Laminar Leakage (IL)

Isothermal liquid element that models laminar leakage flow for various geometries

Since R2020a

Libraries:
Simscape / Foundation Library / Isothermal Liquid / Elements

Description

The Laminar Leakage (IL) block models laminar flow in isothermal liquid networks. The block includes several common flow passage geometries and a custom geometry. Select a Cross-sectional geometry parameter value and then specify other parameter values based on the selected option:

Circular — Provide the diameter and longitudinal length.
Annular — Provide the inner diameter, outer diameter, and longitudinal length.
Rectangular — Provide the width, height, and longitudinal length.
Elliptical — Provide the major axis, minor axis, and longitudinal length.
Equilateral triangular — Provide the length of the triangle side and longitudinal length.
Custom — Provide the flow resistance value, that is, the ratio of pressure loss to mass flow rate. In this configuration, the block acts as a linear hydraulic resistance.

The flow rate calculations are based on the Hagen-Poiseuille equation, which is valid for fully developed laminar flow:

${\dot{m}}_{A} = {\begin{array}{l} \frac{K_{g e o m}}{ν L} (p_{A} - p_{B}), & common geometries \\ \frac{\bar{ρ}}{R} (p_{A} - p_{B}), & custom \end{array}$

$K_{geom} = {\begin{array}{l} \frac{π d^{4}}{128}, & circular \\ \frac{π}{128} (d_{o}^{4} - d_{i}^{4} - \frac{{(d_{o}^{2} - d_{i}^{2})}^{2}}{\log (d_{o} / d_{i})}), & annular \\ \frac{w h^{3}}{12} (1 - \frac{192 h}{w π^{5}} \tanh (\frac{π w}{2 h})), & rectangular \\ \frac{π {(a b)}^{3}}{64 (a^{2} + b^{2})}, & elliptical \\ l_{s i d e}^{4} \frac{\sqrt{3}}{320}, & triangular \end{array}$

$\bar{ρ} = \frac{ρ_{A} + ρ_{B}}{2}$

where:

$\dot{m}$ _A is the mass flow rate through port A.
p_A and p_B are pressures at ports A and B, respectively.
K_geom is the coefficient calculated based on the cross-sectional geometry.
d is the diameter of the circular cross section.
d_o is the outer diameter of the annular cross section.
d_i is the inner diameter of the annular cross section.
w is the width of the rectangular cross section.
h is the height of the rectangular cross section.
a is the major axis of the elliptical cross section.
b is the minor axis of the elliptical cross section.
l_side is the length of the side of the triangular cross section.
L is the longitudinal length.
R is the linear hydraulic resistance for custom geometry.
ν is the liquid kinematic viscosity at atmospheric pressure, which is a global parameter defined by the Isothermal Liquid Properties (IL) block connected to the circuit.
$\bar{ρ}$ is the average fluid mixture density.
ρ_A and ρ_B are fluid mixture density values at ports A and B, respectively. Equations used to compute the fluid mixture density depend on the selected isothermal liquid model. For detailed information, see Isothermal Liquid Modeling Options.

Ports

Conserving

expand all

A — Inlet or outlet
isothermal liquid

Isothermal liquid conserving port associated with the inlet or outlet of the laminar leakage. This block has no intrinsic directionality.

B — Inlet or outlet
isothermal liquid

Isothermal liquid conserving port associated with the inlet or outlet of the laminar leakage. This block has no intrinsic directionality.

Parameters

expand all

Cross-sectional geometry — Select the shape of the leakage cross section
`Circular` (default) | `Annular` | `Rectangular` | `Elliptical` | `Equilateral triangular` | `Custom`

Select a cross-sectional shape and then specify other parameter values based on the selected option.

Diameter — Diameter of the circular cross section
`1e-3 m` (default) | positive scalar

Diameter of the circular cross section.

Dependencies

Enabled when the Cross-sectional geometry parameter is set to Circular.

Inner diameter — Inner diameter of the annular cross section
`5e-4 m` (default) | positive scalar

Inner diameter of the annular cross section.

Dependencies

Enabled when the Cross-sectional geometry parameter is set to Annular.

Outer diameter — Outer diameter of the annular cross section
`1e-3 m` (default) | positive scalar

Outer diameter of the annular cross section.

Dependencies

Enabled when the Cross-sectional geometry parameter is set to Annular.

Width — Width of the rectangular cross section
`1e-3 m` (default) | positive scalar

Width of the rectangular cross section.

Dependencies

Enabled when the Cross-sectional geometry parameter is set to Rectangular.

Height — Height of the rectangular cross section
`0.1 m` (default) | positive scalar

Height of the rectangular cross section.

Dependencies

Enabled when the Cross-sectional geometry parameter is set to Rectangular.

Major axis — Major axis of the elliptical cross section
`1e-3 m` (default) | positive scalar

Major axis of the elliptical cross section.

Dependencies

Enabled when the Cross-sectional geometry parameter is set to Elliptical.

Minor axis — Minor axis of the elliptical cross section
`5e-4 m` (default) | positive scalar

Minor axis of the elliptical cross section.

Dependencies

Enabled when the Cross-sectional geometry parameter is set to Elliptical.

Side length — Length of the triangle side for the equilateral triangular cross section
`1e-3 m` (default) | positive scalar

Length of the triangle side for the equilateral triangular cross section.

Dependencies

Enabled when the Cross-sectional geometry parameter is set to Equilateral triangular.

Longitudinal length — Length of the flow passage
`5 m` (default) | positive scalar

Length of the flow passage.

Linear pressure-flow resistance — Ratio of pressure loss to mass flow rate
1e3 s*MPa/m^3 (default) | positive scalar

Ratio of pressure loss to the mass flow rate. If cross-sectional geometry is not known, the block acts as a linear hydraulic resistance.

Dependencies

Enabled when the Cross-sectional geometry parameter is set to Custom.

References

[1] Manring, N. D., Hydraulic Control Systems. p. 71. Hoboken, New Jersey: John Wiley & Sons, 2005.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2020a

Laminar Leakage (IL)

Description

Ports

Conserving

A — Inlet or outlet
isothermal liquid

B — Inlet or outlet
isothermal liquid

Parameters

Cross-sectional geometry — Select the shape of the leakage cross section
`Circular` (default) | `Annular` | `Rectangular` | `Elliptical` | `Equilateral triangular` | `Custom`

Diameter — Diameter of the circular cross section
`1e-3 m` (default) | positive scalar

Dependencies

Inner diameter — Inner diameter of the annular cross section
`5e-4 m` (default) | positive scalar

Dependencies

Outer diameter — Outer diameter of the annular cross section
`1e-3 m` (default) | positive scalar

Dependencies

Width — Width of the rectangular cross section
`1e-3 m` (default) | positive scalar

Dependencies

Height — Height of the rectangular cross section
`0.1 m` (default) | positive scalar

Dependencies

Major axis — Major axis of the elliptical cross section
`1e-3 m` (default) | positive scalar

Dependencies

Minor axis — Minor axis of the elliptical cross section
`5e-4 m` (default) | positive scalar

Dependencies

Side length — Length of the triangle side for the equilateral triangular cross section
`1e-3 m` (default) | positive scalar

Dependencies

Longitudinal length — Length of the flow passage
`5 m` (default) | positive scalar

Linear pressure-flow resistance — Ratio of pressure loss to mass flow rate
1e3 s*MPa/m^3 (default) | positive scalar

Dependencies

References

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

See Also

Topics

Laminar Leakage (IL)

Description

Ports

Conserving

A — Inlet or outlet isothermal liquid

B — Inlet or outlet isothermal liquid

Parameters

Cross-sectional geometry — Select the shape of the leakage cross section Circular (default) | Annular | Rectangular | Elliptical | Equilateral triangular | Custom

Diameter — Diameter of the circular cross section 1e-3 m (default) | positive scalar

Dependencies

Inner diameter — Inner diameter of the annular cross section 5e-4 m (default) | positive scalar

Dependencies

Outer diameter — Outer diameter of the annular cross section 1e-3 m (default) | positive scalar

Dependencies

Width — Width of the rectangular cross section 1e-3 m (default) | positive scalar

Dependencies

Height — Height of the rectangular cross section 0.1 m (default) | positive scalar

Dependencies

Major axis — Major axis of the elliptical cross section 1e-3 m (default) | positive scalar

Dependencies

Minor axis — Minor axis of the elliptical cross section 5e-4 m (default) | positive scalar

Dependencies

Side length — Length of the triangle side for the equilateral triangular cross section 1e-3 m (default) | positive scalar

Dependencies

Longitudinal length — Length of the flow passage 5 m (default) | positive scalar

Linear pressure-flow resistance — Ratio of pressure loss to mass flow rate 1e3 s*MPa/m^3 (default) | positive scalar

Dependencies

References

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

Version History

See Also

Topics

A — Inlet or outlet
isothermal liquid

B — Inlet or outlet
isothermal liquid

Cross-sectional geometry — Select the shape of the leakage cross section
`Circular` (default) | `Annular` | `Rectangular` | `Elliptical` | `Equilateral triangular` | `Custom`

Diameter — Diameter of the circular cross section
`1e-3 m` (default) | positive scalar

Inner diameter — Inner diameter of the annular cross section
`5e-4 m` (default) | positive scalar

Outer diameter — Outer diameter of the annular cross section
`1e-3 m` (default) | positive scalar

Width — Width of the rectangular cross section
`1e-3 m` (default) | positive scalar

Height — Height of the rectangular cross section
`0.1 m` (default) | positive scalar

Major axis — Major axis of the elliptical cross section
`1e-3 m` (default) | positive scalar

Minor axis — Minor axis of the elliptical cross section
`5e-4 m` (default) | positive scalar

Side length — Length of the triangle side for the equilateral triangular cross section
`1e-3 m` (default) | positive scalar

Longitudinal length — Length of the flow passage
`5 m` (default) | positive scalar

Linear pressure-flow resistance — Ratio of pressure loss to mass flow rate
1e3 s*MPa/m^3 (default) | positive scalar

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.