WOLFRAM SYSTEM MODELER

Pipe

Model of steady, laminar flow through a pipe

Wolfram Language

In[1]:=
SystemModel["Hydraulic.Restrictions.Pipes.Pipe"]
Out[1]:=

Information

This component models pressure losses in a pipe due to friction. It also models delayed flow and handles height difference H between the start and end of the pipe.

It should be used when the pipe is so long that the resistance in the line has to be accounted for. For short lines when the friction losses can be neglected, it is enough to connect the ports to each other without using this model.

Implementation

Compressibility and flow delay is approximated by dividing the pipe into n segments and adding n-1 volumes between them. The pressure-flow equation used in each segment is shown below:



where
:Mass flow rate
:Fluid density
D:Inner pipe diameter
:Pressure difference between ports a and b
g:Standard acceleration of gravity on Earth
H:Height difference between ports a and b
:Kinematic viscosity of the fluid
L:Pipe length

Limitations

This class models steady, incompressible, laminar flow through a pipe. It is only valid for laminar flow, i.e. for Reynolds numbers below 2000.

References

  • F. Young, R. Munson, H. Okiishi, and W. Huebsch, A Brief Introduction to Fluid Mechanics, 4th ed., Hoboken, NJ: Wiley, 2007 p. 284 and 291.
  • C. Nordling and J. Österman, Physics Handbook for Science and Engineering, 7th ed., Lund, Sweden: Studentlitteratur, 2004 p. 183.

Parameters (9)

medium

Value: Oil()

Type: Medium

Description: Medium in the component

n

Value: 10

Type: Integer

Description: Number of segments

D

Value: 0.01

Type: Diameter (m)

Description: Inner pipe diameter

L

Value: 1

Type: Length (m)

Description: Pipe length

H

Value: 1

Type: Length (m)

Description: Height for point B minus height for point A

pLow

Value: 500000.0

Type: Pressure (Pa)

pHigh

Value: 10000000.0

Type: Pressure (Pa)

mdotLow

Value: 1e-005

Type: MassFlowRate (kg/s)

mdotHigh

Value: 1

Type: MassFlowRate (kg/s)

Connectors (2)

port_b

Type: Port_b

Description: Port for hydraulic fluid (unfilled icon)

port_a

Type: Port_a

Description: Port for hydraulic fluid (filled icon)

Components (3)

medium

Type: Medium

Description: Medium in the component

seg

Type: LaminarPipeSegment[n]

Description: Model of steady, incompressible, laminar flow through a pipe

vol

Type: Volume[n - 1]

Description: Fixed volume with fluid storage