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Hydrodynamic calculation Howell-Jet valve

Howell-Jet valve Q max D a b c e f g h i j k l m n o p r q t ELLIPSE s VANES 33° B u 8 d 1 d v w x 10° y VANES ALTERNATE AT 45° DETAIL "B" 33° 40° z +F -F D needle
Howell-Jet valve

Values for calculation

$D$ $\mathrm{mm}$
$D_{needle}$ $\mathrm{mm}$
$d$ $\mathrm{mm}$
$a$ $\mathrm{mm}$
$b$ $\mathrm{mm}$
$c$ $\mathrm{mm}$
$e$ $\mathrm{mm}$
$f$ $\mathrm{mm}$
$g$ $\mathrm{mm}$
$h$ $\mathrm{mm}$
$i$ $\mathrm{mm}$
$j$ $\mathrm{mm}$
$k$ $\mathrm{mm}$
$l$ $\mathrm{mm}$
$m$ $\mathrm{mm}$
$n$ $\mathrm{mm}$
$o$ $\mathrm{mm}$
$p$ $\mathrm{mm}$
$q$ $\mathrm{mm}$
$r$ $\mathrm{mm}$
$t$ $\mathrm{mm}$
$u$ $\mathrm{mm}$
$v$ $\mathrm{mm}$
$w$ $\mathrm{mm}$
$x$ $\mathrm{mm}$
$y$ $\mathrm{mm}$
$z$ $\mathrm{mm}$
$d_1$ $\mathrm{mm}$
$H$ $\mathrm{m}$
$g$ $\mathrm{m/s^2}$
$T$ $\mathrm{°C}$
$ρ$ $\mathrm{kg/m^3}$
$P_{SV}$ $\mathrm{Pa}$
$ΔP$ $\mathrm{m}$
$Σζ$
$h$ $\mathrm{m}$
$ρ_{air}$ $\mathrm{kg/m^3}$
$p_{air}$ $\mathrm{Pa}$

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
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