|
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}[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_{test} |
test |
\mathrm{mm} |
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(h) |
pressure at height (h) |
\mathrm{Pa} |
P_0 |
pressure at sea level |
\mathrm{Pa} |
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 |
standard temperature at sea level |
\mathrm{K} |
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} |