Menu

Multi-stage valve

Values for calculation

$Q_{max}$ $\mathrm{m^3/s}$
$D$ $\mathrm{mm}$
$P_1$ $\mathrm{Pa}$
$P_2$ $\mathrm{Pa}$
$T$ $\mathrm{°C}$
$ρ$ $\mathrm{kg/m^3}$
$P_{SV}$ $\mathrm{Pa}$
$μ$
$d$ $\mathrm{mm}$

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
$S\mathrm{[-]}$
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
$S\mathrm{[-]}$
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
$S\mathrm{[-]}$
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}}}

$I \mathrm{[-]}$
No data
$S\mathrm{[-]}$
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