Menu

Effective closing time factor

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} $
$ \{K_{Q-valve}[1]\in\mathbb{R}\mid K_{Q-valve}[1]>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.
$ K_{Q-valve}[1] $
$ \{K_{Q-valve}[2]\in\mathbb{R}\mid K_{Q-valve}[2]>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.
$ K_{Q-valve}[2] $
$ \{K_{Q-valve}[3]\in\mathbb{R}\mid K_{Q-valve}[3]>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.
$ K_{Q-valve}[3] $
$ \{K_{Q-valve}[4]\in\mathbb{R}\mid K_{Q-valve}[4]>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.
$ K_{Q-valve}[4] $
$ \{K_{Q-valve}[5]\in\mathbb{R}\mid K_{Q-valve}[5]>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.
$ K_{Q-valve}[5] $
$ \{K_{Q-valve}[6]\in\mathbb{R}\mid K_{Q-valve}[6]>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.
$ K_{Q-valve}[6] $
$ \{K_{Q-valve}[7]\in\mathbb{R}\mid K_{Q-valve}[7]>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.
$ K_{Q-valve}[7] $
$ \{K_{Q-valve}[8]\in\mathbb{R}\mid K_{Q-valve}[8]>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.
$ K_{Q-valve}[8] $
$ \{K_{Q-valve}[9]\in\mathbb{R}\mid K_{Q-valve}[9]>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.
$ K_{Q-valve}[9] $
$ \{K_{Q-valve}[10]\in\mathbb{R}\mid K_{Q-valve}[10]>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.
$ K_{Q-valve}[10] $

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
Stroke from open position
Flow coefficient
Loss coefficient
Reduced free flow area in the throttle control system
Relative flow
$ s $ $ K_Q $ $ ζ $ $ f_r $ $ Q_p $
$ \mathrm{\%} $ $ \mathrm{\ } $ $ \mathrm{\ } $ $ \mathrm{\ } $ $ \mathrm{\ } $
No data
Stroke from open position Flow coefficient Loss coefficient Reduced free flow area in the throttle control system Relative flow
$ s $ $ K_Q $ $ ζ $ $ f_r $ $ Q_p $
$ \mathrm{\%} $ $ \mathrm{\ } $ $ \mathrm{\ } $ $ \mathrm{\ } $ $ \mathrm{\ } $
No data
Unrounded data
Stroke from open position;Flow coefficient;Loss coefficient;Reduced free flow area in the throttle control system;Relative flow;
s;K_Q;ζ;f_r;Q_p;
\%; ; ; ; ;

$ 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;
\%; ;

$ 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)}}
On this page