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Hydrodynamic calculation Gate valve (through conduit)

Gate valve (through conduit) Q air D Q max 1,1D 0,3D 1,5D 4D 1,2D 2D +F by +F bx +F x +F y L Q air D Q max 1.2 D +F by +F bx +F x +F y 1.1 D 0.3D 1.5D 4D 2D
Gate valve (through conduit)

Values for calculation

$ \{D\in\mathbb{R}\mid D>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ D $ $ \mathrm{mm} $
$ \{Q_{max}\in\mathbb{R}\mid Q_{max}>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ Q_{max} $ $ \mathrm{m^3/s} $
$ \{H\in\mathbb{R}\mid H>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ H $ $ \mathrm{m} $
$ \{g\in\mathbb{R}\mid g>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ g $ $ \mathrm{m/s^2} $
$ \{T\in\mathbb{R}\mid T\geq0\} $
This set includes all real numbers that are greater than or equal to zero. Therefore, it contains all positive numbers and zero, but no negative numbers.
$ T $ $ \mathrm{°C} $
$ ρ $ $ \mathrm{kg/m^3} $
$ P_{SV} $ $ \mathrm{Pa} $
$ \{ΔP\in\mathbb{R}\mid ΔP>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ ΔP $ $ \mathrm{m} $
$ \{h\in\mathbb{R}\mid h\geq0\} $
This set includes all real numbers that are greater than or equal to zero. Therefore, it contains all positive numbers and zero, but no negative numbers.
$ h $ $ \mathrm{m} $
$ ρ_{air} $ $ \mathrm{kg/m^3} $
$ p_{air} $ $ \mathrm{Pa} $
$ n $
$ \{t\in\mathbb{R}\mid t>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ t $ $ \mathrm{s} $
$ \{L\in\mathbb{R}\mid L\geq0\} $
This set includes all real numbers that are greater than or equal to zero. Therefore, it contains all positive numbers and zero, but no negative numbers.
$ L $ $ \mathrm{m} $

Calculation

Velocity in valve

$$v_{max}=\cfrac{4\cdot 10^6\cdot Q_{max}}{π\cdot D^2}$$
$v_{max}=\cfrac{4\cdot 10^6\cdot Q_{max}}{π\cdot D^2}$
Equations in LaTeX code
v_{max}=\cfrac{4\cdot 10^6\cdot Q_{max}}{π\cdot D^2}

Theoretical pressure in the valve at full opening

$$Δ_h=\cfrac{v_{max}^2}{2\cdot g}\cdot \left({\min\left(ζ\right)}+1\right)$$
$Δ_h=\cfrac{v_{max}^2}{2\cdot g}\cdot \left({\min\left(ζ\right)}+1\right)$
Equations in LaTeX code
Δ_h=\cfrac{v_{max}^2}{2\cdot g}\cdot \left({\min\left(ζ\right)}+1\right)

Pressure parameter

$$p=\cfrac{Δ_h}{H}$$
$p=\cfrac{Δ_h}{H}$
Equations in LaTeX code
p=\cfrac{Δ_h}{H}
$$0 < p \le 1$$
$0 < p \le 1$
Equations in LaTeX code
0 < p \le 1

Effective closing time factor

$$c_{ef}=0.1/\max_{i=1}^{10}{\left(Q_p[i]-Q_p[i+1]\right)}$$
$c_{ef}=0.1/\max_{i=1}^{10}{\left(Q_p[i]-Q_p[i+1]\right)}$
Equations in LaTeX code
c_{ef}=0.1/\max_{i=1}^{10}{\left(Q_p[i]-Q_p[i+1]\right)}
$$c_{ef}\le 1$$
$c_{ef}\le 1$
Equations in LaTeX code
c_{ef}\le 1

Under-pressure behind the valve

$$P_{u}=\max\left(-\cfrac{L\cdot v_{max}}{g\cdot t\cdot c_{ef}}, -\cfrac{p_{air}}{ρ\cdot g}\right)$$
$P_{u}=\max\left(-\cfrac{L\cdot v_{max}}{g\cdot t\cdot c_{ef}}, -\cfrac{p_{air}}{ρ\cdot g}\right)$
Equations in LaTeX code
P_{u}=\max\left(-\cfrac{L\cdot v_{max}}{g\cdot t\cdot c_{ef}}, -\cfrac{p_{air}}{ρ\cdot g}\right)
Stroke from open position
Flow coefficient
Coefficient of hydraulic force on a sliding plate in the axis x
Coefficient of hydraulic force on a sliding plate in the axis y
Coefficient of hydraulic force on body in the axis x
Coefficient of hydraulic force on body in the axis y
$ s $ $ K_Q $ $ K_x $ $ K_y $ $ K_{bx} $ $ K_{by} $
$ \mathrm{\%} $ $ \mathrm{\ } $ $ \mathrm{\ } $ $ \mathrm{\ } $ $ \mathrm{\ } $ $ \mathrm{\ } $
No data
Stroke from open position Flow coefficient Coefficient of hydraulic force on a sliding plate in the axis x Coefficient of hydraulic force on a sliding plate in the axis y Coefficient of hydraulic force on body in the axis x Coefficient of hydraulic force on body in the axis y
$ s $ $ K_Q $ $ K_x $ $ K_y $ $ K_{bx} $ $ K_{by} $
$ \mathrm{\%} $ $ \mathrm{\ } $ $ \mathrm{\ } $ $ \mathrm{\ } $ $ \mathrm{\ } $ $ \mathrm{\ } $
No data
Unrounded data
Stroke from open position;Flow coefficient;Coefficient of hydraulic force on a sliding plate in the axis x;Coefficient of hydraulic force on a sliding plate in the axis y;Coefficient of hydraulic force on body in the axis x;Coefficient of hydraulic force on body in the axis y;
s;K_Q;K_x;K_y;K_{bx};K_{by};
\%; ; ; ; ; ;

$ K_x\ [-] $
$ K_y\ [-] $
$ K_{bx}\ [-] $
$ K_{by}\ [-] $
No data
$ s\ [\mathrm{\%}] $
Coefficient of force

Stroke from open position Coefficient of hydraulic force on a sliding plate in the axis x Coefficient of hydraulic force on a sliding plate in the axis y Coefficient of hydraulic force on body in the axis x Coefficient of hydraulic force on body in the axis y
$ s $ $ K_x $ $ K_y $ $ K_{bx} $ $ K_{by} $
$ \mathrm{\%} $ $ \mathrm{\ } $ $ \mathrm{\ } $ $ \mathrm{\ } $ $ \mathrm{\ } $
No data
Unrounded data
Stroke from open position; Coefficient of hydraulic force on a sliding plate in the axis x; Coefficient of hydraulic force on a sliding plate in the axis y; Coefficient of hydraulic force on body in the axis x; Coefficient of hydraulic force on body in the axis y;
s; K_x; K_y; K_{bx}; K_{by};
\%; ; ; ; ;

$ K_Q\ [-] $
No data
$ s\ [\mathrm{\%}] $
Flow coefficient

Stroke from open position Flow coefficient
$ s $ $ K_Q $
$ \mathrm{\%} $ $ \mathrm{\ } $
No data
Unrounded data
Stroke from open position; Flow coefficient;
s; K_Q;
\%; ;
Stroke from open position
Loss coefficient
Reduced free flow area in the throttle control system
Relative flow
Flow of water in the pipeline
Water velocity in pipeline
$ s $ $ ζ $ $ f_r $ $ Q_p $ $ Q $ $ v $
$ \mathrm{\%} $ $ \mathrm{\ } $ $ \mathrm{\ } $ $ \mathrm{\ } $ $ \mathrm{m^3/s} $ $ \mathrm{m/s} $
No data
Stroke from open position Loss coefficient Reduced free flow area in the throttle control system Relative flow Flow of water in the pipeline Water velocity in pipeline
$ s $ $ ζ $ $ f_r $ $ Q_p $ $ Q $ $ v $
$ \mathrm{\%} $ $ \mathrm{\ } $ $ \mathrm{\ } $ $ \mathrm{\ } $ $ \mathrm{m^3/s} $ $ \mathrm{m/s} $
No data
Unrounded data
Stroke from open position;Loss coefficient;Reduced free flow area in the throttle control system;Relative flow;Flow of water in the pipeline;Water velocity in pipeline;
s;ζ;f_r;Q_p;Q;v;
\%; ; ; ;m^3/s;m/s;

$ ζ\ [-] $
No data
$ s\ [\mathrm{\%}] $
Loss coefficient

Stroke from open position Loss coefficient
$ s $ $ ζ $
$ \mathrm{\%} $ $ \mathrm{\ } $
No data
Unrounded data
Stroke from open position; Loss coefficient;
s; ζ;
\%; ;
$$ζ=\cfrac{1-K_Q^2}{K_Q^2}$$
$ζ=\cfrac{1-K_Q^2}{K_Q^2}$
Equations in LaTeX code
ζ=\cfrac{1-K_Q^2}{K_Q^2}

$ f_r\ [-] $
$ Q_p\ [-] $
No data
$ s\ [\mathrm{\%}] $
Coefficients

Stroke from open position Reduced free flow area in the throttle control system Relative flow
$ s $ $ f_r $ $ Q_p $
$ \mathrm{\%} $ $ \mathrm{\ } $ $ \mathrm{\ } $
No data
Unrounded data
Stroke from open position; Reduced free flow area in the throttle control system; Relative flow;
s; f_r; Q_p;
\%; ; ;
$$f_r=\cfrac{K_Q}{K_{Qmax}}$$
$f_r=\cfrac{K_Q}{K_{Qmax}}$
Equations in LaTeX code
f_r=\cfrac{K_Q}{K_{Qmax}}
$$Q_p=\cfrac{f_r}{\sqrt{p+f_r^2\cdot \left(1-p\right)}}$$
$Q_p=\cfrac{f_r}{\sqrt{p+f_r^2\cdot \left(1-p\right)}}$
Equations in LaTeX code
Q_p=\cfrac{f_r}{\sqrt{p+f_r^2\cdot \left(1-p\right)}}

$ Q\ [\mathrm{m^3/s}] $
$ v\ [\mathrm{m/s}] $
No data
$ s\ [\mathrm{\%}] $
Flow and speed of water in the pipeline

Stroke from open position Flow of water in the pipeline Water velocity in pipeline
$ s $ $ Q $ $ v $
$ \mathrm{\%} $ $ \mathrm{m^3/s} $ $ \mathrm{m/s} $
No data
Unrounded data
Stroke from open position; Flow of water in the pipeline; Water velocity in pipeline;
s; Q; v;
\%; m^3/s; m/s;
$$Q=Q_p\cdot Q_{max}$$
$Q=Q_p\cdot Q_{max}$
Equations in LaTeX code
Q=Q_p\cdot Q_{max}
$$v=Q_p\cdot v_{max}$$
$v=Q_p\cdot v_{max}$
Equations in LaTeX code
v=Q_p\cdot v_{max}
Stroke from open position
Loss of pressure on the valve
Pressure on the valve
Cavitation number
$ s $ $ H_L $ $ H_v $ $ σ $
$ \mathrm{\%} $ $ \mathrm{m} $ $ \mathrm{m} $ $ \mathrm{\ } $
No data
Stroke from open position Loss of pressure on the valve Pressure on the valve Cavitation number
$ s $ $ H_L $ $ H_v $ $ σ $
$ \mathrm{\%} $ $ \mathrm{m} $ $ \mathrm{m} $ $ \mathrm{\ } $
No data
Unrounded data
Stroke from open position;Loss of pressure on the valve;Pressure on the valve;Cavitation number;
s;H_L;H_v;σ;
\%;m;m; ;

$ H_L\ [\mathrm{m}] $
$ H_v\ [\mathrm{m}] $
No data
$ s\ [\mathrm{\%}] $
Loss of height on valve and pressure height on Gate valve

Stroke from open position Loss of pressure on the valve Pressure on the valve
$ s $ $ H_L $ $ H_v $
$ \mathrm{\%} $ $ \mathrm{m} $ $ \mathrm{m} $
No data
Unrounded data
Stroke from open position; Loss of pressure on the valve; Pressure on the valve;
s; H_L; H_v;
\%; m; m;
$$H_L=\cfrac{v^2}{2\cdot g}\cdot ζ$$
$H_L=\cfrac{v^2}{2\cdot g}\cdot ζ$
Equations in LaTeX code
H_L=\cfrac{v^2}{2\cdot g}\cdot ζ
$$H_v=H_L+\cfrac{v^2}{2\cdot g}+\left(1-Q_p\right)\cdot\left(ΔP-P_{u}\right)$$
$H_v=H_L+\cfrac{v^2}{2\cdot g}+\left(1-Q_p\right)\cdot\left(ΔP-P_{u}\right)$
Equations in LaTeX code
H_v=H_L+\cfrac{v^2}{2\cdot g}+\left(1-Q_p\right)\cdot\left(ΔP-P_{u}\right)

$ σ\ [-] $
No data
$ s\ [\mathrm{\%}] $
Cavitation number

Stroke from open position Cavitation number
$ s $ $ σ $
$ \mathrm{\%} $ $ \mathrm{\ } $
No data
Unrounded data
Stroke from open position; Cavitation number;
s; σ;
\%; ;
$$σ=\cfrac{\cfrac{p_{air}-P_{SV}}{ρ\cdot g}+H-H_L}{H_v}$$
$σ=\cfrac{\cfrac{p_{air}-P_{SV}}{ρ\cdot g}+H-H_L}{H_v}$
Equations in LaTeX code
σ=\cfrac{\cfrac{p_{air}-P_{SV}}{ρ\cdot g}+H-H_L}{H_v}
Stroke from open position
Forces on sliding plate in axis x
Forces on sliding plate in axis y
The force at the valve axis x
The force at the valve axis y
$ s $ $ F_x $ $ F_y $ $ F_{bx} $ $ F_{by} $
$ \mathrm{\%} $ $ \mathrm{kN} $ $ \mathrm{kN} $ $ \mathrm{kN} $ $ \mathrm{kN} $
No data
Stroke from open position Forces on sliding plate in axis x Forces on sliding plate in axis y The force at the valve axis x The force at the valve axis y
$ s $ $ F_x $ $ F_y $ $ F_{bx} $ $ F_{by} $
$ \mathrm{\%} $ $ \mathrm{kN} $ $ \mathrm{kN} $ $ \mathrm{kN} $ $ \mathrm{kN} $
No data
Unrounded data
Stroke from open position;Forces on sliding plate in axis x;Forces on sliding plate in axis y;The force at the valve axis x;The force at the valve axis y;
s;F_x;F_y;F_{bx};F_{by};
\%;kN;kN;kN;kN;

$ F_x\ [\mathrm{kN}] $
$ F_y\ [\mathrm{kN}] $
No data
$ s\ [\mathrm{\%}] $
Forces on sliding plate

Stroke from open position Forces on sliding plate in axis x Forces on sliding plate in axis y
$ s $ $ F_x $ $ F_y $
$ \mathrm{\%} $ $ \mathrm{kN} $ $ \mathrm{kN} $
No data
Unrounded data
Stroke from open position; Forces on sliding plate in axis x; Forces on sliding plate in axis y;
s; F_x; F_y;
\%; kN; kN;
$$F_x=\cfrac{π\cdot D^2}{4\cdot 10^9}\cdot ρ\cdot g\cdot H_v\cdot K_x$$
$F_x=\cfrac{π\cdot D^2}{4\cdot 10^9}\cdot ρ\cdot g\cdot H_v\cdot K_x$
Equations in LaTeX code
F_x=\cfrac{π\cdot D^2}{4\cdot 10^9}\cdot ρ\cdot g\cdot H_v\cdot K_x
$$F_y=\cfrac{π\cdot D^2}{4\cdot 10^9}\cdot ρ\cdot g\cdot H_v\cdot K_y$$
$F_y=\cfrac{π\cdot D^2}{4\cdot 10^9}\cdot ρ\cdot g\cdot H_v\cdot K_y$
Equations in LaTeX code
F_y=\cfrac{π\cdot D^2}{4\cdot 10^9}\cdot ρ\cdot g\cdot H_v\cdot K_y

$ F_{bx}\ [\mathrm{kN}] $
No data
$ s\ [\mathrm{\%}] $
The force at the valve axis x

Stroke from open position The force at the valve axis x
$ s $ $ F_{bx} $
$ \mathrm{\%} $ $ \mathrm{kN} $
No data
Unrounded data
Stroke from open position; The force at the valve axis x;
s; F_{bx};
\%; kN;
$\text{if }\ α=90$
$\text{if }\ α=90$
Equations in LaTeX code
\text{if }\ α=90
$$F_{bx}=\cfrac{π\cdot D_s^2}{4\cdot 10^9}\cdot ρ\cdot g\cdot H_v\cdot K_{bx}$$
$F_{bx}=\cfrac{π\cdot D_s^2}{4\cdot 10^9}\cdot ρ\cdot g\cdot H_v\cdot K_{bx}$
Equations in LaTeX code
F_{bx}=\cfrac{π\cdot D_s^2}{4\cdot 10^9}\cdot ρ\cdot g\cdot H_v\cdot K_{bx}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$F_{bx}=\cfrac{π\cdot D^2}{4\cdot 10^9}\cdot ρ\cdot g\cdot H_v\cdot K_{bx}$$
$F_{bx}=\cfrac{π\cdot D^2}{4\cdot 10^9}\cdot ρ\cdot g\cdot H_v\cdot K_{bx}$
Equations in LaTeX code
F_{bx}=\cfrac{π\cdot D^2}{4\cdot 10^9}\cdot ρ\cdot g\cdot H_v\cdot K_{bx}

$ F_{by}\ [\mathrm{kN}] $
No data
$ s\ [\mathrm{\%}] $
The force at the valve axis y

Stroke from open position The force at the valve axis y
$ s $ $ F_{by} $
$ \mathrm{\%} $ $ \mathrm{kN} $
No data
Unrounded data
Stroke from open position; The force at the valve axis y;
s; F_{by};
\%; kN;
$$F_{by}=\cfrac{π\cdot D^2}{4\cdot 10^9}\cdot ρ\cdot g\cdot H_v\cdot K_{by}$$
$F_{by}=\cfrac{π\cdot D^2}{4\cdot 10^9}\cdot ρ\cdot g\cdot H_v\cdot K_{by}$
Equations in LaTeX code
F_{by}=\cfrac{π\cdot D^2}{4\cdot 10^9}\cdot ρ\cdot g\cdot H_v\cdot K_{by}
Stroke from open position
Coefficient of under-pressure of aerated hole
Under-pressure in the aerated pipeline
Air flow
$ s $ $ f_{air} $ $ p_{air} $ $ Q_{air} $
$ \mathrm{\%} $ $ \mathrm{\ } $ $ \mathrm{Pa} $ $ \mathrm{m^3/s} $
No data
Stroke from open position Coefficient of under-pressure of aerated hole Under-pressure in the aerated pipeline Air flow
$ s $ $ f_{air} $ $ p_{air} $ $ Q_{air} $
$ \mathrm{\%} $ $ \mathrm{\ } $ $ \mathrm{Pa} $ $ \mathrm{m^3/s} $
No data
Unrounded data
Stroke from open position;Coefficient of under-pressure of aerated hole;Under-pressure in the aerated pipeline;Air flow;
s;f_{air};p_{air};Q_{air};
\%; ;Pa;m^3/s;

$ f_{air}\ [-] $
No data
$ s\ [\mathrm{\%}] $
Coefficient of under-pressure of aerated hole

Stroke from open position Coefficient of under-pressure of aerated hole
$ s $ $ f_{air} $
$ \mathrm{\%} $ $ \mathrm{\ } $
No data
Unrounded data
Stroke from open position; Coefficient of under-pressure of aerated hole;
s; f_{air};
\%; ;

$ p_{air}\ [\mathrm{Pa}] $
No data
$ s\ [\mathrm{\%}] $
Under-pressure in the aerated pipeline

Stroke from open position Under-pressure in the aerated pipeline
$ s $ $ p_{air} $
$ \mathrm{\%} $ $ \mathrm{Pa} $
No data
Unrounded data
Stroke from open position; Under-pressure in the aerated pipeline;
s; p_{air};
\%; Pa;
$\text{if }\ \text{n}= \text{no}$
$\text{if }\ \text{n}= \text{no}$
Equations in LaTeX code
\text{if }\ \text{n}= \text{no}
$$p_{air}=NAN$$
$p_{air}=NAN$
Equations in LaTeX code
p_{air}=NAN
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$p_{air}=-\min\left(p_{air}, f_{air}\cdot\cfrac{v^2}{2\cdot g}\cdot ρ+\left(1-Q_p\right)\cdot\min\left(\cfrac{L\cdot v_{max}\cdot ρ}{t\cdot c_{ef}}, p_{air}\right)\right)$$
$p_{air}=-\min\left(p_{air}, f_{air}\cdot\cfrac{v^2}{2\cdot g}\cdot ρ+\left(1-Q_p\right)\cdot\min\left(\cfrac{L\cdot v_{max}\cdot ρ}{t\cdot c_{ef}}, p_{air}\right)\right)$
Equations in LaTeX code
p_{air}=-\min\left(p_{air}, f_{air}\cdot\cfrac{v^2}{2\cdot g}\cdot ρ+\left(1-Q_p\right)\cdot\min\left(\cfrac{L\cdot v_{max}\cdot ρ}{t\cdot c_{ef}}, p_{air}\right)\right)

$ Q_{air}\ [\mathrm{m^3/s}] $
No data
$ s\ [\mathrm{\%}] $
Air flow

Stroke from open position Air flow
$ s $ $ Q_{air} $
$ \mathrm{\%} $ $ \mathrm{m^3/s} $
No data
Unrounded data
Stroke from open position; Air flow;
s; Q_{air};
\%; m^3/s;
$\text{if }\ \text{n}= \text{no}$
$\text{if }\ \text{n}= \text{no}$
Equations in LaTeX code
\text{if }\ \text{n}= \text{no}
$$Q_{air}=NAN$$
$Q_{air}=NAN$
Equations in LaTeX code
Q_{air}=NAN
$\text{else if }\ p_{air}<\cfrac{p_{air}}{2}$
$\text{else if }\ p_{air}<\cfrac{p_{air}}{2}$
Equations in LaTeX code
\text{else if }\ p_{air}<\cfrac{p_{air}}{2}
$$Q_{air}=\min\left(Q_{max}-Q, 0.2\cdot Q\right)$$
$Q_{air}=\min\left(Q_{max}-Q, 0.2\cdot Q\right)$
Equations in LaTeX code
Q_{air}=\min\left(Q_{max}-Q, 0.2\cdot Q\right)
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$Q_{air}=\max\left(Q_{max}-Q, 0.2\cdot Q\right)$$
$Q_{air}=\max\left(Q_{max}-Q, 0.2\cdot Q\right)$
Equations in LaTeX code
Q_{air}=\max\left(Q_{max}-Q, 0.2\cdot Q\right)
Stroke from open position
Air velocity
The flow area of the aerated hole
The flow area of the aerated pipeline
$ s $ $ v_{air} $ $ A_{air} $ $ A_{air-pipe} $
$ \mathrm{\%} $ $ \mathrm{m/s} $ $ \mathrm{m^2} $ $ \mathrm{m^2} $
No data
Stroke from open position Air velocity The flow area of the aerated hole The flow area of the aerated pipeline
$ s $ $ v_{air} $ $ A_{air} $ $ A_{air-pipe} $
$ \mathrm{\%} $ $ \mathrm{m/s} $ $ \mathrm{m^2} $ $ \mathrm{m^2} $
No data
Unrounded data
Stroke from open position;Air velocity;The flow area of the aerated hole;The flow area of the aerated pipeline;
s;v_{air};A_{air};A_{air-pipe};
\%;m/s;m^2;m^2;

$ v_{air}\ [\mathrm{m/s}] $
No data
$ s\ [\mathrm{\%}] $
Air velocity

Stroke from open position Air velocity
$ s $ $ v_{air} $
$ \mathrm{\%} $ $ \mathrm{m/s} $
No data
Unrounded data
Stroke from open position; Air velocity;
s; v_{air};
\%; m/s;
$\text{if }\ \text{n}= \text{no}$
$\text{if }\ \text{n}= \text{no}$
Equations in LaTeX code
\text{if }\ \text{n}= \text{no}
$$v_{air}=NAN$$
$v_{air}=NAN$
Equations in LaTeX code
v_{air}=NAN
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$v_{air}=\min\left(0.7\cdot\sqrt{-\cfrac{2\cdot p_{air}}{ρ_{air}}}, 250\right)$$
$v_{air}=\min\left(0.7\cdot\sqrt{-\cfrac{2\cdot p_{air}}{ρ_{air}}}, 250\right)$
Equations in LaTeX code
v_{air}=\min\left(0.7\cdot\sqrt{-\cfrac{2\cdot p_{air}}{ρ_{air}}}, 250\right)

$ A_{air}\ [\mathrm{m^2}] $
No data
$ s\ [\mathrm{\%}] $
The flow area of the aerated hole

Stroke from open position The flow area of the aerated hole
$ s $ $ A_{air} $
$ \mathrm{\%} $ $ \mathrm{m^2} $
No data
Unrounded data
Stroke from open position; The flow area of the aerated hole;
s; A_{air};
\%; m^2;
$\text{if }\ \text{n}= \text{no}$
$\text{if }\ \text{n}= \text{no}$
Equations in LaTeX code
\text{if }\ \text{n}= \text{no}
$$A_{air}=NAN$$
$A_{air}=NAN$
Equations in LaTeX code
A_{air}=NAN
$\text{else if }\ v_{air}=0$
$\text{else if }\ v_{air}=0$
Equations in LaTeX code
\text{else if }\ v_{air}=0
$$A_{air}=0$$
$A_{air}=0$
Equations in LaTeX code
A_{air}=0
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$A_{air}=\cfrac{Q_{air}}{v_{air}}$$
$A_{air}=\cfrac{Q_{air}}{v_{air}}$
Equations in LaTeX code
A_{air}=\cfrac{Q_{air}}{v_{air}}

$ A_{air-pipe}\ [\mathrm{m^2}] $
No data
$ s\ [\mathrm{\%}] $
The flow area of the aerated pipeline

Stroke from open position The flow area of the aerated pipeline
$ s $ $ A_{air-pipe} $
$ \mathrm{\%} $ $ \mathrm{m^2} $
No data
Unrounded data
Stroke from open position; The flow area of the aerated pipeline;
s; A_{air-pipe};
\%; m^2;
$\text{if }\ \text{n}= \text{no}$
$\text{if }\ \text{n}= \text{no}$
Equations in LaTeX code
\text{if }\ \text{n}= \text{no}
$$A_{air-pipe}=NAN$$
$A_{air-pipe}=NAN$
Equations in LaTeX code
A_{air-pipe}=NAN
$\text{else if }\ v_{air}>50$
$\text{else if }\ v_{air}>50$
Equations in LaTeX code
\text{else if }\ v_{air}>50
$$A_{air-pipe}=\cfrac{Q_{air}}{50}$$
$A_{air-pipe}=\cfrac{Q_{air}}{50}$
Equations in LaTeX code
A_{air-pipe}=\cfrac{Q_{air}}{50}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$A_{air-pipe}=A_{air}$$
$A_{air-pipe}=A_{air}$
Equations in LaTeX code
A_{air-pipe}=A_{air}
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