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Hydrodynamic calculation Gate valve (through conduit)

Gate valve (through conduit) Q air D Q max 1,1D 0,3D 1,5D 4D 1,2D 2D +F by +F bx +F x +F y L Q air D Q max 1.2 D +F by +F bx +F x +F y 1.1 D 0.3D 1.5D 4D 2D
Gate valve (through conduit)

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_{SV} \mathrm{Pa}
ΔP \mathrm{m}
h \mathrm{m}
ρ_{air} \mathrm{kg/m^3}
p_{air} \mathrm{Pa}
n
t \mathrm{s}
L \mathrm{m}

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({\min\left(ζ\right)}+1\right)

Pressure parameter

p=\cfrac{Δ_h}{H}

0 < p \le 1

Effective closing time factor

c_{ef}=0.1/\max_{i=1}^{10}{\left(Q_p[i]-Q_p[i+1]\right)}

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)
Stroke from open position
Flow coefficient
Coefficient of hydraulic force on a sliding plate in the axis x
Coefficient of hydraulic force on a sliding plate in the axis y
Coefficient of hydraulic force on body in the axis x
Coefficient of hydraulic force on body in the axis y
s K_Q K_x K_y K_{bx} K_{by}
\mathrm{\%} \mathrm{\ } \mathrm{\ } \mathrm{\ } \mathrm{\ } \mathrm{\ }
No data

K_x\ [-]
K_y\ [-]
K_{bx}\ [-]
K_{by}\ [-]
No data
s\ [\mathrm{\%}]
Coefficient of force

K_Q\ [-]
No data
s\ [\mathrm{\%}]
Flow coefficient

Stroke from open position
Loss coefficient
Reduced free flow area in the throttle control system
Relative flow
Flow of water in the pipeline
Water velocity in pipeline
s ζ f_r Q_p Q v
\mathrm{\%} \mathrm{\ } \mathrm{\ } \mathrm{\ } \mathrm{m^3/s} \mathrm{m/s}
No data

ζ\ [-]
No data
s\ [\mathrm{\%}]
Loss coefficient

ζ=\cfrac{1-K_Q^2}{K_Q^2}

f_r\ [-]
Q_p\ [-]
No data
s\ [\mathrm{\%}]
Coefficients

f_r=\cfrac{K_Q}{K_{Qmax}}
Q_p=\cfrac{f_r}{\sqrt{p+f_r^2\cdot \left(1-p\right)}}

Q\ [\mathrm{m^3/s}]
v\ [\mathrm{m/s}]
No data
s\ [\mathrm{\%}]
Flow and speed of water in the pipeline

Q=Q_p\cdot Q_{max}
v=Q_p\cdot v_{max}
Stroke from open position
Loss of pressure on the valve
Pressure on the valve
Cavitation number
s H_L H_v σ
\mathrm{\%} \mathrm{m} \mathrm{m} \mathrm{\ }
No data

H_L\ [\mathrm{m}]
H_v\ [\mathrm{m}]
No data
s\ [\mathrm{\%}]
Loss of height on valve and pressure height on Gate valve

H_L=\cfrac{v^2}{2\cdot g}\cdot ζ
H_v=H_L+\cfrac{v^2}{2\cdot g}+\left(1-Q_p\right)\cdot\left(ΔP-P_{u}\right)

σ\ [-]
No data
s\ [\mathrm{\%}]
Cavitation number

σ=\cfrac{\cfrac{p_{air}-P_{SV}}{ρ\cdot g}+H-H_L}{H_v}
Stroke from open position
Forces on sliding plate in axis x
Forces on sliding plate in axis y
The force at the valve axis x
The force at the valve axis y
s F_x F_y F_{bx} F_{by}
\mathrm{\%} \mathrm{kN} \mathrm{kN} \mathrm{kN} \mathrm{kN}
No data

F_x\ [\mathrm{kN}]
F_y\ [\mathrm{kN}]
No data
s\ [\mathrm{\%}]
Forces on sliding plate

F_x=\cfrac{π\cdot D^2}{4\cdot 10^9}\cdot ρ\cdot g\cdot H_v\cdot K_x
F_y=\cfrac{π\cdot D^2}{4\cdot 10^9}\cdot ρ\cdot g\cdot H_v\cdot K_y

F_{bx}\ [\mathrm{kN}]
No data
s\ [\mathrm{\%}]
The force at the valve axis x

F_{bx}=\cfrac{π\cdot D^2}{4\cdot 10^9}\cdot ρ\cdot g\cdot H_v\cdot K_{bx}

F_{by}\ [\mathrm{kN}]
No data
s\ [\mathrm{\%}]
The force at the valve axis y

F_{by}=\cfrac{π\cdot D^2}{4\cdot 10^9}\cdot ρ\cdot g\cdot H_v\cdot K_{by}
Stroke from open position
Coefficient of under-pressure of aerated hole
Under-pressure in the aerated pipeline
Air flow
s f_{air} p_{air} Q_{air}
\mathrm{\%} \mathrm{\ } \mathrm{Pa} \mathrm{m^3/s}
No data

f_{air}\ [-]
No data
s\ [\mathrm{\%}]
Coefficient of under-pressure of aerated hole

p_{air}\ [\mathrm{Pa}]
No data
s\ [\mathrm{\%}]
Under-pressure in the aerated pipeline

\text{if }\ \text{n}= \text{no}
p_{air}=NAN
\text{else}
p_{air}=-\min\left(p_{air}, f_{air}\cdot\cfrac{v^2}{2\cdot g}\cdot ρ+\left(1-Q_p\right)\cdot\min\left(\cfrac{L\cdot v_{max}\cdot ρ}{t\cdot c_{ef}}, p_{air}\right)\right)

Q_{air}\ [\mathrm{m^3/s}]
No data
s\ [\mathrm{\%}]
Air flow

\text{if }\ \text{n}= \text{no}
Q_{air}=NAN
\text{else if }\ p_{air}<\cfrac{p_{air}}{2}
Q_{air}=\min\left(Q_{max}-Q, 0.2\cdot Q\right)
\text{else}
Q_{air}=\max\left(Q_{max}-Q, 0.2\cdot Q\right)
Stroke from open position
Air velocity
The flow area of the aerated hole
The flow area of the aerated pipeline
s v_{air} A_{air} A_{air-pipe}
\mathrm{\%} \mathrm{m/s} \mathrm{m^2} \mathrm{m^2}
No data

v_{air}\ [\mathrm{m/s}]
No data
s\ [\mathrm{\%}]
Air velocity

\text{if }\ \text{n}= \text{no}
v_{air}=NAN
\text{else}
v_{air}=\min\left(0.7\cdot\sqrt{-\cfrac{2\cdot p_{air}}{ρ_{air}}}, 250\right)

A_{air}\ [\mathrm{m^2}]
No data
s\ [\mathrm{\%}]
The flow area of the aerated hole

\text{if }\ \text{n}= \text{no}
A_{air}=NAN
\text{else if }\ v_{air}=0
A_{air}=0
\text{else}
A_{air}=\cfrac{Q_{air}}{v_{air}}

A_{air-pipe}\ [\mathrm{m^2}]
No data
s\ [\mathrm{\%}]
The flow area of the aerated pipeline

\text{if }\ \text{n}= \text{no}
A_{air-pipe}=NAN
\text{else if }\ v_{air}>50
A_{air-pipe}=\cfrac{Q_{air}}{50}
\text{else}
A_{air-pipe}=A_{air}