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Hydrodynamic calculation vertical lift gates

Vertical lift gate Q max H s 0 b B s s d' θ a 1 a 2 d r e L s Q air +W +P
Vertical lift gate

Values for calculation

$s_0$ $\mathrm{mm}$
$b$ $\mathrm{mm}$
$B$ $\mathrm{mm}$
$s_s$ $\mathrm{mm}$
$d^´$ $\mathrm{mm}$
$θ$ $\mathrm{°}$
$e/d$
$a_1$ $\mathrm{mm}$
$a_2$ $\mathrm{mm}$
$d$ $\mathrm{mm}$
$r$ $\mathrm{mm}$
$e$ $\mathrm{mm}$
$Q_{max}$ $\mathrm{m^3/s}$
$H$ $\mathrm{m}$
$ΔP$ $\mathrm{m}$
$g$ $\mathrm{m/s^2}$
$T$ $\mathrm{°C}$
$ρ$ $\mathrm{kg/m^3}$
$P_{SV}$ $\mathrm{Pa}$
$h$ $\mathrm{m}$
$ρ_{air}$ $\mathrm{kg/m^3}$
$p_{air}$ $\mathrm{Pa}$
$t$ $\mathrm{s}$
$L$ $\mathrm{m}$

Calculation

Cross-sectional area of the conduit

$$A=\cfrac{s_0\cdot b}{10^6}$$
$A=\cfrac{s_0\cdot b}{10^6}$
Equations in LaTeX code
A=\cfrac{s_0\cdot b}{10^6}

Area of the horizontal projection of the top seal

$$A_s=\cfrac{B\cdot a_2}{10^6}$$
$A_s=\cfrac{B\cdot a_2}{10^6}$
Equations in LaTeX code
A_s=\cfrac{B\cdot a_2}{10^6}

Minimum cross-sectional area between upstream face of the gate and upstream wall of the gate chamber

$$A_1=a_1\cdot b$$
$A_1=a_1\cdot b$
Equations in LaTeX code
A_1=a_1\cdot b

Cross-sectional area of the contracted jet issuing from the gap between the downstream face of the gate and the downstream wall of the gate chamber

$$A_2=a_2\cdot b$$
$A_2=a_2\cdot b$
Equations in LaTeX code
A_2=a_2\cdot b

Coefficient $ K_T $

$$K_T=\cfrac{1}{1+\left(\cfrac{A_2}{A_1}\right)^2}$$
$K_T=\cfrac{1}{1+\left(\cfrac{A_2}{A_1}\right)^2}$
Equations in LaTeX code
K_T=\cfrac{1}{1+\left(\cfrac{A_2}{A_1}\right)^2}

Velocity before the gate

$$v_{max}=\cfrac{10^6\cdot Q_{max}}{s_0\cdot b}$$
$v_{max}=\cfrac{10^6\cdot Q_{max}}{s_0\cdot b}$
Equations in LaTeX code
v_{max}=\cfrac{10^6\cdot Q_{max}}{s_0\cdot b}

Theoretical pressure in the gate 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)

Effective closing time factor

$$c_{ef}=\cfrac{0.1}{\max\left(\left(Q_p\right)[1]-\left(Q_p\right)[2], \left(Q_p\right)[2]-\left(Q_p\right)[3], \left(Q_p\right)[3]-\left(Q_p\right)[4], \left(Q_p\right)[4]-\left(Q_p\right)[5], \left(Q_p\right)[5]-\left(Q_p\right)[6], \left(Q_p\right)[6]-\left(Q_p\right)[7], \left(Q_p\right)[7]-\left(Q_p\right)[8], \left(Q_p\right)[8]-\left(Q_p\right)[9], \left(Q_p\right)[9]-\left(Q_p\right)[10], \left(Q_p\right)[10]-\left(Q_p\right)[11]\right)}$$
$c_{ef}=\cfrac{0.1}{\max\left(\left(Q_p\right)[1]-\left(Q_p\right)[2], \left(Q_p\right)[2]-\left(Q_p\right)[3], \left(Q_p\right)[3]-\left(Q_p\right)[4], \left(Q_p\right)[4]-\left(Q_p\right)[5], \left(Q_p\right)[5]-\left(Q_p\right)[6], \left(Q_p\right)[6]-\left(Q_p\right)[7], \left(Q_p\right)[7]-\left(Q_p\right)[8], \left(Q_p\right)[8]-\left(Q_p\right)[9], \left(Q_p\right)[9]-\left(Q_p\right)[10], \left(Q_p\right)[10]-\left(Q_p\right)[11]\right)}$
Equations in LaTeX code
c_{ef}=\cfrac{0.1}{\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]\right)}

Under-pressure behind the gate

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

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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