Menu

Multi-stage valve

Values for calculation

$ \{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} $
$ \{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} $
$ \{P_1\in\mathbb{R}\mid P_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.
$ P_1 $ $ \mathrm{Pa} $
$ \{P_2\in\mathbb{R}\mid P_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.
$ P_2 $ $ \mathrm{Pa} $
$ \{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} $
$ \{μ\in\mathbb{R}\mid μ>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.
$ μ $
$ \{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} $

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}

Number of stages

$\text{if }\ \left(P_2-0.6\cdot P_{SV}\right)/0.4>P_1$
$\text{if }\ \left(P_2-0.6\cdot P_{SV}\right)/0.4>P_1$
Equations in LaTeX code
\text{if }\ \left(P_2-0.6\cdot P_{SV}\right)/0.4>P_1
$$n_{s}=1$$
$n_{s}=1$
Equations in LaTeX code
n_{s}=1
$\text{else if }\ \left(\left(P_2-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4>P_1$
$\text{else if }\ \left(\left(P_2-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4>P_1$
Equations in LaTeX code
\text{else if }\ \left(\left(P_2-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4>P_1
$$n_{s}=2$$
$n_{s}=2$
Equations in LaTeX code
n_{s}=2
$\text{else if }\ \left(\left(\left(P_2-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4>P_1$
$\text{else if }\ \left(\left(\left(P_2-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4>P_1$
Equations in LaTeX code
\text{else if }\ \left(\left(\left(P_2-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4>P_1
$$n_{s}=3$$
$n_{s}=3$
Equations in LaTeX code
n_{s}=3
$\text{else if }\ \left(\left(\left(\left(P_2-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4>P_1$
$\text{else if }\ \left(\left(\left(\left(P_2-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4>P_1$
Equations in LaTeX code
\text{else if }\ \left(\left(\left(\left(P_2-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4>P_1
$$n_{s}=4$$
$n_{s}=4$
Equations in LaTeX code
n_{s}=4
$\text{else if }\ \left(\left(\left(\left(\left(P_2-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4>P_1$
$\text{else if }\ \left(\left(\left(\left(\left(P_2-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4>P_1$
Equations in LaTeX code
\text{else if }\ \left(\left(\left(\left(\left(P_2-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4>P_1
$$n_{s}=5$$
$n_{s}=5$
Equations in LaTeX code
n_{s}=5
$\text{else if }\ \left(\left(\left(\left(\left(\left(P_2-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4>P_1$
$\text{else if }\ \left(\left(\left(\left(\left(\left(P_2-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4>P_1$
Equations in LaTeX code
\text{else if }\ \left(\left(\left(\left(\left(\left(P_2-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4>P_1
$$n_{s}=6$$
$n_{s}=6$
Equations in LaTeX code
n_{s}=6
$\text{else if }\ \left(\left(\left(\left(\left(\left(\left(P_2-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4>P_1$
$\text{else if }\ \left(\left(\left(\left(\left(\left(\left(P_2-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4>P_1$
Equations in LaTeX code
\text{else if }\ \left(\left(\left(\left(\left(\left(\left(P_2-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4>P_1
$$n_{s}=7$$
$n_{s}=7$
Equations in LaTeX code
n_{s}=7
$\text{else if }\ \left(\left(\left(\left(\left(\left(\left(\left(P_2-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4>P_1$
$\text{else if }\ \left(\left(\left(\left(\left(\left(\left(\left(P_2-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4>P_1$
Equations in LaTeX code
\text{else if }\ \left(\left(\left(\left(\left(\left(\left(\left(P_2-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4-0.6\cdot P_{SV}\right)/0.4>P_1
$$n_{s}=8$$
$n_{s}=8$
Equations in LaTeX code
n_{s}=8
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$n_{s}=9$$
$n_{s}=9$
Equations in LaTeX code
n_{s}=9
Stage
Maximum pressures between stages
Pressure difference between the stages
The flow area
Number of holes
$ S $ $ P_{max-stages} $ $ ΔP_{stages} $ $ A $ $ I $
$ \mathrm{\ } $ $ \mathrm{Pa} $ $ \mathrm{Pa} $ $ \mathrm{m^2} $ $ \mathrm{\ } $
No data
Stage Maximum pressures between stages Pressure difference between the stages The flow area Number of holes
$ S $ $ P_{max-stages} $ $ ΔP_{stages} $ $ A $ $ I $
$ \mathrm{\ } $ $ \mathrm{Pa} $ $ \mathrm{Pa} $ $ \mathrm{m^2} $ $ \mathrm{\ } $
No data
Unrounded data
Stage;Maximum pressures between stages;Pressure difference between the stages;The flow area;Number of holes;
S;P_{max-stages};ΔP_{stages};A;I;
;Pa;Pa;m^2; ;

$ P_{max-stages}\ [\mathrm{Pa}] $
No data
$ S\ [-] $
Maximum pressures between stages

Stage Maximum pressures between stages
$ S $ $ P_{max-stages} $
$ \mathrm{\ } $ $ \mathrm{Pa} $
No data
Unrounded data
Stage; Maximum pressures between stages;
S; P_{max-stages};
; Pa;
$\text{if }\ S=1$
$\text{if }\ S=1$
Equations in LaTeX code
\text{if }\ S=1
$$P_{max-stages}=P_1$$
$P_{max-stages}=P_1$
Equations in LaTeX code
P_{max-stages}=P_1
$\text{else if }\ S=2$
$\text{else if }\ S=2$
Equations in LaTeX code
\text{else if }\ S=2
$$P_{max-stages}=\left(P_1\cdot 0.4+0.6\cdot P_{SV}\right)$$
$P_{max-stages}=\left(P_1\cdot 0.4+0.6\cdot P_{SV}\right)$
Equations in LaTeX code
P_{max-stages}=\left(P_1\cdot 0.4+0.6\cdot P_{SV}\right)
$\text{else if }\ S=3$
$\text{else if }\ S=3$
Equations in LaTeX code
\text{else if }\ S=3
$$P_{max-stages}=\left(\left(P_1\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)$$
$P_{max-stages}=\left(\left(P_1\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)$
Equations in LaTeX code
P_{max-stages}=\left(\left(P_1\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)
$\text{else if }\ S=4$
$\text{else if }\ S=4$
Equations in LaTeX code
\text{else if }\ S=4
$$P_{max-stages}=\left(\left(\left(P_1\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)$$
$P_{max-stages}=\left(\left(\left(P_1\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)$
Equations in LaTeX code
P_{max-stages}=\left(\left(\left(P_1\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)
$\text{else if }\ S=5$
$\text{else if }\ S=5$
Equations in LaTeX code
\text{else if }\ S=5
$$P_{max-stages}=\left(\left(\left(\left(P_1\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)$$
$P_{max-stages}=\left(\left(\left(\left(P_1\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)$
Equations in LaTeX code
P_{max-stages}=\left(\left(\left(\left(P_1\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)
$\text{else if }\ S=6$
$\text{else if }\ S=6$
Equations in LaTeX code
\text{else if }\ S=6
$$P_{max-stages}=\left(\left(\left(\left(\left(P_1\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)$$
$P_{max-stages}=\left(\left(\left(\left(\left(P_1\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)$
Equations in LaTeX code
P_{max-stages}=\left(\left(\left(\left(\left(P_1\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)
$\text{else if }\ S=7$
$\text{else if }\ S=7$
Equations in LaTeX code
\text{else if }\ S=7
$$P_{max-stages}=\left(\left(\left(\left(\left(\left(P_1\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)$$
$P_{max-stages}=\left(\left(\left(\left(\left(\left(P_1\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)$
Equations in LaTeX code
P_{max-stages}=\left(\left(\left(\left(\left(\left(P_1\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$P_{max-stages}=\left(\left(\left(\left(\left(\left(\left(P_1\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)$$
$P_{max-stages}=\left(\left(\left(\left(\left(\left(\left(P_1\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)$
Equations in LaTeX code
P_{max-stages}=\left(\left(\left(\left(\left(\left(\left(P_1\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)\cdot 0.4+0.6\cdot P_{SV}\right)

$ ΔP_{stages}\ [\mathrm{Pa}] $
No data
$ S\ [-] $
Pressure difference between the stages

Stage Pressure difference between the stages
$ S $ $ ΔP_{stages} $
$ \mathrm{\ } $ $ \mathrm{Pa} $
No data
Unrounded data
Stage; Pressure difference between the stages;
S; ΔP_{stages};
; Pa;
$\text{if }\ S=n_{s}$
$\text{if }\ S=n_{s}$
Equations in LaTeX code
\text{if }\ S=n_{s}
$$ΔP_{stages}=P_{max-stages}-P_2+\left(n_{s}-1\right)\cdot\left(\left(P_2-0.6\cdot P_{SV}\right)/0.4-\left(P_{max-stages}\right)[n_{s}]\right)/n_{s}$$
$ΔP_{stages}=P_{max-stages}-P_2+\left(n_{s}-1\right)\cdot\left(\left(P_2-0.6\cdot P_{SV}\right)/0.4-\left(P_{max-stages}\right)[n_{s}]\right)/n_{s}$
Equations in LaTeX code
ΔP_{stages}=P_{max-stages}-P_2+\left(n_{s}-1\right)\cdot\left(\left(P_2-0.6\cdot P_{SV}\right)/0.4-\left(P_{max-stages}\right)[n_{s}]\right)/n_{s}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$ΔP_{stages}=P_{max-stages}-P_{max-stages}[i+1]-\left(\left(P_2-0.6\cdot P_{SV}\right)/0.4-\left(P_{max-stages}\right)[n_{s}]\right)/n_{s}$$
$ΔP_{stages}=P_{max-stages}-P_{max-stages}[i+1]-\left(\left(P_2-0.6\cdot P_{SV}\right)/0.4-\left(P_{max-stages}\right)[n_{s}]\right)/n_{s}$
Equations in LaTeX code
ΔP_{stages}=P_{max-stages}-P_{max-stages}[i+1]-\left(\left(P_2-0.6\cdot P_{SV}\right)/0.4-\left(P_{max-stages}\right)[n_{s}]\right)/n_{s}

$ A\ [\mathrm{m^2}] $
No data
$ S\ [-] $
The flow area

Stage The flow area
$ S $ $ A $
$ \mathrm{\ } $ $ \mathrm{m^2} $
No data
Unrounded data
Stage; The flow area;
S; A;
; m^2;
$$A=\cfrac{Q_{max}}{μ\cdot \sqrt{2\cdot \cfrac{ΔP_{stages}}{ρ}}}$$
$A=\cfrac{Q_{max}}{μ\cdot \sqrt{2\cdot \cfrac{ΔP_{stages}}{ρ}}}$
Equations in LaTeX code
A=\cfrac{Q_{max}}{μ\cdot \sqrt{2\cdot \cfrac{ΔP_{stages}}{ρ}}}

$ I\ [-] $
No data
$ S\ [-] $
Number of holes

Stage Number of holes
$ S $ $ I $
$ \mathrm{\ } $ $ \mathrm{\ } $
No data
Unrounded data
Stage; Number of holes;
S; I;
; ;
$$I=\left\lfloor\cfrac{4\cdot A}{π\cdot d^2\cdot 10^{-6}}\right\rfloor$$
$I=\left\lfloor\cfrac{4\cdot A}{π\cdot d^2\cdot 10^{-6}}\right\rfloor$
Equations in LaTeX code
I=\left\lfloor\cfrac{4\cdot A}{π\cdot d^2\cdot 10^{-6}}\right\rfloor

Requirements

$$ \cfrac{D}{50}\geq d $$
$\cfrac{D}{50}\geq d$
Equations in LaTeX code
\cfrac{D}{50}\geq d
$$ \cfrac{4\cdot 10^6\cdot \max\left(A\right) }{π\cdot D^2}< 0.5 $$
$\cfrac{4\cdot 10^6\cdot \max\left(A\right) }{π\cdot D^2}< 0.5$
Equations in LaTeX code
\cfrac{4\cdot 10^6\cdot \max\left(A\right) }{π\cdot D^2}< 0.5
On this page