| $ $ |
model number for Howell-Bunger valve |
$\mathrm{ }$ |
| $ $ |
flow characteristic |
$\mathrm{ }$ |
| $ $ |
data |
$\mathrm{ }$ |
| $A$ |
the flow area |
$\mathrm{m^2}$ |
| $A$ |
function $ A $ |
$\mathrm{ }$ |
| $A_{air-pipe}$ |
the flow area of the aerated pipeline |
$\mathrm{m^2}$ |
| $A_{air}$ |
the flow area of the aerated hole |
$\mathrm{m^2}$ |
| $B$ |
function $ B $ |
$\mathrm{ }$ |
| $C$ |
function $ C $ |
$\mathrm{ }$ |
| $D$ |
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 |
$\mathrm{mm}$ |
| $D_{HC}$ |
diameter of piston in the hydraulic cylinder |
$\mathrm{mm}$ |
| $D_{needle}$ |
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 |
$\mathrm{kN}$ |
| $F_{HC-flow-with-frictional}$ |
force to the hydraulic cylinder during the closing at flow rate with frictional resistances |
$\mathrm{kN}$ |
| $F_{HC-flow}$ |
force to the hydraulic cylinder during the closing at flow rate without frictional resistances |
$\mathrm{kN}$ |
| $F_{HC-with-frictional}$ |
force to the hydraulic cylinder during the closing without flow rate with frictional resistances |
$\mathrm{kN}$ |
| $F_{HC}$ |
force to the hydraulic cylinder during the closing without flow rate without frictional resistances |
$\mathrm{kN}$ |
| $F_{bx}$ |
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 |
$\mathrm{m}$ |
| $H$ |
geopotential altitude |
$\mathrm{m}$ |
| $H_L$ |
loss of pressure on the valve |
$\mathrm{m}$ |
| $H_b$ |
lower limit geopotential altitude |
$\mathrm{m}$ |
| $H_p$ |
pressure scale height |
$\mathrm{m}$ |
| $H_v$ |
pressure on the valve |
$\mathrm{m}$ |
| $I$ |
number of holes |
$\mathrm{ }$ |
| $I$ |
exponent $ I $ |
$\mathrm{ }$ |
| $I_{total}$ |
total number of holes |
$\mathrm{ }$ |
| $J$ |
exponent $ J $ |
$\mathrm{ }$ |
| $J^o$ |
exponent $ J^o $ |
$\mathrm{ }$ |
| $K$ |
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 |
$\mathrm{ }$ |
| $K_{Pu-0}$ |
coefficient of under-pressure for $ \cfrac{h_l}{D}=0 $ |
$\mathrm{ }$ |
| $K_{Pu-2.5}$ |
coefficient of under-pressure for $ \cfrac{h_l}{D}=2.5 $ |
$\mathrm{ }$ |
| $K_{Pu-2}$ |
coefficient of under-pressure for $ \cfrac{h_l}{D}=2 $ |
$\mathrm{ }$ |
| $K_{Pu-3.5}$ |
coefficient of under-pressure for $ \cfrac{h_l}{D}=3.5 $ |
$\mathrm{ }$ |
| $K_{Pu-3.6}$ |
coefficient of under-pressure for $ \cfrac{h_l}{D}=3.6 $ |
$\mathrm{ }$ |
| $K_{Pu-3.9}$ |
coefficient of under-pressure for $ \cfrac{h_l}{D}=3.9 $ |
$\mathrm{ }$ |
| $K_{Pu-3}$ |
coefficient of under-pressure for $ \cfrac{h_l}{D}=3 $ |
$\mathrm{ }$ |
| $K_{Pu-4.2}$ |
coefficient of under-pressure for $ \cfrac{h_l}{D}=4.2 $ |
$\mathrm{ }$ |
| $K_{Pu-4.5}$ |
coefficient of under-pressure for $ \cfrac{h_l}{D}=4.5 $ |
$\mathrm{ }$ |
| $K_{Pu-4}$ |
coefficient of under-pressure for $ \cfrac{h_l}{D}=4 $ |
$\mathrm{ }$ |
| $K_{Pu-5}$ |
coefficient of under-pressure for $ \cfrac{h_l}{D}=5 $ |
$\mathrm{ }$ |
| $K_{Pu-air1-0}$ |
under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=0 $ |
$\mathrm{ }$ |
| $K_{Pu-air1-2.5}$ |
under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=2.5 $ |
$\mathrm{ }$ |
| $K_{Pu-air1-2}$ |
under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=2 $ |
$\mathrm{ }$ |
| $K_{Pu-air1-3.5}$ |
under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=3.5 $ |
$\mathrm{ }$ |
| $K_{Pu-air1-3.6}$ |
under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=3.6 $ |
$\mathrm{ }$ |
| $K_{Pu-air1-3.9}$ |
under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=3.9 $ |
$\mathrm{ }$ |
| $K_{Pu-air1-3}$ |
under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=3 $ |
$\mathrm{ }$ |
| $K_{Pu-air1-4.2}$ |
under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=4.2 $ |
$\mathrm{ }$ |
| $K_{Pu-air1-4.5}$ |
under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=4.5 $ |
$\mathrm{ }$ |
| $K_{Pu-air1-4}$ |
under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=4 $ |
$\mathrm{ }$ |
| $K_{Pu-air1-5}$ |
under-pressure coefficient in hole 1 for $ \cfrac{h_l}{D}=5 $ |
$\mathrm{ }$ |
| $K_{Pu-air1}$ |
under-pressure coefficient in hole 1 |
$\mathrm{ }$ |
| $K_{Pu-air2-0}$ |
under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=0 $ |
$\mathrm{ }$ |
| $K_{Pu-air2-2.5}$ |
under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=2.5 $ |
$\mathrm{ }$ |
| $K_{Pu-air2-2}$ |
under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=2 $ |
$\mathrm{ }$ |
| $K_{Pu-air2-3.5}$ |
under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=3.5 $ |
$\mathrm{ }$ |
| $K_{Pu-air2-3.6}$ |
under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=3.6 $ |
$\mathrm{ }$ |
| $K_{Pu-air2-3.9}$ |
under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=3.9 $ |
$\mathrm{ }$ |
| $K_{Pu-air2-3}$ |
under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=3 $ |
$\mathrm{ }$ |
| $K_{Pu-air2-4.2}$ |
under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=4.2 $ |
$\mathrm{ }$ |
| $K_{Pu-air2-4.5}$ |
under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=4.5 $ |
$\mathrm{ }$ |
| $K_{Pu-air2-4}$ |
under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=4 $ |
$\mathrm{ }$ |
| $K_{Pu-air2-5}$ |
under-pressure coefficient in hole 2 for $ \cfrac{h_l}{D}=5 $ |
$\mathrm{ }$ |
| $K_{Pu-air2}$ |
under-pressure coefficient in hole 2 |
$\mathrm{ }$ |
| $K_{Pu}$ |
coefficient of under-pressure |
$\mathrm{ }$ |
| $K_{Q-hydraulic-cylinder}$ |
flow coefficient $ K_{Q-hydraulic-cylinder} $ |
$\mathrm{ }$ |
| $K_{Q-valve}$ |
flow coefficient $ K_{Q-valve} $ |
$\mathrm{ }$ |
| $K_{Q-valve}[10]$ |
flow coefficient $ K_{Q-valve}[10] $ |
$\mathrm{ }$ |
| $K_{Q-valve}[1]$ |
flow coefficient $ K_{Q-valve}[1] $ |
$\mathrm{ }$ |
| $K_{Q-valve}[2]$ |
flow coefficient $ K_{Q-valve}[2] $ |
$\mathrm{ }$ |
| $K_{Q-valve}[3]$ |
flow coefficient $ K_{Q-valve}[3] $ |
$\mathrm{ }$ |
| $K_{Q-valve}[4]$ |
flow coefficient $ K_{Q-valve}[4] $ |
$\mathrm{ }$ |
| $K_{Q-valve}[5]$ |
flow coefficient $ K_{Q-valve}[5] $ |
$\mathrm{ }$ |
| $K_{Q-valve}[6]$ |
flow coefficient $ K_{Q-valve}[6] $ |
$\mathrm{ }$ |
| $K_{Q-valve}[7]$ |
flow coefficient $ K_{Q-valve}[7] $ |
$\mathrm{ }$ |
| $K_{Q-valve}[8]$ |
flow coefficient $ K_{Q-valve}[8] $ |
$\mathrm{ }$ |
| $K_{Q-valve}[9]$ |
flow coefficient $ K_{Q-valve}[9] $ |
$\mathrm{ }$ |
| $K_{Q-σ_1}$ |
flow coefficient for $ σ_1 $ |
$\mathrm{ }$ |
| $K_{Q-σ_2}$ |
flow coefficient for $ σ_2 $ |
$\mathrm{ }$ |
| $K_{Q-σ_{min}}$ |
flow coefficient for $ σ_{min} $ |
$\mathrm{ }$ |
| $K_{Qmax}$ |
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 |
$\mathrm{ }$ |
| $K_{x-σ_1}$ |
coefficient of hydraulic force on a needle in the axis x for $ σ_1 $ |
$\mathrm{ }$ |
| $K_{x-σ_2}$ |
coefficient of hydraulic force on a needle in the axis x for $ σ_2 $ |
$\mathrm{ }$ |
| $K_{x-σ_{min}}$ |
coefficient of hydraulic force on a needle in the axis x for $ σ_{min} $ |
$\mathrm{ }$ |
| $L$ |
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 |
$\mathrm{mm}$ |
| $L_c$ |
distance between the centre of gravity of the weight (weight + disc + lever) and the axis of pivot rotation |
$\mathrm{mm}$ |
| $L_c$ |
distance between the centre of gravity of the weight (weight + rotating body + lever) and the axis of pivot rotation |
$\mathrm{mm}$ |
| $L_d$ |
damping phase |
$\mathrm{\%}$ |
| $L_{1-10}$ |
coefficient of lenght $ L_1 $ for $ \cfrac{T_x}{D}=10 $ |
$\mathrm{ }$ |
| $L_{1-20}$ |
coefficient of lenght $ L_1 $ for $ \cfrac{T_x}{D}=20 $ |
$\mathrm{ }$ |
| $L_{1-30}$ |
coefficient of lenght $ L_1 $ for $ \cfrac{T_x}{D}=30 $ |
$\mathrm{ }$ |
| $L_{1-40}$ |
coefficient of lenght $ L_1 $ for $ \cfrac{T_x}{D}=40 $ |
$\mathrm{ }$ |
| $L_{2-10}$ |
coefficient of lenght $ L_2 $ for $ \cfrac{T_x}{D}=10 $ |
$\mathrm{ }$ |
| $L_{2-20}$ |
coefficient of lenght $ L_2 $ for $ \cfrac{T_x}{D}=20 $ |
$\mathrm{ }$ |
| $L_{2-30}$ |
coefficient of lenght $ L_2 $ for $ \cfrac{T_x}{D}=30 $ |
$\mathrm{ }$ |
| $L_{2-40}$ |
coefficient of lenght $ L_2 $ for $ \cfrac{T_x}{D}=40 $ |
$\mathrm{ }$ |
| $L_{2-50}$ |
coefficient of lenght $ L_2 $ for $ \cfrac{T_x}{D}=50 $ |
$\mathrm{ }$ |
| $L_{HC}$ |
distance between the axis of hydraulic cylinder and the axis of valve rotation |
$\mathrm{mm}$ |
| $M$ |
hydraulic torque without eccentricity |
$\mathrm{kNm}$ |
| $M$ |
air molar mass at sea level |
$\mathrm{kg\cdot kmol^{-1}}$ |
| $M_B$ |
friction torque bearing during the closing without flow rate |
$\mathrm{kNm}$ |
| $M_H$ |
hydraulic torque |
$\mathrm{kNm}$ |
| $M_S$ |
friction torque in main sealing |
$\mathrm{kNm}$ |
| $M_W$ |
static torque |
$\mathrm{kNm}$ |
| $M_e$ |
moment from eccentricity |
$\mathrm{kNm}$ |
| $M_{B-flow}$ |
friction torque bearing during the closing at flow rate |
$\mathrm{kNm}$ |
| $M_{F-HC}$ |
friction torque from the hydraulic cylinder |
$\mathrm{kNm}$ |
| $M_{LD}$ |
moment from the axis of the trunnion to the axis of the disc |
$\mathrm{kNm}$ |
| $N_A$ |
Avogadro constant |
$\mathrm{kmol^{-1}}$ |
| $P_1$ |
inlet absolute static pressure |
$\mathrm{Pa}$ |
| $P_2$ |
output absolute static pressure |
$\mathrm{Pa}$ |
| $P_S$ |
contact pressure of the main sealing |
$\mathrm{MPa}$ |
| $P_{HC-flow-with-frictional}$ |
pressure of oil under the hydraulic cylinder piston during the closing at flow rate with frictional resistances |
$\mathrm{MPa}$ |
| $P_{HC-flow}$ |
pressure of oil under the hydraulic cylinder piston during the closing at flow rate without frictional resistances |
$\mathrm{MPa}$ |
| $P_{HC-with-frictional}$ |
pressure of oil under the hydraulic cylinder piston during the closing without flow rate with frictional resistances |
$\mathrm{MPa}$ |
| $P_{HC}$ |
pressure of oil under the hydraulic cylinder piston during the closing without flow rate without frictional resistances |
$\mathrm{MPa}$ |
| $P_{L-HC}$ |
pressure loss in the hydraulic cylinder |
$\mathrm{MPa}$ |
| $P_{SV}$ |
saturated vapor pressure |
$\mathrm{Pa}$ |
| $P_{max-stages}$ |
maximum pressures between stages |
$\mathrm{Pa}$ |
| $P_{u-air1}$ |
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 $ |
$\mathrm{mm}$ |
| $R$ |
specific gas constant |
$\mathrm{J\cdot K^{-1}\cdot kg^{-1}}$ |
| $R$ |
specific gas constant of ordinary water |
$\mathrm{J\cdot kg^{-1}\cdot K^{-1}}$ |
| $R^*$ |
universal gas constant |
$\mathrm{J\cdot K^{-1}\cdot kmol^{-1}}$ |
| $S$ |
dimension $ S $ |
$\mathrm{mm}$ |
| $S$ |
stage |
$\mathrm{ }$ |
| $S$ |
Sutherland's empirical coefficients $ S $ |
$\mathrm{K}$ |
| $S/D$ |
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 |
$\mathrm{\%}$ |
| $S_f$ |
safety factor during the closing without flow rate |
$\mathrm{ }$ |
| $S_{S\%}$ |
stroke percentage |
$\mathrm{\%}$ |
| $S_{f-flow}$ |
safety factor during the closing at flow rate |
$\mathrm{ }$ |
| $S_{max}$ |
stroke |
$\mathrm{mm}$ |
| $T$ |
height $ T $ |
$\mathrm{mm}$ |
| $T$ |
temperature $ T $ |
$\mathrm{K}$ |
| $T$ |
the water temperature |
$\mathrm{°C}$ |
| $T^*$ |
temperature reducing quantity |
$\mathrm{K}$ |
| $T_b$ |
lower limit temperature |
$\mathrm{K}$ |
| $T_c$ |
total closing time |
$\mathrm{s}$ |
| $T_d$ |
damping time |
$\mathrm{s}$ |
| $T_s$ |
time value |
$\mathrm{s}$ |
| $T_x$ |
energy before the valve |
$\mathrm{m}$ |
| $W_D$ |
weight of the disc |
$\mathrm{kg}$ |
| $W_L$ |
weight of the lever |
$\mathrm{kg}$ |
| $W_R$ |
weight of the rotating body |
$\mathrm{kg}$ |
| $W_W$ |
weight of the weight |
$\mathrm{kg}$ |
| $\text{Region}$ |
region |
$\mathrm{ }$ |
| $a$ |
dimension $ a $ |
$\mathrm{mm}$ |
| $a$ |
speed pressure waves in the pipe |
$\mathrm{m/s}$ |
| $a$ |
distance to hydraulic cylinder $ a $ |
$\mathrm{mm}$ |
| $a$ |
speed of Sound |
$\mathrm{m/s}$ |
| $a_1$ |
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 $ |
$\mathrm{mm}$ |
| $c_p$ |
specific isobaric heat capacity |
$\mathrm{J\cdot kg^{-1}\cdot K^{-1}}$ |
| $c_{ef}$ |
effective closing time factor |
$\mathrm{ }$ |
| $c_ν$ |
specific isochoric heat capacity |
$\mathrm{J\cdot kg^{-1}\cdot K^{-1}}$ |
| $d$ |
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 |
$\mathrm{mm}$ |
| $e_S$ |
width of main seal in contact |
$\mathrm{mm}$ |
| $f$ |
dimension $ f $ |
$\mathrm{mm}$ |
| $f_B$ |
the bearing factor of the bushings, defined as the sum of the forces in the bushings divided by the load force |
$\mathrm{ }$ |
| $f_r$ |
reduced free flow area in the throttle control system |
$\mathrm{ }$ |
| $f_{air}$ |
coefficient of under-pressure of aerated hole |
$\mathrm{ }$ |
| $g$ |
dimension $ g $ |
$\mathrm{mm}$ |
| $g$ |
gravitational acceleration |
$\mathrm{m/s^2}$ |
| $h$ |
dimension $ h $ |
$\mathrm{mm}$ |
| $h$ |
specific enthalpy |
$\mathrm{J\cdot kg^{-1}}$ |
| $h$ |
height above sea level |
$\mathrm{m}$ |
| $h_j$ |
water depth behind the hydraulic jump |
$\mathrm{m}$ |
| $h_l$ |
water level |
$\mathrm{m}$ |
| $h_{l-10}$ |
coefficient of water level for $ \cfrac{T_x}{D}=10 $ |
$\mathrm{ }$ |
| $h_{l-20}$ |
coefficient of water level for $ \cfrac{T_x}{D}=20 $ |
$\mathrm{ }$ |
| $h_{l-30}$ |
coefficient of water level for $ \cfrac{T_x}{D}=30 $ |
$\mathrm{ }$ |
| $h_{l-40}$ |
coefficient of water level for $ \cfrac{T_x}{D}=40 $ |
$\mathrm{ }$ |
| $h_{l-50}$ |
coefficient of water level for $ \cfrac{T_x}{D}=50 $ |
$\mathrm{ }$ |
| $i$ |
dimension $ i $ |
$\mathrm{mm}$ |
| $i$ |
number of rows |
$\mathrm{ }$ |
| $j$ |
dimension $ j $ |
$\mathrm{mm}$ |
| $k$ |
dimension $ k $ |
$\mathrm{mm}$ |
| $l$ |
dimension $ l $ |
$\mathrm{mm}$ |
| $l$ |
rod length |
$\mathrm{mm}$ |
| $l$ |
mean free path of air particles |
$\mathrm{m}$ |
| $m$ |
dimension $ m $ |
$\mathrm{mm}$ |
| $n$ |
aeration |
$\mathrm{ }$ |
| $n$ |
dimension $ n $ |
$\mathrm{mm}$ |
| $n$ |
air number density |
$\mathrm{m^{-3}}$ |
| $n$ |
coefficient $ n $ |
$\mathrm{ }$ |
| $n^o$ |
coefficient $ n^o $ |
$\mathrm{ }$ |
| $n_{max}$ |
allowable maximum number of holes in one row |
$\mathrm{ }$ |
| $n_{s}$ |
number of stages |
$\mathrm{ }$ |
| $o$ |
dimension $ o $ |
$\mathrm{mm}$ |
| $p$ |
pressure parameter |
$\mathrm{ }$ |
| $p$ |
dimension $ p $ |
$\mathrm{mm}$ |
| $p$ |
the water pressure |
$\mathrm{Pa}$ |
| $p^*$ |
pressure reducing quantity |
$\mathrm{Pa}$ |
| $p_b$ |
lower limit pressure |
$\mathrm{Pa}$ |
| $p_{air}$ |
under-pressure in the aerated pipeline |
$\mathrm{Pa}$ |
| $p_{air}$ |
atmospheric pressure air |
$\mathrm{Pa}$ |
| $q$ |
dimension $ q $ |
$\mathrm{mm}$ |
| $r$ |
dimension $ r $ |
$\mathrm{mm}$ |
| $r$ |
lever arm length |
$\mathrm{mm}$ |
| $r$ |
nominal earth's radius |
$\mathrm{m}$ |
| $r_T$ |
radius of trunnions for bearings |
$\mathrm{mm}$ |
| $s$ |
stroke from open position |
$\mathrm{\%}$ |
| $s$ |
dimension $ s $ |
$\mathrm{mm}$ |
| $s$ |
specific entropy |
$\mathrm{J\cdot kg^{-1}\cdot K^{-1}}$ |
| $t$ |
closing time |
$\mathrm{s}$ |
| $t$ |
dimension $ t $ |
$\mathrm{mm}$ |
| $t_{ef}$ |
effective closing time |
$\mathrm{s}$ |
| $u$ |
dimension $ u $ |
$\mathrm{mm}$ |
| $u$ |
specific internal energy |
$\mathrm{J\cdot kg^{-1}}$ |
| $v$ |
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 |
$\mathrm{m/s}$ |
| $v̄$ |
mean air-particle speed |
$\mathrm{m/s}$ |
| $w$ |
dimension $ w $ |
$\mathrm{mm}$ |
| $w$ |
speed of sound |
$\mathrm{m\cdot s^{-1}}$ |
| $x$ |
dimension $ x $ |
$\mathrm{mm}$ |
| $y$ |
dimension $ y $ |
$\mathrm{mm}$ |
| $z$ |
dimension $ z $ |
$\mathrm{mm}$ |
| $ΔP$ |
water hammer |
$\mathrm{m}$ |
| $ΔP_{stages}$ |
pressure difference between the stages |
$\mathrm{Pa}$ |
| $Δ_h$ |
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 |
$\mathrm{°}$ |
| $α_c$ |
angle of rotation centre of gravity in open position |
$\mathrm{°}$ |
| $α_p$ |
relative pressure coefficient |
$\mathrm{K^{-1}}$ |
| $α_ν$ |
isobaric cubic expansion coefficient |
$\mathrm{K^{-1}}$ |
| $β$ |
aerated coefficient |
$\mathrm{ }$ |
| $β$ |
swing angle |
$\mathrm{°}$ |
| $β$ |
temperature gradient $ β $ |
$\mathrm{K\cdot m^{-1}}$ |
| $β_S$ |
angle rotation of the rocking motion |
$\mathrm{°}$ |
| $β_p$ |
isothermal stress coefficient |
$\mathrm{kg\cdot m^{-3}}$ |
| $β_s$ |
Sutherland's empirical coefficients $ β_s $ |
$\mathrm{kg\cdot m^{-1}\cdot s^{-1}\cdot K^{-1/2}}$ |
| $γ$ |
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 |
$\mathrm{°}$ |
| $γ$ |
dimensionless Gibbs free energy |
$\mathrm{ }$ |
| $γ^o$ |
ideal-gas part |
$\mathrm{ }$ |
| $γ^o_{ππ}$ |
second partial derivative of $ γ^o $ with respect to $ π $ |
$\mathrm{ }$ |
| $γ^o_{πτ}$ |
cross derivative of $ γ^o $ with respect to $ π $ and temperature $ τ $ |
$\mathrm{ }$ |
| $γ^o_{ττ}$ |
second partial derivative of $ γ^o $ with respect to $ τ $ |
$\mathrm{ }$ |
| $γ^o_π$ |
derivative of $ γ^o $ with respect to the dimensionless pressure $ π $ |
$\mathrm{ }$ |
| $γ^o_τ$ |
partial derivative of $ γ^o $ with respect to $ τ $ |
$\mathrm{ }$ |
| $γ^r$ |
residual part |
$\mathrm{ }$ |
| $γ^r_{ππ}$ |
second partial derivative of $ γ^r $ with respect to $ π $ |
$\mathrm{ }$ |
| $γ^r_{πτ}$ |
cross derivative of $ γ^r $ with respect to $ π $ and temperature $ τ $ |
$\mathrm{ }$ |
| $γ^r_{ττ}$ |
second partial derivative of $ γ^r $ with respect to $ τ $ |
$\mathrm{ }$ |
| $γ^r_π$ |
derivative of $ γ^r $ with respect to the dimensionless pressure $ π $ |
$\mathrm{ }$ |
| $γ^r_τ$ |
partial derivative of $ γ^r $ with respect to $ τ $ |
$\mathrm{ }$ |
| $γ_{air}$ |
specific weight air |
$\mathrm{kg\cdot m^{-2}\cdot s^{-2}}$ |
| $γ_{ππ}$ |
second partial derivative of $ γ $ with respect to $ π $ |
$\mathrm{ }$ |
| $γ_{πτ}$ |
cross derivative of $ γ $ with respect to $ π $ and temperature $ τ $ |
$\mathrm{ }$ |
| $γ_{ττ}$ |
second partial derivative of $ γ $ with respect to $ τ $ |
$\mathrm{ }$ |
| $γ_π$ |
derivative of $ γ $ with respect to the dimensionless pressure $ π $ |
$\mathrm{ }$ |
| $γ_τ$ |
partial derivative of $ γ $ with respect to $ τ $ |
$\mathrm{ }$ |
| $δ$ |
the angle between the lever axis and the imaginary line between the valve axis and the pivot axis of the hydraulic cylinder |
$\mathrm{°}$ |
| $δ$ |
reduced density |
$\mathrm{ }$ |
| $δ_{[0]}$ |
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 |
$\mathrm{°}$ |
| $ζ$ |
loss coefficient |
$\mathrm{ }$ |
| $ζ$ |
valve loss coefficient |
$\mathrm{ }$ |
| $θ$ |
reduced temperature |
$\mathrm{ }$ |
| $θ$ |
transformed temperature |
$\mathrm{ }$ |
| $κ$ |
adiabatic index |
$\mathrm{ }$ |
| $κ_T$ |
isothermal compressibility |
$\mathrm{Pa^{-1}}$ |
| $λ$ |
thermal conductivity |
$\mathrm{W\cdot m^{-1}\cdot K^{-1}}$ |
| $μ$ |
discharge coefficient |
$\mathrm{ }$ |
| $μ$ |
dynamic viscosity |
$\mathrm{kg\cdot m^{-1}\cdot s^{-1}}$ |
| $μ_B$ |
coefficient of friction for bearings |
$\mathrm{ }$ |
| $μ_S$ |
coefficient of friction for main sealing |
$\mathrm{ }$ |
| $ν$ |
kinematic viscosity |
$\mathrm{m^2\cdot s^{-1}}$ |
| $ν$ |
specific volume |
$\mathrm{m^3\cdot kg^{-1}}$ |
| $π$ |
reduced pressure |
$\mathrm{ }$ |
| $ρ$ |
density |
$\mathrm{kg/m^3}$ |
| $ρ$ |
mass density |
$\mathrm{kg\cdot m^{-3}}$ |
| $ρ^*$ |
mass density reducing quantity |
$\mathrm{kg\cdot m^{-3}}$ |
| $ρ_{air}$ |
density air |
$\mathrm{kg/m^3}$ |
| $σ$ |
cavitation number |
$\mathrm{ }$ |
| $σ$ |
effective collision diameter of an air molecule |
$\mathrm{m}$ |
| $σ_1$ |
first stage of cavitation |
$\mathrm{ }$ |
| $σ_2$ |
second stage of cavitation |
$\mathrm{ }$ |
| $σ_{min}$ |
fully developed cavitation |
$\mathrm{ }$ |
| $τ$ |
inverse reduced temperature |
$\mathrm{ }$ |
| $φ$ |
angle between pipe axis and hydraulic force |
$\mathrm{°}$ |
| $φ$ |
lever angle in open position |
$\mathrm{°}$ |
| $φ$ |
dimensionless Helmholtz free energy |
$\mathrm{ }$ |
| $φ_{δδ}$ |
second partial derivative of $ φ $ with respect to $ δ $ |
$\mathrm{ }$ |
| $φ_{δτ}$ |
cross derivative of $ φ $ with respect to $ δ $ and temperature $ τ $ |
$\mathrm{ }$ |
| $φ_{ττ}$ |
second partial derivative of $ φ $ with respect to $ τ $ |
$\mathrm{ }$ |
| $φ_δ$ |
derivative of $ φ $ with respect to the dimensionless density $ δ $ |
$\mathrm{ }$ |
| $φ_τ$ |
partial derivative of $ φ $ with respect to $ τ $ |
$\mathrm{ }$ |
| $ω$ |
air-particle collision frequency |
$\mathrm{Hz}$ |
