Pipe (MF)#

The Pipe (MF) block models a section of a pipeline system that has no heat exchange with the environment. The section has hydrostatic pressure losses and friction pressure losses.

Law of Conservation of Mass (1) :

(1)#\[\dot m_А+\dot m_В=0\]

where:

\(\dot m_A\) – mass flow rate at the input, [kg/s];

\(\dot m_В\) – mass flow rate at the outlet, [kg/s].

Law of conservation of energy (2) :

(2)#\[\phi_А + \phi_В=0\]

where:

\(\phi_А\) – energy flow at the input, [W];

\(\phi_B\) – output energy flow, [W].

Pressure difference (3) :

(3)#\[\Delta P = \Delta P_{тр} + \Delta P_{гидростат}\]

where:

\(\Delta P\) – pressure loss in a pipeline section, [Pa];

\(\Delta P_{tr}\) - pressure loss due to friction, [Pa], (4) :

(4)#\[\Delta P_{тр}= \lambda \cdot \frac{l}{d} \cdot \frac{w^2 \cdot \rho}{2}\]

where:

\(l\) – length of pipeline section, [m];

\(d\) – internal diameter of the pipeline section, [m];

\(w\) – flow velocity of the medium, [m/s];

\(\rho\) – density of the medium, [kg/m\(^3\)];

\(\lambda\) – coefficient of hydraulic losses due to friction along the length.

For laminar flow regime (\(Re < 2300\)) (5) :

(5)#\[\lambda = \frac{64}{Re}\]

where \(Re\) is the Reynolds number.

For the transition mode (\(2300 < Re < 4000\)) (6) :

(6)#\[\lambda=\lambda_{ламинар}+\frac{Re-2300}{1700} \cdot (\lambda_{турбулент,4000} - \lambda_{ламинар,2300})\]

where:

\(Re\) – Reynolds number;

\(\lambda_{laminar}\) – coefficient of hydraulic losses due to friction along the length for the laminar regime;

\(\lambda_{laminar,2300}\) – coefficient of hydraulic losses due to friction along the length at \(Re = 2300\);

\(\lambda_{turbulent,4000}\) – coefficient of hydraulic losses due to friction along the length at \(Re = 4000\).

For turbulent regime (\(Re > 4000\)) (7) :

(7)#\[\lambda = [-1.8 \cdot log_{10}((\frac{\epsilon/ d}{3.7})^{1.11}+ \frac{6.9}{Re})]^{-2}\]

where:

\(Re\) – Reynolds number;

\(\epsilon\) – absolute roughness of the inner wall of the pipeline, [m];

\(d\) – internal diameter of the pipeline section, [m].

\(\Delta P_{hydrostat}\) – hydrostatic pressure loss, [Pa], (8):

(8)#\[\Delta P_{гидростат} = \rho \cdot g \cdot \Delta h\]

where:

\(\rho\) – density of the medium, [kg/m\(^3\)];

\(g\) – acceleration of gravity, [m/s\(^2\)];

\(\Delta h\) – difference in input and output levels, [m].

1. Properties#

Property	Default Value	Description	Units of measurement
Length	10.0	-	m
Inside diameter	0.25	-	m
Absolute roughness	1.5E-5	-	m
Inlet elevation	0.0	-	m
Outlet elevation	0.0	-	m

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Input	Input	-	-	Multicomponent fluid
Output	Output	-	-	Multicomponent fluid

In order to see the connection capabilities of the block, you need to go to page Description of block ports