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Hydrodynamic calculation Butterfly valve lattice disc

Butterfly valve (lattice disc) D s e +F by +F bx +M H L 0.5D D Q max +F y +F x +F Φ Q air α 0.3D 0.5D
Butterfly valve (lattice disc)
Lattice disc c D s a b e 20° L D 140°
Lattice disc

Values for calculation

$D$ $\mathrm{mm}$
$L_D$ $\mathrm{mm}$
$a$ $\mathrm{mm}$
$b$ $\mathrm{mm}$
$c$ $\mathrm{mm}$
$D_s$ $\mathrm{mm}$
$Q_{max}$ $\mathrm{m^3/s}$
$H$ $\mathrm{m}$
$g$ $\mathrm{m/s^2}$
$T$ $\mathrm{°C}$
$ρ$ $\mathrm{kg/m^3}$
$P_{SV}$ $\mathrm{Pa}$
$ΔP$ $\mathrm{m}$
$h$ $\mathrm{m}$
$ρ_{air}$ $\mathrm{kg/m^3}$
$p_{air}$ $\mathrm{Pa}$
$n$
$e$ $\mathrm{mm}$
$t$ $\mathrm{s}$
$L$ $\mathrm{m}$

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}

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

Effective closing time factor

$$c_{ef}=\cfrac{\cfrac{1}{18}}{\max\left(\left(Q_p\right)[1]-\left(Q_p\right)[2], \left(Q_p\right)[2]-\left(Q_p\right)[3], \left(Q_p\right)[3]-\left(Q_p\right)[4], \left(Q_p\right)[4]-\left(Q_p\right)[5], \left(Q_p\right)[5]-\left(Q_p\right)[6], \left(Q_p\right)[6]-\left(Q_p\right)[7], \left(Q_p\right)[7]-\left(Q_p\right)[8], \left(Q_p\right)[8]-\left(Q_p\right)[9], \left(Q_p\right)[9]-\left(Q_p\right)[10], \left(Q_p\right)[10]-\left(Q_p\right)[11], \left(Q_p\right)[11]-\left(Q_p\right)[12], \left(Q_p\right)[12]-\left(Q_p\right)[13], \left(Q_p\right)[13]-\left(Q_p\right)[14], \left(Q_p\right)[14]-\left(Q_p\right)[15], \left(Q_p\right)[15]-\left(Q_p\right)[16], \left(Q_p\right)[16]-\left(Q_p\right)[17], \left(Q_p\right)[17]-\left(Q_p\right)[18], \left(Q_p\right)[18]-\left(Q_p\right)[19]\right)}$$
$c_{ef}=\cfrac{\cfrac{1}{18}}{\max\left(\left(Q_p\right)[1]-\left(Q_p\right)[2], \left(Q_p\right)[2]-\left(Q_p\right)[3], \left(Q_p\right)[3]-\left(Q_p\right)[4], \left(Q_p\right)[4]-\left(Q_p\right)[5], \left(Q_p\right)[5]-\left(Q_p\right)[6], \left(Q_p\right)[6]-\left(Q_p\right)[7], \left(Q_p\right)[7]-\left(Q_p\right)[8], \left(Q_p\right)[8]-\left(Q_p\right)[9], \left(Q_p\right)[9]-\left(Q_p\right)[10], \left(Q_p\right)[10]-\left(Q_p\right)[11], \left(Q_p\right)[11]-\left(Q_p\right)[12], \left(Q_p\right)[12]-\left(Q_p\right)[13], \left(Q_p\right)[13]-\left(Q_p\right)[14], \left(Q_p\right)[14]-\left(Q_p\right)[15], \left(Q_p\right)[15]-\left(Q_p\right)[16], \left(Q_p\right)[16]-\left(Q_p\right)[17], \left(Q_p\right)[17]-\left(Q_p\right)[18], \left(Q_p\right)[18]-\left(Q_p\right)[19]\right)}$
Equations in LaTeX code
c_{ef}=\cfrac{\cfrac{1}{18}}{\max\left(\left(Q_p\right)[1]-\left(Q_p\right)[2], \left(Q_p\right)[2]-\left(Q_p\right)[3], \left(Q_p\right)[3]-\left(Q_p\right)[4], \left(Q_p\right)[4]-\left(Q_p\right)[5], \left(Q_p\right)[5]-\left(Q_p\right)[6], \left(Q_p\right)[6]-\left(Q_p\right)[7], \left(Q_p\right)[7]-\left(Q_p\right)[8], \left(Q_p\right)[8]-\left(Q_p\right)[9], \left(Q_p\right)[9]-\left(Q_p\right)[10], \left(Q_p\right)[10]-\left(Q_p\right)[11], \left(Q_p\right)[11]-\left(Q_p\right)[12], \left(Q_p\right)[12]-\left(Q_p\right)[13], \left(Q_p\right)[13]-\left(Q_p\right)[14], \left(Q_p\right)[14]-\left(Q_p\right)[15], \left(Q_p\right)[15]-\left(Q_p\right)[16], \left(Q_p\right)[16]-\left(Q_p\right)[17], \left(Q_p\right)[17]-\left(Q_p\right)[18], \left(Q_p\right)[18]-\left(Q_p\right)[19]\right)}
$$c_{ef}\le 1$$
$c_{ef}\le 1$
Equations in LaTeX code
c_{ef}\le 1

Under-pressure behind the valve

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