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Hydrodynamic calculation Howell-Bunger valve

Howell-Bunger_valve
Howell-Bunger valve

Values for calculation

$D$ $\mathrm{mm}$
$S$ $\mathrm{mm}$
$R$ $\mathrm{mm}$
$a$ $\mathrm{mm}$
$b$ $\mathrm{mm}$
$c$ $\mathrm{mm}$
$e$ $\mathrm{mm}$
$f$ $\mathrm{mm}$
$g$ $\mathrm{mm}$
$H$ $\mathrm{m}$
$g$ $\mathrm{m/s^2}$
$T$ $\mathrm{°C}$
$ρ$ $\mathrm{kg/m^3}$
$P_T$ $\mathrm{Pa}$
$n$
$ΔP$ $\mathrm{m}$
$Σζ$
$h$ $\mathrm{m}$
$ρ_{air}$ $\mathrm{kg/m^3}$
$p_{a}$ $\mathrm{Pa}$
$h_j$ $\mathrm{m}$
$ζ$

Calculation

Flow

$$Q_{max}=\cfrac{1}{\sqrt{1+Σζ+ζ}}\cdot\cfrac{π\cdot D^2}{4\cdot 10^6}\cdot\sqrt{2\cdot g\cdot H}$$

Velocity in valve

$$v_{max}=\cfrac{4\cdot 10^6\cdot Q_{max}}{π\cdot D^2}$$

Theoretical pressure in the valve at full opening

$$Δ_h=\cfrac{v_{max}^2}{2\cdot g}\cdot \left(ζ+1\right)$$

Pressure parameter

$$p=\cfrac{Δ_h}{H}$$

Requirements

$$0 < p \le 1$$