flag to include (if true) or exclude (if false) fluid inertial effects
parameter add_inertia::Boolean = false
# Calculated hydraulic diameter of the tube
final parameter d_h::Length = 4*area/perimeter
# Density of the fluid
variable rho::Density
# Dynamic viscosity of the fluid
variable mu::DynamicViscosity
# Average velocity of the fluid in the tube
variable velocity::Velocity
# Pressure drop component due to frictional shear
variable sheer::Pressure
# Darcy friction factor
variable ff::Real
# Initial guess or value for the mass flow rate
parameter m_flow0::MassFlowRate
relations
continuity(port_a.medium, port_b.medium)
port_a.m_flow+port_b.m_flow = 0
Δp = port_a.p-port_b.p
initial m_flow = m_flow0
rho = density(port_a.medium, port_a.p)
mu = viscosity(port_a.medium)
velocity = m_flow/(rho*area)
ff = friction_factor(m_flow, area, d_h, mu, shape_factor)
sheer = 0.5*rho*reg_pow(velocity, 2)*ff*head_factor*(length/d_h)
Δp = if add_inertia then sheer+(length/area)*der(m_flow) else sheer
m_flow = port_a.m_flow
metadata {}
end
Test Cases
No test cases defined.
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