Menu

Hydrodynamic calculation Needle valve closing flow against the direction of movement of the piston

Needle valve closing flow against the direction of movement of the piston D Q max -F +F 0.912 D 0.975 D 0.4D L
Needle valve closing flow against the direction of movement of the piston
needle-valve-2 0.133 D - 4 d 1 0.183 D - 8 d 1 0.26 D - 12 d 1 0.35 D - 16 d 1 0.45 D - 20 d 1 0.56 D - 24 d 1 0.666 D - 28 d 1 0.773 D - 32 d 1 0.975 D d 1 =0.03 D
Needle

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} $
$ \{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)

$ [-] $
Hydraulic profile of the needle valve

Stroke from open position
First stage of cavitation
Second stage of cavitation
Fully developed cavitation
$ s $ $ σ_1 $ $ σ_2 $ $ σ_{min} $
$ \mathrm{\%} $ $ \mathrm{\ } $ $ \mathrm{\ } $ $ \mathrm{\ } $
No data
Stroke from open position First stage of cavitation Second stage of cavitation Fully developed cavitation
$ s $ $ σ_1 $ $ σ_2 $ $ σ_{min} $
$ \mathrm{\%} $ $ \mathrm{\ } $ $ \mathrm{\ } $ $ \mathrm{\ } $
No data
Unrounded data
Stroke from open position;First stage of cavitation;Second stage of cavitation;Fully developed cavitation;
s;σ_1;σ_2;σ_{min};
\%; ; ; ;

$ σ_1\ [-] $
$ σ_2\ [-] $
$ σ_{min}\ [-] $
No data
$ s\ [\mathrm{\%}] $
Stage of cavitation

Stroke from open position First stage of cavitation Second stage of cavitation Fully developed cavitation
$ s $ $ σ_1 $ $ σ_2 $ $ σ_{min} $
$ \mathrm{\%} $ $ \mathrm{\ } $ $ \mathrm{\ } $ $ \mathrm{\ } $
No data
Unrounded data
Stroke from open position; First stage of cavitation; Second stage of cavitation; Fully developed cavitation;
s; σ_1; σ_2; σ_{min};
\%; ; ; ;
Stroke from open position
Flow coefficient for $ σ_1 $
Flow coefficient for $ σ_2 $
Flow coefficient for $ σ_{min} $
$ s $ $ K_{Q-σ_1} $ $ K_{Q-σ_2} $ $ K_{Q-σ_{min}} $
$ \mathrm{\%} $ $ \mathrm{\ } $ $ \mathrm{\ } $ $ \mathrm{\ } $
No data
Stroke from open position Flow coefficient for $ σ_1 $ Flow coefficient for $ σ_2 $ Flow coefficient for $ σ_{min} $
$ s $ $ K_{Q-σ_1} $ $ K_{Q-σ_2} $ $ K_{Q-σ_{min}} $
$ \mathrm{\%} $ $ \mathrm{\ } $ $ \mathrm{\ } $ $ \mathrm{\ } $
No data
Unrounded data
Stroke from open position;Flow coefficient for $ σ_1 $ ;Flow coefficient for $ σ_2 $ ;Flow coefficient for $ σ_{min} $ ;
s;K_{Q-σ_1};K_{Q-σ_2};K_{Q-σ_{min}};
\%; ; ; ;

$ K_{Q-σ_1}\ [-] $
$ K_{Q-σ_2}\ [-] $
$ K_{Q-σ_{min}}\ [-] $
No data
$ s\ [\mathrm{\%}] $
Flow coefficient for stages of cavitation

Stroke from open position Flow coefficient for $ σ_1 $ Flow coefficient for $ σ_2 $ Flow coefficient for $ σ_{min} $
$ s $ $ K_{Q-σ_1} $ $ K_{Q-σ_2} $ $ K_{Q-σ_{min}} $
$ \mathrm{\%} $ $ \mathrm{\ } $ $ \mathrm{\ } $ $ \mathrm{\ } $
No data
Unrounded data
Stroke from open position; Flow coefficient for $ σ_1 $ ; Flow coefficient for $ σ_2 $ ; Flow coefficient for $ σ_{min} $ ;
s; K_{Q-σ_1}; K_{Q-σ_2}; K_{Q-σ_{min}};
\%; ; ; ;
Stroke from open position
Coefficient of hydraulic force on a needle in the axis x for $ σ_1 $
Coefficient of hydraulic force on a needle in the axis x for $ σ_2 $
Coefficient of hydraulic force on a needle in the axis x for $ σ_{min} $
$ s $ $ K_{x-σ_1} $ $ K_{x-σ_2} $ $ K_{x-σ_{min}} $
$ \mathrm{\%} $ $ \mathrm{\ } $ $ \mathrm{\ } $ $ \mathrm{\ } $
No data
Stroke from open position Coefficient of hydraulic force on a needle in the axis x for $ σ_1 $ Coefficient of hydraulic force on a needle in the axis x for $ σ_2 $ Coefficient of hydraulic force on a needle in the axis x for $ σ_{min} $
$ s $ $ K_{x-σ_1} $ $ K_{x-σ_2} $ $ K_{x-σ_{min}} $
$ \mathrm{\%} $ $ \mathrm{\ } $ $ \mathrm{\ } $ $ \mathrm{\ } $
No data
Unrounded data
Stroke from open position;Coefficient of hydraulic force on a needle in the axis x for $ σ_1 $ ;Coefficient of hydraulic force on a needle in the axis x for $ σ_2 $ ;Coefficient of hydraulic force on a needle in the axis x for $ σ_{min} $ ;
s;K_{x-σ_1};K_{x-σ_2};K_{x-σ_{min}};
\%; ; ; ;

$ K_{x-σ_1}\ [-] $
$ K_{x-σ_2}\ [-] $
$ K_{x-σ_{min}}\ [-] $
No data
$ s\ [\mathrm{\%}] $
Coefficient of hydraulic force on a needle in the axis x for stages of cavitation

Stroke from open position Coefficient of hydraulic force on a needle in the axis x for $ σ_1 $ Coefficient of hydraulic force on a needle in the axis x for $ σ_2 $ Coefficient of hydraulic force on a needle in the axis x for $ σ_{min} $
$ s $ $ K_{x-σ_1} $ $ K_{x-σ_2} $ $ K_{x-σ_{min}} $
$ \mathrm{\%} $ $ \mathrm{\ } $ $ \mathrm{\ } $ $ \mathrm{\ } $
No data
Unrounded data
Stroke from open position; Coefficient of hydraulic force on a needle in the axis x for $ σ_1 $ ; Coefficient of hydraulic force on a needle in the axis x for $ σ_2 $ ; Coefficient of hydraulic force on a needle in the axis x for $ σ_{min} $ ;
s; K_{x-σ_1}; K_{x-σ_2}; K_{x-σ_{min}};
\%; ; ; ;
Stroke from open position
Flow coefficient
Coefficient of hydraulic force on a needle in the axis x
$ s $ $ K_Q $ $ K_x $
$ \mathrm{\%} $ $ \mathrm{\ } $ $ \mathrm{\ } $
No data
Stroke from open position Flow coefficient Coefficient of hydraulic force on a needle in the axis x
$ s $ $ K_Q $ $ K_x $
$ \mathrm{\%} $ $ \mathrm{\ } $ $ \mathrm{\ } $
No data
Unrounded data
Stroke from open position;Flow coefficient;Coefficient of hydraulic force on a needle in the axis x;
s;K_Q;K_x;
\%; ; ;

$ 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;
\%; ;
$\text{if }\ σ> σ_1$
$\text{if }\ σ> σ_1$
Equations in LaTeX code
\text{if }\ σ> σ_1
$$K_Q=K_{Q-σ_1}$$
$K_Q=K_{Q-σ_1}$
Equations in LaTeX code
K_Q=K_{Q-σ_1}
$\text{else if }\ σ> σ_2$
$\text{else if }\ σ> σ_2$
Equations in LaTeX code
\text{else if }\ σ> σ_2
$$K_Q=K_{Q-σ_2}$$
$K_Q=K_{Q-σ_2}$
Equations in LaTeX code
K_Q=K_{Q-σ_2}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$K_Q=K_{Q-σ_{min}}$$
$K_Q=K_{Q-σ_{min}}$
Equations in LaTeX code
K_Q=K_{Q-σ_{min}}

$ K_x\ [-] $
No data
$ s\ [\mathrm{\%}] $
Coefficient of hydraulic force on a needle in the axis x

Stroke from open position Coefficient of hydraulic force on a needle in the axis x
$ s $ $ K_x $
$ \mathrm{\%} $ $ \mathrm{\ } $
No data
Unrounded data
Stroke from open position; Coefficient of hydraulic force on a needle in the axis x;
s; K_x;
\%; ;
$\text{if }\ σ> σ_1$
$\text{if }\ σ> σ_1$
Equations in LaTeX code
\text{if }\ σ> σ_1
$$K_x=K_{x-σ_1}$$
$K_x=K_{x-σ_1}$
Equations in LaTeX code
K_x=K_{x-σ_1}
$\text{else if }\ σ> σ_2$
$\text{else if }\ σ> σ_2$
Equations in LaTeX code
\text{else if }\ σ> σ_2
$$K_x=K_{x-σ_2}$$
$K_x=K_{x-σ_2}$
Equations in LaTeX code
K_x=K_{x-σ_2}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$K_x=K_{x-σ_{min}}$$
$K_x=K_{x-σ_{min}}$
Equations in LaTeX code
K_x=K_{x-σ_{min}}
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
Forces on the needle
$ s $ $ H_L $ $ H_v $ $ σ $ $ F_x $
$ \mathrm{\%} $ $ \mathrm{m} $ $ \mathrm{m} $ $ \mathrm{\ } $ $ \mathrm{kN} $
No data
Stroke from open position Loss of pressure on the valve Pressure on the valve Cavitation number Forces on the needle
$ s $ $ H_L $ $ H_v $ $ σ $ $ F_x $
$ \mathrm{\%} $ $ \mathrm{m} $ $ \mathrm{m} $ $ \mathrm{\ } $ $ \mathrm{kN} $
No data
Unrounded data
Stroke from open position;Loss of pressure on the valve;Pressure on the valve;Cavitation number;Forces on the needle;
s;H_L;H_v;σ;F_x;
\%;m;m; ;kN;

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

$ F_x\ [\mathrm{kN}] $
No data
$ s\ [\mathrm{\%}] $
Forces on the needle

Stroke from open position Forces on the needle
$ s $ $ F_x $
$ \mathrm{\%} $ $ \mathrm{kN} $
No data
Unrounded data
Stroke from open position; Forces on the needle;
s; F_x;
\%; kN;
$$F_x=\cfrac{π\cdot D}{4\cdot 10^9}\cdot ρ\cdot g\cdot H_v\cdot K_x$$
$F_x=\cfrac{π\cdot D}{4\cdot 10^9}\cdot ρ\cdot g\cdot H_v\cdot K_x$
Equations in LaTeX code
F_x=\cfrac{π\cdot D}{4\cdot 10^9}\cdot ρ\cdot g\cdot H_v\cdot K_x
On this page