Flow resistance (P)#

The Flow resistance (P) block simulates the pressure drop in the pneumatic network section based on the specified nominal operating conditions.

Law of conservation of mass(1):

(1)#\[\dot m_A+\dot m_B=0\]

where:

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

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

__ Energy conservation law__(2):

(2)#\[\phi_A+\phi_B=0\]

where:

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

\(\phi_B\) – energy flow at the output, [W].

Differential pressure

The differential pressure is determined according to the following formula (3):

(3)#\[\Delta p=\xi \cdot \frac{\dot m \cdot \sqrt {\dot m^2 + \dot m_{кр}^2}}{2 \cdot \rho \cdot S^2}\]

where:

\(\xi\) – loss factor;

\(\dot m\) – mass flow rate, [kg/s];

\(\dot m_{frc}\) – mass flow rate of transition to laminar flow mode, [kg/s];

\( ho\) – gas density;

S – flow area.

The loss factor is calculated from the nominal values specified by user (4):

(4)#\[\xi=\frac{2\cdot S^2 \cdot \rho_{ном}\cdot \Delta p{ном}}{\dot m_{ном}^2}\]

where:

\( ho_{nom}\) – nominal gas density;

\(\Delta p_{nom}\) – nominal differential pressure, [Pa];

\(\dot m_{nom}\) – nominal mass flow rate, [kg/s].

1. Properties#

Property	Default Value	Description	Units of measurement
Nominal pressure drop	0.002	-	MPa
Nominal mass flow rate	0.2	-	kg/s
Nominal gas density	1.2	-	kg/m\(^3\)
Ports cross-sectional area	0.01	-	m\(^2\)
Fraction of nominal mass flow rate for laminar flow mode	0.001	-	-

Parameters	Input/Output	Description	Units of measurement	Port type
Input	Input	-	-	Pneumatics
Output	Output	-	-	Pneumatics

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