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Hydrodynamic calculation Howell-Bunger valve

Howell-Bunger valve D 90° 48° R 72° S 25° 40° a b c e f g +F x
Howell-Bunger valve

Values for calculation

$D$ $\mathrm{mm}$
$S$ $\mathrm{mm}$
$R$ $\mathrm{mm}$
$a$ $\mathrm{mm}$
$b$ $\mathrm{mm}$
$c$ $\mathrm{mm}$
$e$ $\mathrm{mm}$
$f$ $\mathrm{mm}$
$g$ $\mathrm{mm}$
$H$ $\mathrm{m}$
$g$ $\mathrm{m/s^2}$
$T$ $\mathrm{°C}$
$ρ$ $\mathrm{kg/m^3}$
$P_{SV}$ $\mathrm{Pa}$
$n$
$ΔP$ $\mathrm{m}$
$Σζ$
$h$ $\mathrm{m}$
$ρ_{air}$ $\mathrm{kg/m^3}$
$p_{air}$ $\mathrm{Pa}$
$h_j$ $\mathrm{m}$
Hydraulic jump behind the valve - model no.1 D 2.5 D L 1 L 2 h l h j
Hydraulic jump behind the valve - model no.1
Dimensional sketch - model no.1 x D 1.25 D 1 D 45° 2.5 D 2.5 D 30° 3 D 6 D 0.4D 2.76D 0.39D 0.86D 1.36D 1.39D 2.77 D 3.08 D 45° P u P u P 1 u-air P 2 u-air P 1 u-air P 2 u-air
Dimensional sketch - model no.1
Hydraulic jump behind the valve - model no.2 D 2.5 D L 1 L 2 h l h j
Hydraulic jump behind the valve - model no.2
Dimensional sketch - model no.2 D 2.82 D 3.33 D 45° 1.36D 3 D 6 D 30° 0.39D 2.56D 1.94D 0.39D 0.58D 45° 0.64D 2.5 D 1.11D 0.6D 0.44 D 0.1 D 4.36D 1.5 D 1.5 D P u P u P 1 u-air P 1 u-air P 2 u-air P 2 u-air
Dimensional sketch - model no.2
Hydraulic jump behind the valve - model no.3 h l h j D 1.2 D L 1 L 2
Hydraulic jump behind the valve - model no.3
Dimensional sketch - model no.3 D 1.82 D 2.33 D 45° 1.36D 3 D 6 D 30° 0.39D 2.56D 1.94D 45° 1.2 D 1.11D 0.6D 0.1 D 4.36D 1.5 D 1.5 D P u P u P 1 u-air P 1 u-air P 2 u-air P 2 u-air
Dimensional sketch - model no.3

Calculation

Flow

$$Q_{max}=\cfrac{1}{\sqrt{1+Σζ+\min\left(ζ\right)}}\cdot\cfrac{π\cdot D^2}{4\cdot 10^6}\cdot\sqrt{2\cdot g\cdot H}$$
$Q_{max}=\cfrac{1}{\sqrt{1+Σζ+\min\left(ζ\right)}}\cdot\cfrac{π\cdot D^2}{4\cdot 10^6}\cdot\sqrt{2\cdot g\cdot H}$
Equations in LaTeX code
Q_{max}=\cfrac{1}{\sqrt{1+Σζ+\min\left(ζ\right)}}\cdot\cfrac{π\cdot D^2}{4\cdot 10^6}\cdot\sqrt{2\cdot g\cdot H}

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
Valve position
Flow coefficient
Coefficient of hydraulic force on body in the axis x
Loss coefficient
Reduced free flow area in the throttle control system
Relative flow
$S/D$ $K_Q$ $K_{bx}$ $ζ$ $f_r$ $Q_p$
$\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$
No data
Valve position Flow coefficient Coefficient of hydraulic force on body in the axis x Loss coefficient Reduced free flow area in the throttle control system Relative flow
$S/D$ $K_Q$ $K_{bx}$ $ζ$ $f_r$ $Q_p$
$\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$
No data
Unrounded data
Valve position;Flow coefficient;Coefficient of hydraulic force on body in the axis x;Loss coefficient;Reduced free flow area in the throttle control system;Relative flow;
S/D;K_Q;K_{bx};ζ;f_r;Q_p;
; ; ; ; ; ;

$K_Q \mathrm{[-]}$
No data
$S/D\mathrm{[-]}$
Flow coefficient

Valve position Flow coefficient
$S/D$ $K_Q$
$\mathrm{ }$ $\mathrm{ }$
No data
Unrounded data
Valve position; Flow coefficient;
S/D; K_Q;
; ;

$K_{bx} \mathrm{[-]}$
No data
$S/D\mathrm{[-]}$
Coefficient of hydraulic force on body in the axis x

Valve position Coefficient of hydraulic force on body in the axis x
$S/D$ $K_{bx}$
$\mathrm{ }$ $\mathrm{ }$
No data
Unrounded data
Valve position; Coefficient of hydraulic force on body in the axis x;
S/D; K_{bx};
; ;

$ζ \mathrm{[-]}$
No data
$S/D\mathrm{[-]}$
Loss coefficient

Valve position Loss coefficient
$S/D$ $ζ$
$\mathrm{ }$ $\mathrm{ }$
No data
Unrounded data
Valve position; Loss coefficient;
S/D; 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}

$f_r \mathrm{[-]}$
$Q_p \mathrm{[-]}$
No data
$S/D\mathrm{[-]}$
Coefficients

Valve position Reduced free flow area in the throttle control system Relative flow
$S/D$ $f_r$ $Q_p$
$\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$
No data
Unrounded data
Valve position; Reduced free flow area in the throttle control system; Relative flow;
S/D; 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)}}
Valve position
Flow of water in the pipeline
Water velocity in pipeline
Energy before the valve
$S/D$ $Q$ $v$ $T_x$
$\mathrm{ }$ $\mathrm{m^3/s}$ $\mathrm{m/s}$ $\mathrm{m}$
No data
Valve position Flow of water in the pipeline Water velocity in pipeline Energy before the valve
$S/D$ $Q$ $v$ $T_x$
$\mathrm{ }$ $\mathrm{m^3/s}$ $\mathrm{m/s}$ $\mathrm{m}$
No data
Unrounded data
Valve position;Flow of water in the pipeline;Water velocity in pipeline;Energy before the valve;
S/D;Q;v;T_x;
;m^3/s;m/s;m;

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

Valve position Flow of water in the pipeline Water velocity in pipeline
$S/D$ $Q$ $v$
$\mathrm{ }$ $\mathrm{m^3/s}$ $\mathrm{m/s}$
No data
Unrounded data
Valve position; Flow of water in the pipeline; Water velocity in pipeline;
S/D; 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}

$T_x \mathrm{[m]}$
No data
$S/D\mathrm{[-]}$
Energy before the valve

Valve position Energy before the valve
$S/D$ $T_x$
$\mathrm{ }$ $\mathrm{m}$
No data
Unrounded data
Valve position; Energy before the valve;
S/D; T_x;
; m;
$\text{if }\ \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 3$
$\text{if }\ \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 3$
Equations in LaTeX code
\text{if }\ \text{model }$$\text{number }$$\text{for }$$\text{Howell-Bunger }$$\text{valve}= 3
$$T_x=H+\cfrac{v^2}{2\cdot g}+1.5\cdot \cfrac{D}{1000}-\cfrac{v^2}{2\cdot g}\cdot Σζ$$
$T_x=H+\cfrac{v^2}{2\cdot g}+1.5\cdot \cfrac{D}{1000}-\cfrac{v^2}{2\cdot g}\cdot Σζ$
Equations in LaTeX code
T_x=H+\cfrac{v^2}{2\cdot g}+1.5\cdot \cfrac{D}{1000}-\cfrac{v^2}{2\cdot g}\cdot Σζ
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$T_x=H+\cfrac{v^2}{2\cdot g}+2.5\cdot \cfrac{D}{1000}-\cfrac{v^2}{2\cdot g}\cdot Σζ$$
$T_x=H+\cfrac{v^2}{2\cdot g}+2.5\cdot \cfrac{D}{1000}-\cfrac{v^2}{2\cdot g}\cdot Σζ$
Equations in LaTeX code
T_x=H+\cfrac{v^2}{2\cdot g}+2.5\cdot \cfrac{D}{1000}-\cfrac{v^2}{2\cdot g}\cdot Σζ
Valve position
Coefficient of water level for $ \cfrac{T_x}{D}=10 $
Coefficient of water level for $ \cfrac{T_x}{D}=20 $
Coefficient of water level for $ \cfrac{T_x}{D}=30 $
Coefficient of water level for $ \cfrac{T_x}{D}=40 $
Coefficient of water level for $ \cfrac{T_x}{D}=50 $
Water level
$S/D$ $h_{l-10}$ $h_{l-20}$ $h_{l-30}$ $h_{l-40}$ $h_{l-50}$ $h_l$
$\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{m}$
No data
Valve position Coefficient of water level for $ \cfrac{T_x}{D}=10 $ Coefficient of water level for $ \cfrac{T_x}{D}=20 $ Coefficient of water level for $ \cfrac{T_x}{D}=30 $ Coefficient of water level for $ \cfrac{T_x}{D}=40 $ Coefficient of water level for $ \cfrac{T_x}{D}=50 $ Water level
$S/D$ $h_{l-10}$ $h_{l-20}$ $h_{l-30}$ $h_{l-40}$ $h_{l-50}$ $h_l$
$\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{m}$
No data
Unrounded data
Valve position;Coefficient of water level for $ \cfrac{T_x}{D}=10 $ ;Coefficient of water level for $ \cfrac{T_x}{D}=20 $ ;Coefficient of water level for $ \cfrac{T_x}{D}=30 $ ;Coefficient of water level for $ \cfrac{T_x}{D}=40 $ ;Coefficient of water level for $ \cfrac{T_x}{D}=50 $ ;Water level;
S/D;h_{l-10};h_{l-20};h_{l-30};h_{l-40};h_{l-50};h_l;
; ; ; ; ; ;m;

$h_{l-10} \mathrm{[-]}$
$h_{l-20} \mathrm{[-]}$
$h_{l-30} \mathrm{[-]}$
$h_{l-40} \mathrm{[-]}$
$h_{l-50} \mathrm{[-]}$
No data
$S/D\mathrm{[-]}$
Coefficient of water level

Valve position Coefficient of water level for $ \cfrac{T_x}{D}=10 $ Coefficient of water level for $ \cfrac{T_x}{D}=20 $ Coefficient of water level for $ \cfrac{T_x}{D}=30 $ Coefficient of water level for $ \cfrac{T_x}{D}=40 $ Coefficient of water level for $ \cfrac{T_x}{D}=50 $
$S/D$ $h_{l-10}$ $h_{l-20}$ $h_{l-30}$ $h_{l-40}$ $h_{l-50}$
$\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$
No data
Unrounded data
Valve position; Coefficient of water level for $ \cfrac{T_x}{D}=10 $ ; Coefficient of water level for $ \cfrac{T_x}{D}=20 $ ; Coefficient of water level for $ \cfrac{T_x}{D}=30 $ ; Coefficient of water level for $ \cfrac{T_x}{D}=40 $ ; Coefficient of water level for $ \cfrac{T_x}{D}=50 $ ;
S/D; h_{l-10}; h_{l-20}; h_{l-30}; h_{l-40}; h_{l-50};
; ; ; ; ; ;

$h_l \mathrm{[m]}$
No data
$S/D\mathrm{[-]}$
Water level

Valve position Water level
$S/D$ $h_l$
$\mathrm{ }$ $\mathrm{m}$
No data
Unrounded data
Valve position; Water level;
S/D; h_l;
; m;
$\text{if }\ \cfrac{T_x\cdot 10^3}{D}< 10$
$\text{if }\ \cfrac{T_x\cdot 10^3}{D}< 10$
Equations in LaTeX code
\text{if }\ \cfrac{T_x\cdot 10^3}{D}< 10
$$h_l=h_{l-10}\cdot\cfrac{D}{1000}$$
$h_l=h_{l-10}\cdot\cfrac{D}{1000}$
Equations in LaTeX code
h_l=h_{l-10}\cdot\cfrac{D}{1000}
$\text{else if }\ \cfrac{T_x\cdot 10^3}{D}< 20$
$\text{else if }\ \cfrac{T_x\cdot 10^3}{D}< 20$
Equations in LaTeX code
\text{else if }\ \cfrac{T_x\cdot 10^3}{D}< 20
$$h_l=h_{l-20}\cdot\cfrac{D}{1000}$$
$h_l=h_{l-20}\cdot\cfrac{D}{1000}$
Equations in LaTeX code
h_l=h_{l-20}\cdot\cfrac{D}{1000}
$\text{else if }\ \cfrac{T_x\cdot 10^3}{D}< 30$
$\text{else if }\ \cfrac{T_x\cdot 10^3}{D}< 30$
Equations in LaTeX code
\text{else if }\ \cfrac{T_x\cdot 10^3}{D}< 30
$$h_l=h_{l-30}\cdot\cfrac{D}{1000}$$
$h_l=h_{l-30}\cdot\cfrac{D}{1000}$
Equations in LaTeX code
h_l=h_{l-30}\cdot\cfrac{D}{1000}
$\text{else if }\ \cfrac{T_x\cdot 10^3}{D}< 40$
$\text{else if }\ \cfrac{T_x\cdot 10^3}{D}< 40$
Equations in LaTeX code
\text{else if }\ \cfrac{T_x\cdot 10^3}{D}< 40
$$h_l=h_{l-40}\cdot\cfrac{D}{1000}$$
$h_l=h_{l-40}\cdot\cfrac{D}{1000}$
Equations in LaTeX code
h_l=h_{l-40}\cdot\cfrac{D}{1000}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$h_l=h_{l-50}\cdot\cfrac{D}{1000}$$
$h_l=h_{l-50}\cdot\cfrac{D}{1000}$
Equations in LaTeX code
h_l=h_{l-50}\cdot\cfrac{D}{1000}
Valve position
Coefficient of under-pressure for $ \cfrac{h_l}{D}=0 $
Coefficient of under-pressure for $ \cfrac{h_l}{D}=2 $
Coefficient of under-pressure for $ \cfrac{h_l}{D}=2.5 $
Coefficient of under-pressure for $ \cfrac{h_l}{D}=3 $
Coefficient of under-pressure for $ \cfrac{h_l}{D}=3.5 $
$S/D$ $K_{Pu-0}$ $K_{Pu-2}$ $K_{Pu-2.5}$ $K_{Pu-3}$ $K_{Pu-3.5}$
$\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$
No data
Valve position Coefficient of under-pressure for $ \cfrac{h_l}{D}=0 $ Coefficient of under-pressure for $ \cfrac{h_l}{D}=2 $ Coefficient of under-pressure for $ \cfrac{h_l}{D}=2.5 $ Coefficient of under-pressure for $ \cfrac{h_l}{D}=3 $ Coefficient of under-pressure for $ \cfrac{h_l}{D}=3.5 $
$S/D$ $K_{Pu-0}$ $K_{Pu-2}$ $K_{Pu-2.5}$ $K_{Pu-3}$ $K_{Pu-3.5}$
$\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$
No data
Unrounded data
Valve position;Coefficient of under-pressure for $ \cfrac{h_l}{D}=0 $ ;Coefficient of under-pressure for $ \cfrac{h_l}{D}=2 $ ;Coefficient of under-pressure for $ \cfrac{h_l}{D}=2.5 $ ;Coefficient of under-pressure for $ \cfrac{h_l}{D}=3 $ ;Coefficient of under-pressure for $ \cfrac{h_l}{D}=3.5 $ ;
S/D;K_{Pu-0};K_{Pu-2};K_{Pu-2.5};K_{Pu-3};K_{Pu-3.5};
; ; ; ; ; ;

$K_{Pu-0} \mathrm{[-]}$
$K_{Pu-2} \mathrm{[-]}$
$K_{Pu-2.5} \mathrm{[-]}$
$K_{Pu-3} \mathrm{[-]}$
$K_{Pu-3.5} \mathrm{[-]}$
No data
$S/D\mathrm{[-]}$
Coefficient of under-pressure for $ \cfrac{h_l}{D}=0\ \text{to}\ 3.5 $

Valve position Coefficient of under-pressure for $ \cfrac{h_l}{D}=0 $ Coefficient of under-pressure for $ \cfrac{h_l}{D}=2 $ Coefficient of under-pressure for $ \cfrac{h_l}{D}=2.5 $ Coefficient of under-pressure for $ \cfrac{h_l}{D}=3 $ Coefficient of under-pressure for $ \cfrac{h_l}{D}=3.5 $
$S/D$ $K_{Pu-0}$ $K_{Pu-2}$ $K_{Pu-2.5}$ $K_{Pu-3}$ $K_{Pu-3.5}$
$\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$
No data
Unrounded data
Valve position; Coefficient of under-pressure for $ \cfrac{h_l}{D}=0 $ ; Coefficient of under-pressure for $ \cfrac{h_l}{D}=2 $ ; Coefficient of under-pressure for $ \cfrac{h_l}{D}=2.5 $ ; Coefficient of under-pressure for $ \cfrac{h_l}{D}=3 $ ; Coefficient of under-pressure for $ \cfrac{h_l}{D}=3.5 $ ;
S/D; K_{Pu-0}; K_{Pu-2}; K_{Pu-2.5}; K_{Pu-3}; K_{Pu-3.5};
; ; ; ; ; ;
Valve position
Coefficient of under-pressure for $ \cfrac{h_l}{D}=3.6 $
Coefficient of under-pressure for $ \cfrac{h_l}{D}=3.9 $
Coefficient of under-pressure for $ \cfrac{h_l}{D}=4 $
Coefficient of under-pressure for $ \cfrac{h_l}{D}=4.2 $
Coefficient of under-pressure for $ \cfrac{h_l}{D}=4.5 $
Coefficient of under-pressure for $ \cfrac{h_l}{D}=5 $
$S/D$ $K_{Pu-3.6}$ $K_{Pu-3.9}$ $K_{Pu-4}$ $K_{Pu-4.2}$ $K_{Pu-4.5}$ $K_{Pu-5}$
$\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$
No data
Valve position Coefficient of under-pressure for $ \cfrac{h_l}{D}=3.6 $ Coefficient of under-pressure for $ \cfrac{h_l}{D}=3.9 $ Coefficient of under-pressure for $ \cfrac{h_l}{D}=4 $ Coefficient of under-pressure for $ \cfrac{h_l}{D}=4.2 $ Coefficient of under-pressure for $ \cfrac{h_l}{D}=4.5 $ Coefficient of under-pressure for $ \cfrac{h_l}{D}=5 $
$S/D$ $K_{Pu-3.6}$ $K_{Pu-3.9}$ $K_{Pu-4}$ $K_{Pu-4.2}$ $K_{Pu-4.5}$ $K_{Pu-5}$
$\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$
No data
Unrounded data
Valve position;Coefficient of under-pressure for $ \cfrac{h_l}{D}=3.6 $ ;Coefficient of under-pressure for $ \cfrac{h_l}{D}=3.9 $ ;Coefficient of under-pressure for $ \cfrac{h_l}{D}=4 $ ;Coefficient of under-pressure for $ \cfrac{h_l}{D}=4.2 $ ;Coefficient of under-pressure for $ \cfrac{h_l}{D}=4.5 $ ;Coefficient of under-pressure for $ \cfrac{h_l}{D}=5 $ ;
S/D;K_{Pu-3.6};K_{Pu-3.9};K_{Pu-4};K_{Pu-4.2};K_{Pu-4.5};K_{Pu-5};
; ; ; ; ; ; ;

$K_{Pu-3.6} \mathrm{[-]}$
$K_{Pu-3.9} \mathrm{[-]}$
$K_{Pu-4} \mathrm{[-]}$
$K_{Pu-4.2} \mathrm{[-]}$
$K_{Pu-4.5} \mathrm{[-]}$
$K_{Pu-5} \mathrm{[-]}$
No data
$S/D\mathrm{[-]}$
Coefficient of under-pressure for $ \cfrac{h_l}{D}=3.6\ \text{to}\ 5 $

Valve position Coefficient of under-pressure for $ \cfrac{h_l}{D}=3.6 $ Coefficient of under-pressure for $ \cfrac{h_l}{D}=3.9 $ Coefficient of under-pressure for $ \cfrac{h_l}{D}=4 $ Coefficient of under-pressure for $ \cfrac{h_l}{D}=4.2 $ Coefficient of under-pressure for $ \cfrac{h_l}{D}=4.5 $ Coefficient of under-pressure for $ \cfrac{h_l}{D}=5 $
$S/D$ $K_{Pu-3.6}$ $K_{Pu-3.9}$ $K_{Pu-4}$ $K_{Pu-4.2}$ $K_{Pu-4.5}$ $K_{Pu-5}$
$\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$
No data
Unrounded data
Valve position; Coefficient of under-pressure for $ \cfrac{h_l}{D}=3.6 $ ; Coefficient of under-pressure for $ \cfrac{h_l}{D}=3.9 $ ; Coefficient of under-pressure for $ \cfrac{h_l}{D}=4 $ ; Coefficient of under-pressure for $ \cfrac{h_l}{D}=4.2 $ ; Coefficient of under-pressure for $ \cfrac{h_l}{D}=4.5 $ ; Coefficient of under-pressure for $ \cfrac{h_l}{D}=5 $ ;
S/D; K_{Pu-3.6}; K_{Pu-3.9}; K_{Pu-4}; K_{Pu-4.2}; K_{Pu-4.5}; K_{Pu-5};
; ; ; ; ; ; ;
Valve position
Coefficient of under-pressure
Under-pressure behind the valve
Loss of pressure on the valve
Pressure on the valve
Cavitation number
$S/D$ $K_{Pu}$ $P_{u}$ $H_L$ $H_v$ $σ$
$\mathrm{ }$ $\mathrm{ }$ $\mathrm{m}$ $\mathrm{m}$ $\mathrm{m}$ $\mathrm{ }$
No data
Valve position Coefficient of under-pressure Under-pressure behind the valve Loss of pressure on the valve Pressure on the valve Cavitation number
$S/D$ $K_{Pu}$ $P_{u}$ $H_L$ $H_v$ $σ$
$\mathrm{ }$ $\mathrm{ }$ $\mathrm{m}$ $\mathrm{m}$ $\mathrm{m}$ $\mathrm{ }$
No data
Unrounded data
Valve position;Coefficient of under-pressure;Under-pressure behind the valve;Loss of pressure on the valve;Pressure on the valve;Cavitation number;
S/D;K_{Pu};P_{u};H_L;H_v;σ;
; ;m;m;m; ;

$K_{Pu} \mathrm{[-]}$
No data
$S/D\mathrm{[-]}$
Coefficient of under-pressure

Valve position Coefficient of under-pressure
$S/D$ $K_{Pu}$
$\mathrm{ }$ $\mathrm{ }$
No data
Unrounded data
Valve position; Coefficient of under-pressure;
S/D; K_{Pu};
; ;
$\text{if }\ \cfrac{h_l\cdot 10^3}{D}\le 0$
$\text{if }\ \cfrac{h_l\cdot 10^3}{D}\le 0$
Equations in LaTeX code
\text{if }\ \cfrac{h_l\cdot 10^3}{D}\le 0
$$K_{Pu}=K_{Pu-0}$$
$K_{Pu}=K_{Pu-0}$
Equations in LaTeX code
K_{Pu}=K_{Pu-0}
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 2$
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 2$
Equations in LaTeX code
\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 2
$$K_{Pu}=K_{Pu-2}$$
$K_{Pu}=K_{Pu-2}$
Equations in LaTeX code
K_{Pu}=K_{Pu-2}
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 2.5$
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 2.5$
Equations in LaTeX code
\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 2.5
$$K_{Pu}=K_{Pu-2.5}$$
$K_{Pu}=K_{Pu-2.5}$
Equations in LaTeX code
K_{Pu}=K_{Pu-2.5}
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3$
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3$
Equations in LaTeX code
\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3
$$K_{Pu}=K_{Pu-3}$$
$K_{Pu}=K_{Pu-3}$
Equations in LaTeX code
K_{Pu}=K_{Pu-3}
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3.5$
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3.5$
Equations in LaTeX code
\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3.5
$$K_{Pu}=K_{Pu-3.5}$$
$K_{Pu}=K_{Pu-3.5}$
Equations in LaTeX code
K_{Pu}=K_{Pu-3.5}
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3.6$
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3.6$
Equations in LaTeX code
\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3.6
$$K_{Pu}=K_{Pu-3.6}$$
$K_{Pu}=K_{Pu-3.6}$
Equations in LaTeX code
K_{Pu}=K_{Pu-3.6}
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3.9$
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3.9$
Equations in LaTeX code
\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3.9
$$K_{Pu}=K_{Pu-3.9}$$
$K_{Pu}=K_{Pu-3.9}$
Equations in LaTeX code
K_{Pu}=K_{Pu-3.9}
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 4$
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 4$
Equations in LaTeX code
\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 4
$$K_{Pu}=K_{Pu-4}$$
$K_{Pu}=K_{Pu-4}$
Equations in LaTeX code
K_{Pu}=K_{Pu-4}
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 4.2$
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 4.2$
Equations in LaTeX code
\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 4.2
$$K_{Pu}=K_{Pu-4.2}$$
$K_{Pu}=K_{Pu-4.2}$
Equations in LaTeX code
K_{Pu}=K_{Pu-4.2}
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 4.5$
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 4.5$
Equations in LaTeX code
\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 4.5
$$K_{Pu}=K_{Pu-4.5}$$
$K_{Pu}=K_{Pu-4.5}$
Equations in LaTeX code
K_{Pu}=K_{Pu-4.5}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$K_{Pu}=K_{Pu-5}$$
$K_{Pu}=K_{Pu-5}$
Equations in LaTeX code
K_{Pu}=K_{Pu-5}

$P_{u} \mathrm{[m]}$
No data
$S/D\mathrm{[-]}$
Under-pressure behind the valve

Valve position Under-pressure behind the valve
$S/D$ $P_{u}$
$\mathrm{ }$ $\mathrm{m}$
No data
Unrounded data
Valve position; Under-pressure behind the valve;
S/D; P_{u};
; m;
$$P_{u}=\max\left(K_{Pu}\cdot H_v, -\cfrac{p_{air}}{ρ\cdot g}\right)$$
$P_{u}=\max\left(K_{Pu}\cdot H_v, -\cfrac{p_{air}}{ρ\cdot g}\right)$
Equations in LaTeX code
P_{u}=\max\left(K_{Pu}\cdot H_v, -\cfrac{p_{air}}{ρ\cdot g}\right)

$H_L \mathrm{[m]}$
$H_v \mathrm{[m]}$
No data
$S/D\mathrm{[-]}$
Loss of height on valve and pressure height on Howell-Bunger valve

Valve position Loss of pressure on the valve Pressure on the valve
$S/D$ $H_L$ $H_v$
$\mathrm{ }$ $\mathrm{m}$ $\mathrm{m}$
No data
Unrounded data
Valve position; Loss of pressure on the valve; Pressure on the valve;
S/D; 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
$$H_v=H-P_{u}+\cfrac{v^2}{2\cdot g}-\cfrac{v^2}{2\cdot g}\cdot Σζ+\left(1-Q_p\right)\cdot ΔP$$
$H_v=H-P_{u}+\cfrac{v^2}{2\cdot g}-\cfrac{v^2}{2\cdot g}\cdot Σζ+\left(1-Q_p\right)\cdot ΔP$
Equations in LaTeX code
H_v=H-P_{u}+\cfrac{v^2}{2\cdot g}-\cfrac{v^2}{2\cdot g}\cdot Σζ+\left(1-Q_p\right)\cdot ΔP

$σ \mathrm{[-]}$
No data
$S/D\mathrm{[-]}$
Cavitation number

Valve position Cavitation number
$S/D$ $σ$
$\mathrm{ }$ $\mathrm{ }$
No data
Unrounded data
Valve position; Cavitation number;
S/D; 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}
Valve position
Coefficient of lenght $ L_1 $ for $ \cfrac{T_x}{D}=10 $
Coefficient of lenght $ L_1 $ for $ \cfrac{T_x}{D}=20 $
Coefficient of lenght $ L_1 $ for $ \cfrac{T_x}{D}=30 $
Coefficient of lenght $ L_1 $ for $ \cfrac{T_x}{D}=40 $
Lenght $ L_1 $
$S/D$ $L_{1-10}$ $L_{1-20}$ $L_{1-30}$ $L_{1-40}$ $L_1$
$\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{m}$
No data
Valve position Coefficient of lenght $ L_1 $ for $ \cfrac{T_x}{D}=10 $ Coefficient of lenght $ L_1 $ for $ \cfrac{T_x}{D}=20 $ Coefficient of lenght $ L_1 $ for $ \cfrac{T_x}{D}=30 $ Coefficient of lenght $ L_1 $ for $ \cfrac{T_x}{D}=40 $ Lenght $ L_1 $
$S/D$ $L_{1-10}$ $L_{1-20}$ $L_{1-30}$ $L_{1-40}$ $L_1$
$\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{m}$
No data
Unrounded data
Valve position;Coefficient of lenght $ L_1 $ for $ \cfrac{T_x}{D}=10 $ ;Coefficient of lenght $ L_1 $ for $ \cfrac{T_x}{D}=20 $ ;Coefficient of lenght $ L_1 $ for $ \cfrac{T_x}{D}=30 $ ;Coefficient of lenght $ L_1 $ for $ \cfrac{T_x}{D}=40 $ ;Lenght $ L_1 $ ;
S/D;L_{1-10};L_{1-20};L_{1-30};L_{1-40};L_1;
; ; ; ; ;m;

$L_{1-10} \mathrm{[-]}$
$L_{1-20} \mathrm{[-]}$
$L_{1-30} \mathrm{[-]}$
$L_{1-40} \mathrm{[-]}$
No data
$S/D\mathrm{[-]}$
Coefficient of lenght $ L_1 $

Valve position Coefficient of lenght $ L_1 $ for $ \cfrac{T_x}{D}=10 $ Coefficient of lenght $ L_1 $ for $ \cfrac{T_x}{D}=20 $ Coefficient of lenght $ L_1 $ for $ \cfrac{T_x}{D}=30 $ Coefficient of lenght $ L_1 $ for $ \cfrac{T_x}{D}=40 $
$S/D$ $L_{1-10}$ $L_{1-20}$ $L_{1-30}$ $L_{1-40}$
$\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$
No data
Unrounded data
Valve position; Coefficient of lenght $ L_1 $ for $ \cfrac{T_x}{D}=10 $ ; Coefficient of lenght $ L_1 $ for $ \cfrac{T_x}{D}=20 $ ; Coefficient of lenght $ L_1 $ for $ \cfrac{T_x}{D}=30 $ ; Coefficient of lenght $ L_1 $ for $ \cfrac{T_x}{D}=40 $ ;
S/D; L_{1-10}; L_{1-20}; L_{1-30}; L_{1-40};
; ; ; ; ;

$L_1 \mathrm{[m]}$
No data
$S/D\mathrm{[-]}$
Lenght $ L_1 $

Valve position Lenght $ L_1 $
$S/D$ $L_1$
$\mathrm{ }$ $\mathrm{m}$
No data
Unrounded data
Valve position; Lenght $ L_1 $ ;
S/D; L_1;
; m;
$\text{if }\ \cfrac{T_x\cdot 10^3}{D}< 10$
$\text{if }\ \cfrac{T_x\cdot 10^3}{D}< 10$
Equations in LaTeX code
\text{if }\ \cfrac{T_x\cdot 10^3}{D}< 10
$$L_1=L_{1-10}\cdot\cfrac{D}{1000}$$
$L_1=L_{1-10}\cdot\cfrac{D}{1000}$
Equations in LaTeX code
L_1=L_{1-10}\cdot\cfrac{D}{1000}
$\text{else if }\ \cfrac{T_x\cdot 10^3}{D}< 20$
$\text{else if }\ \cfrac{T_x\cdot 10^3}{D}< 20$
Equations in LaTeX code
\text{else if }\ \cfrac{T_x\cdot 10^3}{D}< 20
$$L_1=L_{1-20}\cdot\cfrac{D}{1000}$$
$L_1=L_{1-20}\cdot\cfrac{D}{1000}$
Equations in LaTeX code
L_1=L_{1-20}\cdot\cfrac{D}{1000}
$\text{else if }\ \cfrac{T_x\cdot 10^3}{D}< 30$
$\text{else if }\ \cfrac{T_x\cdot 10^3}{D}< 30$
Equations in LaTeX code
\text{else if }\ \cfrac{T_x\cdot 10^3}{D}< 30
$$L_1=L_{1-30}\cdot\cfrac{D}{1000}$$
$L_1=L_{1-30}\cdot\cfrac{D}{1000}$
Equations in LaTeX code
L_1=L_{1-30}\cdot\cfrac{D}{1000}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$L_1=L_{1-40}\cdot\cfrac{D}{1000}$$
$L_1=L_{1-40}\cdot\cfrac{D}{1000}$
Equations in LaTeX code
L_1=L_{1-40}\cdot\cfrac{D}{1000}
Valve position
Coefficient of lenght $ L_2 $ for $ \cfrac{T_x}{D}=10 $
Coefficient of lenght $ L_2 $ for $ \cfrac{T_x}{D}=20 $
Coefficient of lenght $ L_2 $ for $ \cfrac{T_x}{D}=30 $
Coefficient of lenght $ L_2 $ for $ \cfrac{T_x}{D}=40 $
Coefficient of lenght $ L_2 $ for $ \cfrac{T_x}{D}=50 $
Lenght $ L_2 $
$S/D$ $L_{2-10}$ $L_{2-20}$ $L_{2-30}$ $L_{2-40}$ $L_{2-50}$ $L_2$
$\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{m}$
No data
Valve position Coefficient of lenght $ L_2 $ for $ \cfrac{T_x}{D}=10 $ Coefficient of lenght $ L_2 $ for $ \cfrac{T_x}{D}=20 $ Coefficient of lenght $ L_2 $ for $ \cfrac{T_x}{D}=30 $ Coefficient of lenght $ L_2 $ for $ \cfrac{T_x}{D}=40 $ Coefficient of lenght $ L_2 $ for $ \cfrac{T_x}{D}=50 $ Lenght $ L_2 $
$S/D$ $L_{2-10}$ $L_{2-20}$ $L_{2-30}$ $L_{2-40}$ $L_{2-50}$ $L_2$
$\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{m}$
No data
Unrounded data
Valve position;Coefficient of lenght $ L_2 $ for $ \cfrac{T_x}{D}=10 $ ;Coefficient of lenght $ L_2 $ for $ \cfrac{T_x}{D}=20 $ ;Coefficient of lenght $ L_2 $ for $ \cfrac{T_x}{D}=30 $ ;Coefficient of lenght $ L_2 $ for $ \cfrac{T_x}{D}=40 $ ;Coefficient of lenght $ L_2 $ for $ \cfrac{T_x}{D}=50 $ ;Lenght $ L_2 $ ;
S/D;L_{2-10};L_{2-20};L_{2-30};L_{2-40};L_{2-50};L_2;
; ; ; ; ; ;m;

$L_{2-10} \mathrm{[-]}$
$L_{2-20} \mathrm{[-]}$
$L_{2-30} \mathrm{[-]}$
$L_{2-40} \mathrm{[-]}$
$L_{2-50} \mathrm{[-]}$
No data
$S/D\mathrm{[-]}$
Coefficient of lenght $ L_2 $

Valve position Coefficient of lenght $ L_2 $ for $ \cfrac{T_x}{D}=10 $ Coefficient of lenght $ L_2 $ for $ \cfrac{T_x}{D}=20 $ Coefficient of lenght $ L_2 $ for $ \cfrac{T_x}{D}=30 $ Coefficient of lenght $ L_2 $ for $ \cfrac{T_x}{D}=40 $ Coefficient of lenght $ L_2 $ for $ \cfrac{T_x}{D}=50 $
$S/D$ $L_{2-10}$ $L_{2-20}$ $L_{2-30}$ $L_{2-40}$ $L_{2-50}$
$\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$
No data
Unrounded data
Valve position; Coefficient of lenght $ L_2 $ for $ \cfrac{T_x}{D}=10 $ ; Coefficient of lenght $ L_2 $ for $ \cfrac{T_x}{D}=20 $ ; Coefficient of lenght $ L_2 $ for $ \cfrac{T_x}{D}=30 $ ; Coefficient of lenght $ L_2 $ for $ \cfrac{T_x}{D}=40 $ ; Coefficient of lenght $ L_2 $ for $ \cfrac{T_x}{D}=50 $ ;
S/D; L_{2-10}; L_{2-20}; L_{2-30}; L_{2-40}; L_{2-50};
; ; ; ; ; ;

$L_2 \mathrm{[m]}$
No data
$S/D\mathrm{[-]}$
Lenght $ L_2 $

Valve position Lenght $ L_2 $
$S/D$ $L_2$
$\mathrm{ }$ $\mathrm{m}$
No data
Unrounded data
Valve position; Lenght $ L_2 $ ;
S/D; L_2;
; m;
$\text{if }\ \cfrac{T_x\cdot 10^3}{D}< 10$
$\text{if }\ \cfrac{T_x\cdot 10^3}{D}< 10$
Equations in LaTeX code
\text{if }\ \cfrac{T_x\cdot 10^3}{D}< 10
$$L_2=L_{2-10}\cdot\cfrac{D}{1000}$$
$L_2=L_{2-10}\cdot\cfrac{D}{1000}$
Equations in LaTeX code
L_2=L_{2-10}\cdot\cfrac{D}{1000}
$\text{else if }\ \cfrac{T_x\cdot 10^3}{D}< 20$
$\text{else if }\ \cfrac{T_x\cdot 10^3}{D}< 20$
Equations in LaTeX code
\text{else if }\ \cfrac{T_x\cdot 10^3}{D}< 20
$$L_2=L_{2-20}\cdot\cfrac{D}{1000}$$
$L_2=L_{2-20}\cdot\cfrac{D}{1000}$
Equations in LaTeX code
L_2=L_{2-20}\cdot\cfrac{D}{1000}
$\text{else if }\ \cfrac{T_x\cdot 10^3}{D}< 30$
$\text{else if }\ \cfrac{T_x\cdot 10^3}{D}< 30$
Equations in LaTeX code
\text{else if }\ \cfrac{T_x\cdot 10^3}{D}< 30
$$L_2=L_{2-30}\cdot\cfrac{D}{1000}$$
$L_2=L_{2-30}\cdot\cfrac{D}{1000}$
Equations in LaTeX code
L_2=L_{2-30}\cdot\cfrac{D}{1000}
$\text{else if }\ \cfrac{T_x\cdot 10^3}{D}< 40$
$\text{else if }\ \cfrac{T_x\cdot 10^3}{D}< 40$
Equations in LaTeX code
\text{else if }\ \cfrac{T_x\cdot 10^3}{D}< 40
$$L_2=L_{2-40}\cdot\cfrac{D}{1000}$$
$L_2=L_{2-40}\cdot\cfrac{D}{1000}$
Equations in LaTeX code
L_2=L_{2-40}\cdot\cfrac{D}{1000}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$L_2=L_{2-50}\cdot\cfrac{D}{1000}$$
$L_2=L_{2-50}\cdot\cfrac{D}{1000}$
Equations in LaTeX code
L_2=L_{2-50}\cdot\cfrac{D}{1000}
Valve position
Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=0 $
Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=2 $
Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=2.5 $
Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=3 $
Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=3.5 $
$S/D$ $K_{Pu-air1-0}$ $K_{Pu-air1-2}$ $K_{Pu-air1-2.5}$ $K_{Pu-air1-3}$ $K_{Pu-air1-3.5}$
$\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$
No data
Valve position Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=0 $ Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=2 $ Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=2.5 $ Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=3 $ Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=3.5 $
$S/D$ $K_{Pu-air1-0}$ $K_{Pu-air1-2}$ $K_{Pu-air1-2.5}$ $K_{Pu-air1-3}$ $K_{Pu-air1-3.5}$
$\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$
No data
Unrounded data
Valve position;Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=0 $ ;Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=2 $ ;Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=2.5 $ ;Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=3 $ ;Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=3.5 $ ;
S/D;K_{Pu-air1-0};K_{Pu-air1-2};K_{Pu-air1-2.5};K_{Pu-air1-3};K_{Pu-air1-3.5};
; ; ; ; ; ;

$K_{Pu-air1-0} \mathrm{[-]}$
$K_{Pu-air1-2} \mathrm{[-]}$
$K_{Pu-air1-2.5} \mathrm{[-]}$
$K_{Pu-air1-3} \mathrm{[-]}$
$K_{Pu-air1-3.5} \mathrm{[-]}$
No data
$S/D\mathrm{[-]}$
Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=0\ \text{to}\ 3.5 $

Valve position Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=0 $ Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=2 $ Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=2.5 $ Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=3 $ Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=3.5 $
$S/D$ $K_{Pu-air1-0}$ $K_{Pu-air1-2}$ $K_{Pu-air1-2.5}$ $K_{Pu-air1-3}$ $K_{Pu-air1-3.5}$
$\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$
No data
Unrounded data
Valve position; Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=0 $ ; Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=2 $ ; Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=2.5 $ ; Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=3 $ ; Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=3.5 $ ;
S/D; K_{Pu-air1-0}; K_{Pu-air1-2}; K_{Pu-air1-2.5}; K_{Pu-air1-3}; K_{Pu-air1-3.5};
; ; ; ; ; ;
Valve position
Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=3.6 $
Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=3.9 $
Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=4 $
Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=4.2 $
Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=4.5 $
Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=5 $
$S/D$ $K_{Pu-air1-3.6}$ $K_{Pu-air1-3.9}$ $K_{Pu-air1-4}$ $K_{Pu-air1-4.2}$ $K_{Pu-air1-4.5}$ $K_{Pu-air1-5}$
$\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$
No data
Valve position Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=3.6 $ Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=3.9 $ Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=4 $ Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=4.2 $ Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=4.5 $ Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=5 $
$S/D$ $K_{Pu-air1-3.6}$ $K_{Pu-air1-3.9}$ $K_{Pu-air1-4}$ $K_{Pu-air1-4.2}$ $K_{Pu-air1-4.5}$ $K_{Pu-air1-5}$
$\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$
No data
Unrounded data
Valve position;Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=3.6 $ ;Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=3.9 $ ;Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=4 $ ;Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=4.2 $ ;Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=4.5 $ ;Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=5 $ ;
S/D;K_{Pu-air1-3.6};K_{Pu-air1-3.9};K_{Pu-air1-4};K_{Pu-air1-4.2};K_{Pu-air1-4.5};K_{Pu-air1-5};
; ; ; ; ; ; ;

$K_{Pu-air1-3.6} \mathrm{[-]}$
$K_{Pu-air1-3.9} \mathrm{[-]}$
$K_{Pu-air1-4} \mathrm{[-]}$
$K_{Pu-air1-4.2} \mathrm{[-]}$
$K_{Pu-air1-4.5} \mathrm{[-]}$
$K_{Pu-air1-5} \mathrm{[-]}$
No data
$S/D\mathrm{[-]}$
Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=3.6\ \text{to}\ 5 $

Valve position Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=3.6 $ Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=3.9 $ Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=4 $ Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=4.2 $ Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=4.5 $ Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=5 $
$S/D$ $K_{Pu-air1-3.6}$ $K_{Pu-air1-3.9}$ $K_{Pu-air1-4}$ $K_{Pu-air1-4.2}$ $K_{Pu-air1-4.5}$ $K_{Pu-air1-5}$
$\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$
No data
Unrounded data
Valve position; Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=3.6 $ ; Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=3.9 $ ; Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=4 $ ; Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=4.2 $ ; Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=4.5 $ ; Under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=5 $ ;
S/D; K_{Pu-air1-3.6}; K_{Pu-air1-3.9}; K_{Pu-air1-4}; K_{Pu-air1-4.2}; K_{Pu-air1-4.5}; K_{Pu-air1-5};
; ; ; ; ; ; ;
Valve position
Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=0 $
Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=2 $
Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=2.5 $
Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=3 $
Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=3.5 $
$S/D$ $K_{Pu-air2-0}$ $K_{Pu-air2-2}$ $K_{Pu-air2-2.5}$ $K_{Pu-air2-3}$ $K_{Pu-air2-3.5}$
$\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$
No data
Valve position Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=0 $ Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=2 $ Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=2.5 $ Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=3 $ Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=3.5 $
$S/D$ $K_{Pu-air2-0}$ $K_{Pu-air2-2}$ $K_{Pu-air2-2.5}$ $K_{Pu-air2-3}$ $K_{Pu-air2-3.5}$
$\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$
No data
Unrounded data
Valve position;Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=0 $ ;Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=2 $ ;Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=2.5 $ ;Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=3 $ ;Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=3.5 $ ;
S/D;K_{Pu-air2-0};K_{Pu-air2-2};K_{Pu-air2-2.5};K_{Pu-air2-3};K_{Pu-air2-3.5};
; ; ; ; ; ;

$K_{Pu-air2-0} \mathrm{[-]}$
$K_{Pu-air2-2} \mathrm{[-]}$
$K_{Pu-air2-2.5} \mathrm{[-]}$
$K_{Pu-air2-3} \mathrm{[-]}$
$K_{Pu-air2-3.5} \mathrm{[-]}$
No data
$S/D\mathrm{[-]}$
Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=0\ \text{to}\ 3.5 $

Valve position Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=0 $ Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=2 $ Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=2.5 $ Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=3 $ Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=3.5 $
$S/D$ $K_{Pu-air2-0}$ $K_{Pu-air2-2}$ $K_{Pu-air2-2.5}$ $K_{Pu-air2-3}$ $K_{Pu-air2-3.5}$
$\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$
No data
Unrounded data
Valve position; Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=0 $ ; Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=2 $ ; Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=2.5 $ ; Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=3 $ ; Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=3.5 $ ;
S/D; K_{Pu-air2-0}; K_{Pu-air2-2}; K_{Pu-air2-2.5}; K_{Pu-air2-3}; K_{Pu-air2-3.5};
; ; ; ; ; ;
Valve position
Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=3.6 $
Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=3.9 $
Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=4 $
Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=4.2 $
Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=4.5 $
Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=5 $
$S/D$ $K_{Pu-air2-3.6}$ $K_{Pu-air2-3.9}$ $K_{Pu-air2-4}$ $K_{Pu-air2-4.2}$ $K_{Pu-air2-4.5}$ $K_{Pu-air2-5}$
$\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$
No data
Valve position Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=3.6 $ Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=3.9 $ Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=4 $ Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=4.2 $ Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=4.5 $ Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=5 $
$S/D$ $K_{Pu-air2-3.6}$ $K_{Pu-air2-3.9}$ $K_{Pu-air2-4}$ $K_{Pu-air2-4.2}$ $K_{Pu-air2-4.5}$ $K_{Pu-air2-5}$
$\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$
No data
Unrounded data
Valve position;Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=3.6 $ ;Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=3.9 $ ;Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=4 $ ;Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=4.2 $ ;Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=4.5 $ ;Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=5 $ ;
S/D;K_{Pu-air2-3.6};K_{Pu-air2-3.9};K_{Pu-air2-4};K_{Pu-air2-4.2};K_{Pu-air2-4.5};K_{Pu-air2-5};
; ; ; ; ; ; ;

$K_{Pu-air2-3.6} \mathrm{[-]}$
$K_{Pu-air2-3.9} \mathrm{[-]}$
$K_{Pu-air2-4} \mathrm{[-]}$
$K_{Pu-air2-4.2} \mathrm{[-]}$
$K_{Pu-air2-4.5} \mathrm{[-]}$
$K_{Pu-air2-5} \mathrm{[-]}$
No data
$S/D\mathrm{[-]}$
Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=3.6\ \text{to}\ 5 $

Valve position Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=3.6 $ Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=3.9 $ Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=4 $ Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=4.2 $ Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=4.5 $ Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=5 $
$S/D$ $K_{Pu-air2-3.6}$ $K_{Pu-air2-3.9}$ $K_{Pu-air2-4}$ $K_{Pu-air2-4.2}$ $K_{Pu-air2-4.5}$ $K_{Pu-air2-5}$
$\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{ }$
No data
Unrounded data
Valve position; Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=3.6 $ ; Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=3.9 $ ; Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=4 $ ; Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=4.2 $ ; Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=4.5 $ ; Under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=5 $ ;
S/D; K_{Pu-air2-3.6}; K_{Pu-air2-3.9}; K_{Pu-air2-4}; K_{Pu-air2-4.2}; K_{Pu-air2-4.5}; K_{Pu-air2-5};
; ; ; ; ; ; ;
Valve position
The force at the valve axis x
Under-pressure coefficient in hole 1
Under-pressure coefficient in hole 2
Under-pressure in hole 1
Under-pressure in hole 2
$S/D$ $F_{bx}$ $K_{Pu-air1}$ $K_{Pu-air2}$ $P_{u-air1}$ $P_{u-air2}$
$\mathrm{ }$ $\mathrm{kN}$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{m}$ $\mathrm{m}$
No data
Valve position The force at the valve axis x Under-pressure coefficient in hole 1 Under-pressure coefficient in hole 2 Under-pressure in hole 1 Under-pressure in hole 2
$S/D$ $F_{bx}$ $K_{Pu-air1}$ $K_{Pu-air2}$ $P_{u-air1}$ $P_{u-air2}$
$\mathrm{ }$ $\mathrm{kN}$ $\mathrm{ }$ $\mathrm{ }$ $\mathrm{m}$ $\mathrm{m}$
No data
Unrounded data
Valve position;The force at the valve axis x;Under-pressure coefficient in hole 1;Under-pressure coefficient in hole 2;Under-pressure in hole 1;Under-pressure in hole 2;
S/D;F_{bx};K_{Pu-air1};K_{Pu-air2};P_{u-air1};P_{u-air2};
;kN; ; ;m;m;

$F_{bx} \mathrm{[kN]}$
No data
$S/D\mathrm{[-]}$
The force at the valve axis x

Valve position The force at the valve axis x
$S/D$ $F_{bx}$
$\mathrm{ }$ $\mathrm{kN}$
No data
Unrounded data
Valve position; The force at the valve axis x;
S/D; F_{bx};
; kN;
$$F_{bx}=\cfrac{π\cdot D^2}{4\cdot 10^9}\cdot ρ\cdot g\cdot H_v\cdot K_{bx}$$
$F_{bx}=\cfrac{π\cdot D^2}{4\cdot 10^9}\cdot ρ\cdot g\cdot H_v\cdot K_{bx}$
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}

$K_{Pu-air1} \mathrm{[-]}$
No data
$S/D\mathrm{[-]}$
Under-pressure coefficient in hole 1

Valve position Under-pressure coefficient in hole 1
$S/D$ $K_{Pu-air1}$
$\mathrm{ }$ $\mathrm{ }$
No data
Unrounded data
Valve position; Under-pressure coefficient in hole 1;
S/D; K_{Pu-air1};
; ;
$\text{if }\ \cfrac{h_l\cdot 10^3}{D}\le 0$
$\text{if }\ \cfrac{h_l\cdot 10^3}{D}\le 0$
Equations in LaTeX code
\text{if }\ \cfrac{h_l\cdot 10^3}{D}\le 0
$$K_{Pu-air1}=K_{Pu-air1-0}$$
$K_{Pu-air1}=K_{Pu-air1-0}$
Equations in LaTeX code
K_{Pu-air1}=K_{Pu-air1-0}
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 2$
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 2$
Equations in LaTeX code
\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 2
$$K_{Pu-air1}=K_{Pu-air1-2}$$
$K_{Pu-air1}=K_{Pu-air1-2}$
Equations in LaTeX code
K_{Pu-air1}=K_{Pu-air1-2}
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 2.5$
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 2.5$
Equations in LaTeX code
\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 2.5
$$K_{Pu-air1}=K_{Pu-air1-2.5}$$
$K_{Pu-air1}=K_{Pu-air1-2.5}$
Equations in LaTeX code
K_{Pu-air1}=K_{Pu-air1-2.5}
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3$
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3$
Equations in LaTeX code
\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3
$$K_{Pu-air1}=K_{Pu-air1-3}$$
$K_{Pu-air1}=K_{Pu-air1-3}$
Equations in LaTeX code
K_{Pu-air1}=K_{Pu-air1-3}
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3.5$
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3.5$
Equations in LaTeX code
\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3.5
$$K_{Pu-air1}=K_{Pu-air1-3.5}$$
$K_{Pu-air1}=K_{Pu-air1-3.5}$
Equations in LaTeX code
K_{Pu-air1}=K_{Pu-air1-3.5}
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3.6$
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3.6$
Equations in LaTeX code
\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3.6
$$K_{Pu-air1}=K_{Pu-air1-3.6}$$
$K_{Pu-air1}=K_{Pu-air1-3.6}$
Equations in LaTeX code
K_{Pu-air1}=K_{Pu-air1-3.6}
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3.9$
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3.9$
Equations in LaTeX code
\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3.9
$$K_{Pu-air1}=K_{Pu-air1-3.9}$$
$K_{Pu-air1}=K_{Pu-air1-3.9}$
Equations in LaTeX code
K_{Pu-air1}=K_{Pu-air1-3.9}
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 4$
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 4$
Equations in LaTeX code
\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 4
$$K_{Pu-air1}=K_{Pu-air1-4}$$
$K_{Pu-air1}=K_{Pu-air1-4}$
Equations in LaTeX code
K_{Pu-air1}=K_{Pu-air1-4}
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 4.2$
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 4.2$
Equations in LaTeX code
\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 4.2
$$K_{Pu-air1}=K_{Pu-air1-4.2}$$
$K_{Pu-air1}=K_{Pu-air1-4.2}$
Equations in LaTeX code
K_{Pu-air1}=K_{Pu-air1-4.2}
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 4.5$
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 4.5$
Equations in LaTeX code
\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 4.5
$$K_{Pu-air1}=K_{Pu-air1-4.5}$$
$K_{Pu-air1}=K_{Pu-air1-4.5}$
Equations in LaTeX code
K_{Pu-air1}=K_{Pu-air1-4.5}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$K_{Pu-air1}=K_{Pu-air1-5}$$
$K_{Pu-air1}=K_{Pu-air1-5}$
Equations in LaTeX code
K_{Pu-air1}=K_{Pu-air1-5}

$K_{Pu-air2} \mathrm{[-]}$
No data
$S/D\mathrm{[-]}$
Under-pressure coefficient in hole 2

Valve position Under-pressure coefficient in hole 2
$S/D$ $K_{Pu-air2}$
$\mathrm{ }$ $\mathrm{ }$
No data
Unrounded data
Valve position; Under-pressure coefficient in hole 2;
S/D; K_{Pu-air2};
; ;
$\text{if }\ \cfrac{h_l\cdot 10^3}{D}\le 0$
$\text{if }\ \cfrac{h_l\cdot 10^3}{D}\le 0$
Equations in LaTeX code
\text{if }\ \cfrac{h_l\cdot 10^3}{D}\le 0
$$K_{Pu-air2}=K_{Pu-air2-0}$$
$K_{Pu-air2}=K_{Pu-air2-0}$
Equations in LaTeX code
K_{Pu-air2}=K_{Pu-air2-0}
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 2$
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 2$
Equations in LaTeX code
\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 2
$$K_{Pu-air2}=K_{Pu-air2-2}$$
$K_{Pu-air2}=K_{Pu-air2-2}$
Equations in LaTeX code
K_{Pu-air2}=K_{Pu-air2-2}
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 2.5$
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 2.5$
Equations in LaTeX code
\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 2.5
$$K_{Pu-air2}=K_{Pu-air2-2.5}$$
$K_{Pu-air2}=K_{Pu-air2-2.5}$
Equations in LaTeX code
K_{Pu-air2}=K_{Pu-air2-2.5}
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3$
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3$
Equations in LaTeX code
\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3
$$K_{Pu-air2}=K_{Pu-air2-3}$$
$K_{Pu-air2}=K_{Pu-air2-3}$
Equations in LaTeX code
K_{Pu-air2}=K_{Pu-air2-3}
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3.5$
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3.5$
Equations in LaTeX code
\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3.5
$$K_{Pu-air2}=K_{Pu-air2-3.5}$$
$K_{Pu-air2}=K_{Pu-air2-3.5}$
Equations in LaTeX code
K_{Pu-air2}=K_{Pu-air2-3.5}
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3.6$
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3.6$
Equations in LaTeX code
\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3.6
$$K_{Pu-air2}=K_{Pu-air2-3.6}$$
$K_{Pu-air2}=K_{Pu-air2-3.6}$
Equations in LaTeX code
K_{Pu-air2}=K_{Pu-air2-3.6}
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3.9$
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3.9$
Equations in LaTeX code
\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 3.9
$$K_{Pu-air2}=K_{Pu-air2-3.9}$$
$K_{Pu-air2}=K_{Pu-air2-3.9}$
Equations in LaTeX code
K_{Pu-air2}=K_{Pu-air2-3.9}
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 4$
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 4$
Equations in LaTeX code
\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 4
$$K_{Pu-air2}=K_{Pu-air2-4}$$
$K_{Pu-air2}=K_{Pu-air2-4}$
Equations in LaTeX code
K_{Pu-air2}=K_{Pu-air2-4}
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 4.2$
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 4.2$
Equations in LaTeX code
\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 4.2
$$K_{Pu-air2}=K_{Pu-air2-4.2}$$
$K_{Pu-air2}=K_{Pu-air2-4.2}$
Equations in LaTeX code
K_{Pu-air2}=K_{Pu-air2-4.2}
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 4.5$
$\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 4.5$
Equations in LaTeX code
\text{else if }\ \cfrac{h_l\cdot 10^3}{D}\le 4.5
$$K_{Pu-air2}=K_{Pu-air2-4.5}$$
$K_{Pu-air2}=K_{Pu-air2-4.5}$
Equations in LaTeX code
K_{Pu-air2}=K_{Pu-air2-4.5}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$K_{Pu-air2}=K_{Pu-air2-5}$$
$K_{Pu-air2}=K_{Pu-air2-5}$
Equations in LaTeX code
K_{Pu-air2}=K_{Pu-air2-5}

$P_{u-air1} \mathrm{[m]}$
No data
$S/D\mathrm{[-]}$
Under-pressure in hole 1

Valve position Under-pressure in hole 1
$S/D$ $P_{u-air1}$
$\mathrm{ }$ $\mathrm{m}$
No data
Unrounded data
Valve position; Under-pressure in hole 1;
S/D; P_{u-air1};
; m;
$$P_{u-air1}=\max\left(K_{Pu-air1}\cdot H_v, -\cfrac{p_{air}}{ρ\cdot g}\right)$$
$P_{u-air1}=\max\left(K_{Pu-air1}\cdot H_v, -\cfrac{p_{air}}{ρ\cdot g}\right)$
Equations in LaTeX code
P_{u-air1}=\max\left(K_{Pu-air1}\cdot H_v, -\cfrac{p_{air}}{ρ\cdot g}\right)

$P_{u-air2} \mathrm{[m]}$
No data
$S/D\mathrm{[-]}$
Under-pressure in hole 2

Valve position Under-pressure in hole 2
$S/D$ $P_{u-air2}$
$\mathrm{ }$ $\mathrm{m}$
No data
Unrounded data
Valve position; Under-pressure in hole 2;
S/D; P_{u-air2};
; m;
$$P_{u-air2}=\max\left(K_{Pu-air2}\cdot H_v, -\cfrac{p_{air}}{ρ\cdot g}\right)$$
$P_{u-air2}=\max\left(K_{Pu-air2}\cdot H_v, -\cfrac{p_{air}}{ρ\cdot g}\right)$
Equations in LaTeX code
P_{u-air2}=\max\left(K_{Pu-air2}\cdot H_v, -\cfrac{p_{air}}{ρ\cdot g}\right)
Valve position
Air flow
Air velocity in hole 1
Air velocity in hole 2
The flow area of the aerated hole
$S/D$ $Q_{air}$ $v_{air1}$ $v_{air2}$ $A_{air}$
$\mathrm{ }$ $\mathrm{m^3/s}$ $\mathrm{m/s}$ $\mathrm{m/s}$ $\mathrm{m^2}$
No data
Valve position Air flow Air velocity in hole 1 Air velocity in hole 2 The flow area of the aerated hole
$S/D$ $Q_{air}$ $v_{air1}$ $v_{air2}$ $A_{air}$
$\mathrm{ }$ $\mathrm{m^3/s}$ $\mathrm{m/s}$ $\mathrm{m/s}$ $\mathrm{m^2}$
No data
Unrounded data
Valve position;Air flow;Air velocity in hole 1;Air velocity in hole 2;The flow area of the aerated hole;
S/D;Q_{air};v_{air1};v_{air2};A_{air};
;m^3/s;m/s;m/s;m^2;

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

Valve position Air flow
$S/D$ $Q_{air}$
$\mathrm{ }$ $\mathrm{m^3/s}$
No data
Unrounded data
Valve position; Air flow;
S/D; 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
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$Q_{air}=0.04\cdot Q$$
$Q_{air}=0.04\cdot Q$
Equations in LaTeX code
Q_{air}=0.04\cdot Q

$v_{air1} \mathrm{[m/s]}$
$v_{air2} \mathrm{[m/s]}$
No data
$S/D\mathrm{[-]}$
Air velocity

Valve position Air velocity in hole 1 Air velocity in hole 2
$S/D$ $v_{air1}$ $v_{air2}$
$\mathrm{ }$ $\mathrm{m/s}$ $\mathrm{m/s}$
No data
Unrounded data
Valve position; Air velocity in hole 1; Air velocity in hole 2;
S/D; v_{air1}; v_{air2};
; m/s; m/s;
$\text{if }\ \text{n}= \text{no}$
$\text{if }\ \text{n}= \text{no}$
Equations in LaTeX code
\text{if }\ \text{n}= \text{no}
$$v_{air1}=NAN$$
$v_{air1}=NAN$
Equations in LaTeX code
v_{air1}=NAN
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$v_{air1}=\min\left(0.7\cdot\sqrt{-\cfrac{2\cdot P_{u-air1}\cdot g\cdot ρ}{ρ_{air}}}, 250\right)$$
$v_{air1}=\min\left(0.7\cdot\sqrt{-\cfrac{2\cdot P_{u-air1}\cdot g\cdot ρ}{ρ_{air}}}, 250\right)$
Equations in LaTeX code
v_{air1}=\min\left(0.7\cdot\sqrt{-\cfrac{2\cdot P_{u-air1}\cdot g\cdot ρ}{ρ_{air}}}, 250\right)
$\text{if }\ \text{n}= \text{no}$
$\text{if }\ \text{n}= \text{no}$
Equations in LaTeX code
\text{if }\ \text{n}= \text{no}
$$v_{air2}=NAN$$
$v_{air2}=NAN$
Equations in LaTeX code
v_{air2}=NAN
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$v_{air2}=\min\left(0.7\cdot\sqrt{-\cfrac{2\cdot P_{u-air2}\cdot g\cdot ρ}{ρ_{air}}}, 250\right)$$
$v_{air2}=\min\left(0.7\cdot\sqrt{-\cfrac{2\cdot P_{u-air2}\cdot g\cdot ρ}{ρ_{air}}}, 250\right)$
Equations in LaTeX code
v_{air2}=\min\left(0.7\cdot\sqrt{-\cfrac{2\cdot P_{u-air2}\cdot g\cdot ρ}{ρ_{air}}}, 250\right)

$A_{air} \mathrm{[m^2]}$
No data
$S/D\mathrm{[-]}$
The flow area of the aerated hole

Valve position The flow area of the aerated hole
$S/D$ $A_{air}$
$\mathrm{ }$ $\mathrm{m^2}$
No data
Unrounded data
Valve position; The flow area of the aerated hole;
S/D; 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
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$A_{air}=\cfrac{Q_{air}}{v_{air1}+v_{air2}}$$
$A_{air}=\cfrac{Q_{air}}{v_{air1}+v_{air2}}$
Equations in LaTeX code
A_{air}=\cfrac{Q_{air}}{v_{air1}+v_{air2}}
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