Pneumatics resistance (P)#

Pneumatics resistance (P) block models pressure loss due to user-specified pipe resistances in pneumatic system.

You can specify different loss factors for forward and reverse flows through a pipe segment.

The loss coefficient is parameterized either by a constant dependence, based on pipe pressure or tabular data provided by the user, in the form of a dependence of loss coefficients on the number Reynolds.

1.Loss coefficient table

a) Constant coefficients

Segments with loss factors that remain constant over a range of flow rates are calculated as (1):

(1)#\[ k_{loss}\:=\:k_{loss,BA}+\frac{k_{loss,AB}\:-\:k_{loss,BA}}{2}\:\cdot\:\tanh{(\frac{3\:\:\Delta p}{\Delta p_{crit}}+1)} \]

where:

$k_{loss,AB}$ и $k_{loss,BA}$ - parameters of forward flow loss factor (from A to B) and return flow loss factor (from B to A), respectively;

$Δp$ – pressure difference $p_A$ – $p_B$, [Pa].

Critical pressure differential, $Δp_{crit}$, is the pressure differential associated with the critical Reynolds number, $Re_{crit}$, which is the transition point of the flow condition between laminar and turbulent flow (2) :

(2)#\[ \Delta p_{crit}\:=\:\frac{\bar{\rho}}{2} k_{loss,crit}\:\:(\frac{\nu\:\cdot\:Re_{crit}}{D_{h}})^2 \]

where:

$k_{loss,crit}$ — is the loss coefficient associated with critical pressure, which is based on the average of the forward and reverse loss factors;

$ν$ – liquid kinematic viscosity, [m$^2$/s];

$\bar ρ$ – average liquid density, [kg/m$^3$];

$Dh$, [m] – hydraulic diameter of the segment, which is the equivalent diameter of the non-circular pipe (3):

(3)#\[D_{h}\:=\:\sqrt{\frac{4\cdot \:A_{flow}}{\pi}}\]

where:

$A_{flow}$ — flow area, [m$^2$].

b) Loss coefficient table

The loss factor may alternatively be interpolated based on user-provided Reynolds numbers and loss factor data. A vector of Reynolds numbers can have both positive and negative values, indicating forward and backward flow, respectively (4):

(4)#\[ k_{loss}\:=\:f(Re) \]

2. Mass flow calculation

Law of Conservation of Energy (5) :

(5)#\[ \dot m_{A}+\dot m_{B}\:=\:0 \]

The mass flow through the resistance is calculated using the following formula (6):

(6)#\[ \dot m\:=\:A_{flow}\:\:\sqrt{\frac{2\:\cdot \bar{\rho}}{k_{loss}}}\cdot \:\:\frac{\Delta p}{(\Delta p^2 + \Delta p_{crit}^2)^{1/4}} \]

where $k_loss$ is the flow loss factor that is chosen between the forward flow loss factor (A to B) and the reverse flow loss factor (B to A) depending on the flow direction of the unit.

3. Energy balance

Law of Conservation of Energy (7) :

(7)#\[ \phi_{A}+ \phi_{B}\:=\:0 \]

where:

$\phi_A$ - input energy flow, [W];

$\phi_{B}$ - energy flow at the output, [W].

1. Properties#

Property	Default value	Description	Units of measurement
Method of loss calculation: Constant coefficients; Variable coefficients; Tabulated data: K$_{loss}$ = f(Re); Tabulated data: dP = f(m’)	Constant coefficients	-	-
Straight flow loss coefficient, available when selecting `Method of loss calculation` - `Constant coefficients`	1.0	-	-
Reverse flow loss coefficient, available when selecting `Method of loss calculation` - `Constant coefficients`	1.0	-	-
Reynolds numbers vector, available when selecting `Method of loss calculation` - `Tabulated data: K$_{loss}$ = f(Re)`	-500.0;-200.0;-100.0;-50.0;-40.0;-30.0; -20.0;-10.0;10.0;20.0;30.0;40.0;50.0; 100.0;200.0;500.0;1000.0;2000.0;	-	-
Loss coefficient vector, available when selecting `Method of loss calculation` - `Tabulated data: K$_{loss}$ = f(Re)`	0.65;0.75;0.9;1.15;1.35;1.65; 2.3;3.1;4.0;2.7;1.8;1.46;1.3; 0.9;0.65;0.42;0.3;0.2;	-	-
Pressure drop vector, available when selecting `Method of loss calculation` - `Tabulated data: dP = f(m')`	1272.0;3000.0;4128.0; 6150.0;7718.0;10400.0;	-	Pa
Mass flow vector, available when selecting `Method of loss calculation` - `Tabulated data: dP = f(m')`	0.105;0.175;0.21; 0.2625;0.2975;0.35;	-	kg/s
Flow area	0.2	-	m$^2$
Critical Reynolds number	150.0	The Reynolds number at which the transition from laminar to turbulent flow occurs	-
Laminar flow pressure ratio	0.999	-	-

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Input	Input	-	-	Pneumatics
Output	Output	-	-	Pneumatics
Loss coefficient (straight flow), available when selecting `Method of loss calculation` - `Variable coefficients`	Input	-	-	Automation
Loss coefficient (reverse flow), available when selecting `Method of loss calculation` - `Constant coefficients`	Input	-	-	Automation

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