Ball valve (P)#

block — Block appearance in REPEAT VISION#

The Ball valve (P) simulates the operation of this shutoff and control device in a pneumatic system.

Note

The user has the ability to adjust the maximum area of gas flow through the crane and the maximum throughput of the crane in dimensions:

[m$^3$/h] - for coefficient $K_v$;
[gpm] - for coefficient $С_v$, through which one can calculate the recovery factor $C_d$ using the following formulas (1) and (2) :

(1)#\[C_d=\frac{K_v}{A}\cdot\sqrt{\frac{\rho_{water, 15^0C}}{2\cdot \Delta p_{K_v}}}\]

(2)#\[C_d=\frac{C_v}{A}\cdot\sqrt{\frac{\rho_{water, 60^0F}}{2\cdot \Delta p_{C_v}}}\]

The degree of valve opening in degrees is set through the external automation port.

Note

Zero signal means a fully closed valve.

Calculation of the open area for gas flow is made according to Idelchik handbook for cylindrical pipe according to the following figure :

Note

Also, the user can select a table data setting by specifying a pair of vectors in three different ways:

First way:

Coefficient vector $K_v$ and valve rotation angle vector

Second way:

Coefficient vector $C_v$ and valve rotation angle vector

Third way:

Crane cross-sectional area vector and valve rotation angle vector

The block retains mass so that (3) :

(3)#\[\dot m_{A}\:+\:\dot m_{B}\:=\:\rho\:\cdot \:\nu_{A}\:\cdot \:A_{A}\:+\: \rho\:\cdot \:\nu_{B}\:\cdot \:A_{B}\:=\:0\]

This mass balance implies that the velocity increases as the area decreases and decreases when the flow discharges over a larger area. According to Bernoulli’s principle, this change in velocity results in a region of lower pressure in the hole and higher pressure in the expansion area. The resulting increase in pressure, called pressure recovery, depends on the pressure recovery loss ratio and the area ratio of the hole and port.

Law of conservation of energy (4) :

(4)#\[\phi_А+\phi_В=0\]

where:

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

$\phi_B$ - energy flow at the output, [W].

1. Properties#

Property	Default Value	Description	Units of measurement
Valve parametrization: Area; Table	Area	-	-
Flow coefficient parametrization: $K_v$; $C_v$; $C_d$ and area	$K_v$	-	-
Maximum valve flow factor, available when `Valve parametrization` - `Area`, `Flow coefficient parametrization` - $K_v$	49.0	-	m$^3$/h
Maximum valve flow coefficient, available when `Valve parametrization` - `Area`, `Flow coefficient parametrization` - $C_v$	32.0	-	gpm
Discharge coefficient, available when `Valve parametrization` - `Area`, `Flow coefficient parametrization` - `$C_d$ and area`	0.64	-	-
Area port, available when `Valve parametrization` - `Area`	0.09	-	m$^2$
Area ball bore, available when `Valve parametrization` - `Area`	0.07	-	m$^2$
Leakage area, available when `Valve parametrization` - `Area`	1.0E-10	-	m$^2$
Laminar flow pressure ratio	0.999	-	-
Kv vector, available when `Valve parametrization` - `Table`, `Flow coefficient parametrization` - $K_v$	{1.0E-6; 0.34; 0.76; 1.6; 2.45; 4.1; 5.75; 9.4; 13.0; 28.0; 50.0}	-	m$^3$/h
Cv vector, available when `Valve parametrization` - `Table`, `Flow coefficient parametrization` - $C_v$	{1.0E-6; 0.58; 1.15; 1.9; 2.8; 4.3; 7.0; 10.5; 17.0; 26.0; 32.0}	-	gpm
Ball rotation vector, available when `Valve parametrization` - `Table`	{0.0; 0.15707963267948966; 0.3141592653589793; 0.47123889803846897; 0.6283185307179586; 0.7853981633974483; 0.9424777960769379; 1.0995574287564276; 1.2566370614359172; 1.413716694115407; 1.5707963267948966}	-	rad
Area vector, available when `Valve parametrization` - `Table`, `Flow coefficient parametrization` - - `$C_d$ and area`	{1.0E-16; 6.25E-5; 1.25E-4; 1.875E-4; 2.5E-4; 3.125E-4; 3.75E-4; 4.37E-4; 5.0E-4; 5.625E-4; 6.25E-4}	-	m$^2$

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Opening angle	Input	-	-	Automation
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

Property	Default Value	Description	Units of measurement
Valve parametrization: Area; Table	Area	-	-
Flow coefficient parametrization: \(K_v\); \(C_v\); \(C_d\) and area	\(K_v\)	-	-
Maximum valve flow factor, available when `Valve parametrization` - `Area`, `Flow coefficient parametrization` - $K_v$	49.0	-	m\(^3\)/h
Maximum valve flow coefficient, available when `Valve parametrization` - `Area`, `Flow coefficient parametrization` - \(C_v\)	32.0	-	gpm
Discharge coefficient, available when `Valve parametrization` - `Area`, `Flow coefficient parametrization` - `$C_d$ and area`	0.64	-	-
Area port, available when `Valve parametrization` - `Area`	0.09	-	m\(^2\)
Area ball bore, available when `Valve parametrization` - `Area`	0.07	-	m\(^2\)
Leakage area, available when `Valve parametrization` - `Area`	1.0E-10	-	m\(^2\)
Laminar flow pressure ratio	0.999	-	-
Kv vector, available when `Valve parametrization` - `Table`, `Flow coefficient parametrization` - $K_v$	{1.0E-6; 0.34; 0.76; 1.6; 2.45; 4.1; 5.75; 9.4; 13.0; 28.0; 50.0}	-	m\(^3\)/h
Cv vector, available when `Valve parametrization` - `Table`, `Flow coefficient parametrization` - $C_v$	{1.0E-6; 0.58; 1.15; 1.9; 2.8; 4.3; 7.0; 10.5; 17.0; 26.0; 32.0}	-	gpm
Ball rotation vector, available when `Valve parametrization` - `Table`	{0.0; 0.15707963267948966; 0.3141592653589793; 0.47123889803846897; 0.6283185307179586; 0.7853981633974483; 0.9424777960769379; 1.0995574287564276; 1.2566370614359172; 1.413716694115407; 1.5707963267948966}	-	rad
Area vector, available when `Valve parametrization` - `Table`, `Flow coefficient parametrization` - - `$C_d$ and area`	{1.0E-16; 6.25E-5; 1.25E-4; 1.875E-4; 2.5E-4; 3.125E-4; 3.75E-4; 4.37E-4; 5.0E-4; 5.625E-4; 6.25E-4}	-	m\(^2\)