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Hydrodynamic calculation Needle valve

needle valve D Q max L 0.85D 1.9D Q Bair Q Aair -F +F 0.912 D 0.975 D 0.4D
Needle valve
needle-valve-2 0.133 D - 4 d 1 0.183 D - 8 d 1 0.26 D - 12 d 1 0.35 D - 16 d 1 0.45 D - 20 d 1 0.56 D - 24 d 1 0.666 D - 28 d 1 0.773 D - 32 d 1 0.975 D d 1 =0.03 D
Needle

Values for calculation

$D$ $\mathrm{mm}$
$Q_{max}$ $\mathrm{m^3/s}$
$H$ $\mathrm{m}$
$g$ $\mathrm{m/s^2}$
$T$ $\mathrm{°C}$
$ρ$ $\mathrm{kg/m^3}$
$P_T$ $\mathrm{Pa}$
$ΔP$ $\mathrm{m}$
$h$ $\mathrm{m}$
$ρ_{air}$ $\mathrm{kg/m^3}$
$p_{a}$ $\mathrm{Pa}$
$n$
$t$ $\mathrm{s}$
$L$ $\mathrm{m}$
$ζ$

Calculation

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

$$p=\cfrac{Δ_h}{H}$$
$$0 < p \le 1$$

Effective closing time factor

$$c_{ef}=0$$
$$c_{ef}\le 1$$

Under-pressure behind the valve

$$P_{u}=\max\left(-\cfrac{L\cdot v_{max}}{g\cdot t\cdot c_{ef}}, -\cfrac{p_{a}}{ρ\cdot g}\right)$$

$\mathrm{[-]}$
Hydraulic profile of the needle valve