$ $ | model number for Howell-Bunger valve | $\mathrm{ }$ |
$ $ | flow characteristic | $\mathrm{ }$ |
$A$ | the flow area | $\mathrm{m^2}$ |
$A_{air-pipe}$ | the flow area of the aerated pipeline | $\mathrm{m^2}$ |
$A_{air}$ | the flow area of the aerated hole | $\mathrm{m^2}$ |
$D$ | valve diameter | $\mathrm{mm}$ |
$D_c$ | inner diameter of the cage | $\mathrm{mm}$ |
$D_p$ | internal pipe diameter | $\mathrm{mm}$ |
$D_s$ | max diameter of the disc seal | $\mathrm{mm}$ |
$D_s$ | max diameter seal on the rotating body | $\mathrm{mm}$ |
$D_{needle}$ | diameter needle | $\mathrm{mm}$ |
$E$ | Young's modulus for pipe | $\mathrm{Pa}$ |
$F$ | forces on disc | $\mathrm{kN}$ |
$F$ | forces on rotating body | $\mathrm{kN}$ |
$F_x$ | forces on disc in axis x | $\mathrm{kN}$ |
$F_x$ | forces on rotating body in axis x | $\mathrm{kN}$ |
$F_x$ | forces on the needle | $\mathrm{kN}$ |
$F_x$ | forces on sliding plate in axis x | $\mathrm{kN}$ |
$F_y$ | forces on disc in axis y | $\mathrm{kN}$ |
$F_y$ | forces on rotating body in axis y | $\mathrm{kN}$ |
$F_y$ | forces on sliding plate in axis y | $\mathrm{kN}$ |
$F_{bx}$ | the force at the valve axis x | $\mathrm{kN}$ |
$F_{by}$ | the force at the valve axis y | $\mathrm{kN}$ |
$F_{e1}$ | force parallel to the axis of the disc | $\mathrm{kN}$ |
$F_{e1}$ | force parallel to the axis of the rotating body | $\mathrm{kN}$ |
$F_{e2}$ | force perpendicular to the axis of the disc | $\mathrm{kN}$ |
$F_{e2}$ | force perpendicular to the axis of the rotating body | $\mathrm{kN}$ |
$H$ | static head | $\mathrm{m}$ |
$H_L$ | loss of pressure on the valve | $\mathrm{m}$ |
$H_v$ | pressure on the valve | $\mathrm{m}$ |
$I$ | number of holes | $\mathrm{ }$ |
$K$ | volume elastic modulus | $\mathrm{Pa}$ |
$K_Q$ | flow coefficient | $\mathrm{ }$ |
$K_m$ | hydraulic torque coefficient | $\mathrm{ }$ |
$K_x$ | coefficient of hydraulic force on a disc in the axis x | $\mathrm{ }$ |
$K_x$ | coefficient of hydraulic force on a rotating body in the axis x | $\mathrm{ }$ |
$K_x$ | Coefficient of hydraulic force on a needle in the axis x | $\mathrm{ }$ |
$K_x$ | coefficient of hydraulic force on a sliding plate in the axis x | $\mathrm{ }$ |
$K_y$ | coefficient of hydraulic force on a disc in the axis y | $\mathrm{ }$ |
$K_y$ | coefficient of hydraulic force on a rotating body in the axis y | $\mathrm{ }$ |
$K_y$ | coefficient of hydraulic force on a sliding plate in the axis y | $\mathrm{ }$ |
$K_{Pu-air1}$ | under-pressure coefficient in hole 1 | $\mathrm{ }$ |
$K_{Pu-air2}$ | under-pressure coefficient in hole 2 | $\mathrm{ }$ |
$K_{Pu}$ | coefficient of under-pressure | $\mathrm{ }$ |
$K_{Q-hydraulic-cylinder}$ | flow coefficient $ K_{Q-hydraulic-cylinder} $ | $\mathrm{ }$ |
$K_{Q-valve[0]}$ | flow coefficient $ K_{Q-valve[0]} $ | $\mathrm{ }$ |
$K_{Q-valve[10]}$ | flow coefficient $ K_{Q-valve[10]} $ | $\mathrm{ }$ |
$K_{Q-valve[20]}$ | flow coefficient $ K_{Q-valve[20]} $ | $\mathrm{ }$ |
$K_{Q-valve[30]}$ | flow coefficient $ K_{Q-valve[30]} $ | $\mathrm{ }$ |
$K_{Q-valve[40]}$ | flow coefficient $ K_{Q-valve[40]} $ | $\mathrm{ }$ |
$K_{Q-valve[50]}$ | flow coefficient $ K_{Q-valve[50]} $ | $\mathrm{ }$ |
$K_{Q-valve[60]}$ | flow coefficient $ K_{Q-valve[60]} $ | $\mathrm{ }$ |
$K_{Q-valve[70]}$ | flow coefficient $ K_{Q-valve[70]} $ | $\mathrm{ }$ |
$K_{Q-valve[80]}$ | flow coefficient $ K_{Q-valve[80]} $ | $\mathrm{ }$ |
$K_{Q-valve[90]}$ | flow coefficient $ K_{Q-valve[90]} $ | $\mathrm{ }$ |
$K_{Q-valve[s+10]}$ | flow coefficient $ K_{Q-valve[s+10]} $ | $\mathrm{ }$ |
$K_{Q-valve[s-10]}$ | flow coefficient $ K_{Q-valve[s-10]} $ | $\mathrm{ }$ |
$K_{Q-valve}$ | flow coefficient $ K_{Q-valve} $ | $\mathrm{ }$ |
$K_{Qmax}$ | max flow coefficient | $\mathrm{ }$ |
$K_{bx}$ | coefficient of hydraulic force on body in the axis x | $\mathrm{ }$ |
$K_{by}$ | coefficient of hydraulic force on body in the axis y | $\mathrm{ }$ |
$K_{x-upstream}$ | Coefficient of hydraulic force on a needle upstream in the axis x | $\mathrm{ }$ |
$L$ | pipe length | $\mathrm{m}$ |
$L$ | cage length | $\mathrm{mm}$ |
$L$ | distance between the axis of rotation of the valve and the axis of the hydraulic cylinder | $\mathrm{mm}$ |
$L$ | pipe length behind valve | $\mathrm{m}$ |
$L_1$ | lenght $ L_1 $ | $\mathrm{m}$ |
$L_2$ | lenght $ L_2 $ | $\mathrm{m}$ |
$L_D$ | length from the axis of rotation to the outer edge of the disc | $\mathrm{mm}$ |
$L_d$ | damping phase | $\mathrm{\%}$ |
$M$ | hydraulic torque without eccentricity | $\mathrm{kNm}$ |
$M_H$ | hydraulic torque | $\mathrm{kNm}$ |
$M_e$ | moment from eccentricity | $\mathrm{kNm}$ |
$M_{LD}$ | moment from the axis of the trunnion to the axis of the disc | $\mathrm{kNm}$ |
$P_1$ | inlet absolute static pressure | $\mathrm{Pa}$ |
$P_2$ | output absolute static pressure | $\mathrm{Pa}$ |
$P_T$ | saturated vapor pressure | $\mathrm{Pa}$ |
$P_{u-air1}$ | under-pressure in hole 1 | $\mathrm{m}$ |
$P_{u-air2}$ | under-pressure in hole 2 | $\mathrm{m}$ |
$P_{u}$ | under-pressure behind the valve | $\mathrm{m}$ |
$Q$ | flow of water in the pipeline | $\mathrm{m^3/s}$ |
$Q_p$ | relative flow | $\mathrm{ }$ |
$Q_{air}$ | air flow | $\mathrm{m^3/s}$ |
$Q_{max}$ | flow | $\mathrm{m^3/s}$ |
$R$ | dimension $ R $ | $\mathrm{mm}$ |
$S$ | dimension $ S $ | $\mathrm{mm}$ |
$S/D$ | valve position | $\mathrm{ }$ |
$S_S$ | stroke in the pivot position | $\mathrm{mm}$ |
$S_S$ | the distance between the axis of the hydraulic cylinder and the axis of the eye of the hydraulic cylinder | $\mathrm{mm}$ |
$S_T$ | percentage of hydraulic cylinder stroke at a given time | $\mathrm{\%}$ |
$S_{S\%}$ | stroke percentage | $\mathrm{\%}$ |
$S_{max}$ | stroke | $\mathrm{mm}$ |
$T$ | height $ T $ | $\mathrm{mm}$ |
$T$ | the water temperature | $\mathrm{°C}$ |
$T_c$ | total closing time | $\mathrm{s}$ |
$T_d$ | damping time | $\mathrm{s}$ |
$T_s$ | time value | $\mathrm{s}$ |
$T_x$ | energy before the valve | $\mathrm{m}$ |
$a$ | dimension $ a $ | $\mathrm{mm}$ |
$a$ | speed pressure waves in the pipe | $\mathrm{m/s}$ |
$a$ | distance to hydraulic cylinder $ a $ | $\mathrm{mm}$ |
$a_1$ | length $ a_1 $ | $\mathrm{mm}$ |
$a_2$ | length $ a_2 $ | $\mathrm{mm}$ |
$b$ | dimension $ b $ | $\mathrm{mm}$ |
$b$ | distance to hydraulic cylinder $ b $ | $\mathrm{mm}$ |
$c$ | dimension $ c $ | $\mathrm{mm}$ |
$c_{ef}$ | effective closing time factor | $\mathrm{ }$ |
$d$ | diameter of the hole | $\mathrm{mm}$ |
$d$ | inner diameter | $\mathrm{mm}$ |
$d_1$ | dimension $ d_1 $ | $\mathrm{mm}$ |
$e$ | thickness of the pipe wall | $\mathrm{mm}$ |
$e$ | dimension $ e $ | $\mathrm{mm}$ |
$e$ | eccentricity | $\mathrm{mm}$ |
$f$ | dimension $ f $ | $\mathrm{mm}$ |
$f_r$ | reduced free flow area in the throttle control system | $\mathrm{ }$ |
$f_{air}$ | coefficient of under-pressure of aerated hole | $\mathrm{ }$ |
$g$ | gravitational acceleration | $\mathrm{m/s^2}$ |
$g$ | dimension $ g $ | $\mathrm{mm}$ |
$h$ | dimension $ h $ | $\mathrm{mm}$ |
$h$ | valve axis position to sea level | $\mathrm{m}$ |
$h_j$ | water depth behind the hydraulic jump | $\mathrm{m}$ |
$h_l$ | water level | $\mathrm{m}$ |
$i$ | dimension $ i $ | $\mathrm{mm}$ |
$j$ | dimension $ j $ | $\mathrm{mm}$ |
$k$ | dimension $ k $ | $\mathrm{mm}$ |
$l$ | dimension $ l $ | $\mathrm{mm}$ |
$l$ | rod length | $\mathrm{mm}$ |
$m$ | dimension $ m $ | $\mathrm{mm}$ |
$n$ | aeration | $\mathrm{ }$ |
$n$ | dimension $ n $ | $\mathrm{mm}$ |
$n_{max}$ | allowable maximum number of holes in one row | $\mathrm{ }$ |
$o$ | dimension $ o $ | $\mathrm{mm}$ |
$p$ | pressure parameter | $\mathrm{ }$ |
$p$ | dimension $ p $ | $\mathrm{mm}$ |
$p_{air}$ | under-pressure in the aerated pipeline | $\mathrm{Pa}$ |
$p_{a}$ | atmospheric pressure | $\mathrm{Pa}$ |
$q$ | dimension $ q $ | $\mathrm{mm}$ |
$r$ | dimension $ r $ | $\mathrm{mm}$ |
$r$ | lever arm length | $\mathrm{mm}$ |
$s$ | stroke from open position | $\mathrm{\%}$ |
$s$ | dimension $ s $ | $\mathrm{mm}$ |
$t$ | closing time | $\mathrm{s}$ |
$t$ | dimension $ t $ | $\mathrm{mm}$ |
$t_{ef}$ | effective closing time | $\mathrm{s}$ |
$u$ | dimension $ u $ | $\mathrm{mm}$ |
$v$ | water velocity in pipeline | $\mathrm{m/s}$ |
$v$ | dimension $ v $ | $\mathrm{mm}$ |
$v_p$ | speed in the pipe | $\mathrm{m/s}$ |
$v_{air1}$ | air velocity in hole 1 | $\mathrm{m/s}$ |
$v_{air2}$ | air velocity in hole 2 | $\mathrm{m/s}$ |
$v_{air}$ | air velocity | $\mathrm{m/s}$ |
$v_{max}$ | velocity in valve | $\mathrm{m/s}$ |
$w$ | speed of sound | $\mathrm{m/s}$ |
$w$ | dimension $ w $ | $\mathrm{mm}$ |
$x$ | dimension $ x $ | $\mathrm{mm}$ |
$y$ | dimension $ y $ | $\mathrm{mm}$ |
$z$ | dimension $ z $ | $\mathrm{mm}$ |
$ΔP$ | water hammer | $\mathrm{m}$ |
$Δ_h$ | theoretical pressure in the valve at full opening | $\mathrm{m}$ |
$Σζ$ | loss before valve | $\mathrm{ }$ |
$α$ | angle from open position | $\mathrm{°}$ |
$α$ | lever angle in closed position | $\mathrm{°}$ |
$β$ | aerated coefficient | $\mathrm{ }$ |
$β$ | swing angle | $\mathrm{°}$ |
$β_S$ | angle rotation of the rocking motion | $\mathrm{°}$ |
$β_{S[s-10]}$ | angle rotation of the rocking motion | $\mathrm{°}$ |
$ζ$ | loss coefficient | $\mathrm{ }$ |
$ζ$ | valve loss coefficient | $\mathrm{ }$ |
$μ$ | output coefficient | $\mathrm{ }$ |
$ρ$ | density | $\mathrm{kg/m^3}$ |
$ρ_{air}$ | air density | $\mathrm{kg/m^3}$ |
$σ$ | cavitation number | $\mathrm{ }$ |
$ϕ$ | angle between pipe axis and hydraulic force | $\mathrm{°}$ |
$𝛾$ | the angle between the axis of the hydraulic cylinder and the imaginary line between the axis of the closure and the pivot axis of the hydraulic cylinder | $\mathrm{°}$ |
$𝛿$ | the angle between the lever axis and the imaginary line between the valve axis and the pivot axis of the hydraulic cylinder | $\mathrm{°}$ |
$𝛿_{[0]}$ | the angle between the axis of the lever and the imaginary line between the axis of the valve and the pivot axis of the hydraulic cylinder in the open position | $\mathrm{°}$ |