| $A$ |
cross-sectional area of the conduit |
$\mathrm{m^2}$ |
| $A$ |
function $ A $ |
$\mathrm{ }$ |
| $A_1$ |
minimum cross-sectional area between upstream face of the gate and upstream wall of the gate chamber |
$\mathrm{mm^2}$ |
| $A_2$ |
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 |
$\mathrm{mm^2}$ |
| $A_s$ |
area of the horizontal projection of the top seal |
$\mathrm{m^2}$ |
| $A_{air-pipe}$ |
the flow area of the aerated pipeline |
$\mathrm{m^2}$ |
| $A_{air}$ |
the flow area of the aerated hole |
$\mathrm{m^2}$ |
| $B$ |
width of the gate |
$\mathrm{mm}$ |
| $B$ |
function $ B $ |
$\mathrm{ }$ |
| $C$ |
function $ C $ |
$\mathrm{ }$ |
| $C_c$ |
coefficient of contraction |
$\mathrm{ }$ |
| $F_c$ |
Froude number |
$\mathrm{ }$ |
| $H$ |
total head in the reservoir |
$\mathrm{m}$ |
| $H$ |
height of the flap gate at the maximum angle of erection |
$\mathrm{mm}$ |
| $H$ |
geopotential altitude |
$\mathrm{m}$ |
| $H_L$ |
loss of pressure on the gate |
$\mathrm{m}$ |
| $H_b$ |
lower limit geopotential altitude |
$\mathrm{m}$ |
| $H_p$ |
pressure scale height |
$\mathrm{m}$ |
| $H_v$ |
pressure on the gate |
$\mathrm{m}$ |
| $I$ |
exponent $ I $ |
$\mathrm{ }$ |
| $J$ |
exponent $ J $ |
$\mathrm{ }$ |
| $J^o$ |
exponent $ J^o $ |
$\mathrm{ }$ |
| $K_B$ |
coefficient $ K_B $ |
$\mathrm{ }$ |
| $K_Q$ |
flow coefficient |
$\mathrm{ }$ |
| $K_T$ |
coefficient $ K_T $ |
$\mathrm{ }$ |
| $K_{m-air-face}$ |
coefficient of moment on the flap air face |
$\mathrm{ }$ |
| $K_{m-guide-face}$ |
coefficient of moment on the flap guide face |
$\mathrm{ }$ |
| $K_{position-0°-air-face}$ |
coefficient of load on the flap air face in the 0° position |
$\mathrm{ }$ |
| $K_{position-0°-guide-face}$ |
coefficient of load on the flap guide face in the 0° position |
$\mathrm{ }$ |
| $K_{position-10°-air-face}$ |
coefficient of load on the flap air face in the 10° position |
$\mathrm{ }$ |
| $K_{position-10°-guide-face}$ |
coefficient of load on the flap guide face in the 10° position |
$\mathrm{ }$ |
| $K_{position-15°-air-face}$ |
coefficient of load on the flap air face in the 15° position |
$\mathrm{ }$ |
| $K_{position-15°-guide-face}$ |
coefficient of load on the flap guide face in the 15° position |
$\mathrm{ }$ |
| $K_{position-20°-air-face}$ |
coefficient of load on the flap air face in the 20° position |
$\mathrm{ }$ |
| $K_{position-20°-guide-face}$ |
coefficient of load on the flap guide face in the 20° position |
$\mathrm{ }$ |
| $K_{position-25°-air-face}$ |
coefficient of load on the flap air face in the 25° position |
$\mathrm{ }$ |
| $K_{position-25°-guide-face}$ |
coefficient of load on the flap guide face in the 25° position |
$\mathrm{ }$ |
| $K_{position-30°-air-face}$ |
coefficient of load on the flap air face in the 30° position |
$\mathrm{ }$ |
| $K_{position-30°-guide-face}$ |
coefficient of load on the flap guide face in the 30° position |
$\mathrm{ }$ |
| $K_{position-35°-air-face}$ |
coefficient of load on the flap air face in the 35° position |
$\mathrm{ }$ |
| $K_{position-35°-guide-face}$ |
coefficient of load on the flap guide face in the 35° position |
$\mathrm{ }$ |
| $K_{position-40°-air-face}$ |
coefficient of load on the flap air face in the 40° position |
$\mathrm{ }$ |
| $K_{position-40°-guide-face}$ |
coefficient of load on the flap guide face in the 40° position |
$\mathrm{ }$ |
| $K_{position-45°-air-face}$ |
coefficient of load on the flap air face in the 45° position |
$\mathrm{ }$ |
| $K_{position-45°-guide-face}$ |
coefficient of load on the flap guide face in the 45° position |
$\mathrm{ }$ |
| $K_{position-50°-air-face}$ |
coefficient of load on the flap air face in the 50° position |
$\mathrm{ }$ |
| $K_{position-50°-guide-face}$ |
coefficient of load on the flap guide face in the 50° position |
$\mathrm{ }$ |
| $K_{position-55°-air-face}$ |
coefficient of load on the flap air face in the 55° position |
$\mathrm{ }$ |
| $K_{position-55°-guide-face}$ |
coefficient of load on the flap guide face in the 55° position |
$\mathrm{ }$ |
| $K_{position-5°-air-face}$ |
coefficient of load on the flap air face in the 5° position |
$\mathrm{ }$ |
| $K_{position-5°-guide-face}$ |
coefficient of load on the flap guide face in the 5° position |
$\mathrm{ }$ |
| $K_{position-60°-air-face}$ |
coefficient of load on the flap air face in the 60° position |
$\mathrm{ }$ |
| $K_{position-60°-guide-face}$ |
coefficient of load on the flap guide face in the 60° position |
$\mathrm{ }$ |
| $K_{position-65°-air-face}$ |
coefficient of load on the flap air face in the 65° position |
$\mathrm{ }$ |
| $K_{position-65°-guide-face}$ |
coefficient of load on the flap guide face in the 65° position |
$\mathrm{ }$ |
| $K_{position-70°-air-face}$ |
coefficient of load on the flap air face in the 70° position |
$\mathrm{ }$ |
| $K_{position-70°-guide-face}$ |
coefficient of load on the flap guide face in the 70° position |
$\mathrm{ }$ |
| $K_{position-75°-air-face}$ |
coefficient of load on the flap air face in the 75° position |
$\mathrm{ }$ |
| $K_{position-75°-guide-face}$ |
coefficient of load on the flap guide face in the 75° position |
$\mathrm{ }$ |
| $K_{position-80°-air-face}$ |
coefficient of load on the flap air face in the 80° position |
$\mathrm{ }$ |
| $K_{position-80°-guide-face}$ |
coefficient of load on the flap guide face in the 80° position |
$\mathrm{ }$ |
| $K_{position-85°-air-face}$ |
coefficient of load on the flap air face in the 85° position |
$\mathrm{ }$ |
| $K_{position-85°-guide-face}$ |
coefficient of load on the flap guide face in the 85° position |
$\mathrm{ }$ |
| $L$ |
pipe length behind the gate |
$\mathrm{m}$ |
| $M$ |
air molar mass at sea level |
$\mathrm{kg\cdot kmol^{-1}}$ |
| $M_T$ |
total moment on the flap |
$\mathrm{kNm}$ |
| $M_{air-face}$ |
moment on the flap air face |
$\mathrm{kNm}$ |
| $M_{guide-face}$ |
moment on the flap guide face |
$\mathrm{kNm}$ |
| $N_A$ |
Avogadro constant |
$\mathrm{kmol^{-1}}$ |
| $P$ |
downpull force |
$\mathrm{kN}$ |
| $P$ |
dimension $ P $ |
$\mathrm{mm}$ |
| $P(h)$ |
pressure at height $ (h) $ |
$\mathrm{Pa}$ |
| $P_0$ |
pressure at sea level |
$\mathrm{Pa}$ |
| $P_1$ |
downpull resulting from the difference between the pressures acting on the top and bottom surfaces of the gate |
$\mathrm{kN}$ |
| $P_2$ |
downpull resulting from the pressure differential acting on the horizontal protrusions of the gate |
$\mathrm{kN}$ |
| $P_3$ |
downpull resulting from the lip |
$\mathrm{kN}$ |
| $P_{SV}$ |
saturated vapor pressure |
$\mathrm{Pa}$ |
| $P_{air-face}$ |
points on the air face |
$\mathrm{ }$ |
| $P_{guide-face}$ |
points on the guide face |
$\mathrm{ }$ |
| $P_{u}$ |
under-pressure behind the gate |
$\mathrm{m}$ |
| $Q$ |
flow of water before the gate |
$\mathrm{m^3/s}$ |
| $Q_p$ |
relative flow |
$\mathrm{ }$ |
| $Q_{air}$ |
air flow |
$\mathrm{m^3/s}$ |
| $Q_{max}$ |
flow |
$\mathrm{m^3/s}$ |
| $R$ |
radius of the guide face of the flap gate |
$\mathrm{mm}$ |
| $R$ |
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 |
$\mathrm{J\cdot K^{-1}\cdot kmol^{-1}}$ |
| $R_1$ |
radius of the air face of the flap gate |
$\mathrm{mm}$ |
| $S$ |
Sutherland's empirical coefficients $ S $ |
$\mathrm{K}$ |
| $T$ |
temperature $ T $ |
$\mathrm{K}$ |
| $T$ |
standard temperature at sea level |
$\mathrm{K}$ |
| $T$ |
the water temperature |
$\mathrm{°C}$ |
| $T^*$ |
temperature reducing quantity |
$\mathrm{K}$ |
| $T_b$ |
lower limit temperature |
$\mathrm{K}$ |
| $W$ |
force on gate |
$\mathrm{kN}$ |
| $\text{Region}$ |
region |
$\mathrm{ }$ |
| $a$ |
speed of Sound |
$\mathrm{m/s}$ |
| $a_1$ |
width of clearance between upstream face of the gate and upstream wall of the gate chamber |
$\mathrm{mm}$ |
| $a_2$ |
width of clearance between the downstream face of the gate and the downstream wall of the gate chamber |
$\mathrm{mm}$ |
| $b$ |
clear width of the conduit at the gate section |
$\mathrm{mm}$ |
| $c_p$ |
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 |
$\mathrm{J\cdot kg^{-1}\cdot K^{-1}}$ |
| $d$ |
gate thickness |
$\mathrm{mm}$ |
| $d^´$ |
thickness of the skinplate |
$\mathrm{mm}$ |
| $e$ |
projection of the skinplate |
$\mathrm{mm}$ |
| $e/d$ |
ratio $ e/d $ |
$\mathrm{ }$ |
| $f_r$ |
reduced free flow area in the throttle control system |
$\mathrm{ }$ |
| $f_{air}$ |
coefficient of under-pressure of aerated hole |
$\mathrm{ }$ |
| $g$ |
gravitational acceleration |
$\mathrm{m/s^2}$ |
| $h$ |
specific enthalpy |
$\mathrm{J\cdot kg^{-1}}$ |
| $h$ |
height above sea level |
$\mathrm{m}$ |
| $h_b$ |
depth of bottom water below flap gate |
$\mathrm{mm}$ |
| $h_c$ |
depth of water at vena contracta |
$\mathrm{m}$ |
| $h_t$ |
depth of top water above flap gate |
$\mathrm{mm}$ |
| $l$ |
mean free path of air particles |
$\mathrm{m}$ |
| $n$ |
air number density |
$\mathrm{m^{-3}}$ |
| $n$ |
coefficient $ n $ |
$\mathrm{ }$ |
| $n^o$ |
coefficient $ n^o $ |
$\mathrm{ }$ |
| $p$ |
pressure parameter |
$\mathrm{ }$ |
| $p$ |
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 |
$\mathrm{Pa}$ |
| $p_{position-0°-air-face}$ |
pressure values at the point of sampling on the flap air face in the 0° position |
$\mathrm{Pa}$ |
| $p_{position-0°-guide-face}$ |
pressure values at the point of sampling on the flap guide face in the 0° position |
$\mathrm{Pa}$ |
| $p_{position-10°-air-face}$ |
pressure values at the point of sampling on the flap air face in the 10° position |
$\mathrm{Pa}$ |
| $p_{position-10°-guide-face}$ |
pressure values at the point of sampling on the flap guide face in the 10° position |
$\mathrm{Pa}$ |
| $p_{position-15°-air-face}$ |
pressure values at the point of sampling on the flap air face in the 15° position |
$\mathrm{Pa}$ |
| $p_{position-15°-guide-face}$ |
pressure values at the point of sampling on the flap guide face in the 15° position |
$\mathrm{Pa}$ |
| $p_{position-20°-air-face}$ |
pressure values at the point of sampling on the flap air face in the 20° position |
$\mathrm{Pa}$ |
| $p_{position-20°-guide-face}$ |
pressure values at the point of sampling on the flap guide face in the 20° position |
$\mathrm{Pa}$ |
| $p_{position-25°-air-face}$ |
pressure values at the point of sampling on the flap air face in the 25° position |
$\mathrm{Pa}$ |
| $p_{position-25°-guide-face}$ |
pressure values at the point of sampling on the flap guide face in the 25° position |
$\mathrm{Pa}$ |
| $p_{position-30°-air-face}$ |
pressure values at the point of sampling on the flap air face in the 30° position |
$\mathrm{Pa}$ |
| $p_{position-30°-guide-face}$ |
pressure values at the point of sampling on the flap guide face in the 30° position |
$\mathrm{Pa}$ |
| $p_{position-35°-air-face}$ |
pressure values at the point of sampling on the flap air face in the 35° position |
$\mathrm{Pa}$ |
| $p_{position-35°-guide-face}$ |
pressure values at the point of sampling on the flap guide face in the 35° position |
$\mathrm{Pa}$ |
| $p_{position-40°-air-face}$ |
pressure values at the point of sampling on the flap air face in the 40° position |
$\mathrm{Pa}$ |
| $p_{position-40°-guide-face}$ |
pressure values at the point of sampling on the flap guide face in the 40° position |
$\mathrm{Pa}$ |
| $p_{position-45°-air-face}$ |
pressure values at the point of sampling on the flap air face in the 45° position |
$\mathrm{Pa}$ |
| $p_{position-45°-guide-face}$ |
pressure values at the point of sampling on the flap guide face in the 45° position |
$\mathrm{Pa}$ |
| $p_{position-50°-air-face}$ |
pressure values at the point of sampling on the flap air face in the 50° position |
$\mathrm{Pa}$ |
| $p_{position-50°-guide-face}$ |
pressure values at the point of sampling on the flap guide face in the 50° position |
$\mathrm{Pa}$ |
| $p_{position-55°-air-face}$ |
pressure values at the point of sampling on the flap air face in the 55° position |
$\mathrm{Pa}$ |
| $p_{position-55°-guide-face}$ |
pressure values at the point of sampling on the flap guide face in the 55° position |
$\mathrm{Pa}$ |
| $p_{position-5°-air-face}$ |
pressure values at the point of sampling on the flap air face in the 5° position |
$\mathrm{Pa}$ |
| $p_{position-5°-guide-face}$ |
pressure values at the point of sampling on the flap guide face in the 5° position |
$\mathrm{Pa}$ |
| $p_{position-60°-air-face}$ |
pressure values at the point of sampling on the flap air face in the 60° position |
$\mathrm{Pa}$ |
| $p_{position-60°-guide-face}$ |
pressure values at the point of sampling on the flap guide face in the 60° position |
$\mathrm{Pa}$ |
| $p_{position-65°-air-face}$ |
pressure values at the point of sampling on the flap air face in the 65° position |
$\mathrm{Pa}$ |
| $p_{position-65°-guide-face}$ |
pressure values at the point of sampling on the flap guide face in the 65° position |
$\mathrm{Pa}$ |
| $p_{position-70°-air-face}$ |
pressure values at the point of sampling on the flap air face in the 70° position |
$\mathrm{Pa}$ |
| $p_{position-70°-guide-face}$ |
pressure values at the point of sampling on the flap guide face in the 70° position |
$\mathrm{Pa}$ |
| $p_{position-75°-air-face}$ |
pressure values at the point of sampling on the flap air face in the 75° position |
$\mathrm{Pa}$ |
| $p_{position-75°-guide-face}$ |
pressure values at the point of sampling on the flap guide face in the 75° position |
$\mathrm{Pa}$ |
| $p_{position-80°-air-face}$ |
pressure values at the point of sampling on the flap air face in the 80° position |
$\mathrm{Pa}$ |
| $p_{position-80°-guide-face}$ |
pressure values at the point of sampling on the flap guide face in the 80° position |
$\mathrm{Pa}$ |
| $p_{position-85°-air-face}$ |
pressure values at the point of sampling on the flap air face in the 85° position |
$\mathrm{Pa}$ |
| $p_{position-85°-guide-face}$ |
pressure values at the point of sampling on the flap guide face in the 85° position |
$\mathrm{Pa}$ |
| $r$ |
radius of curvature for the rounding of the gate lip |
$\mathrm{mm}$ |
| $r$ |
nominal earth's radius |
$\mathrm{m}$ |
| $s$ |
gate opening |
$\mathrm{mm}$ |
| $s$ |
specific entropy |
$\mathrm{J\cdot kg^{-1}\cdot K^{-1}}$ |
| $s/s_0$ |
gate position |
$\mathrm{ }$ |
| $s_0$ |
conduit height immediately upstream from the gate |
$\mathrm{mm}$ |
| $s_s$ |
gate sealing height |
$\mathrm{mm}$ |
| $t$ |
closing time |
$\mathrm{s}$ |
| $u$ |
specific internal energy |
$\mathrm{J\cdot kg^{-1}}$ |
| $v$ |
water velocity before the gate |
$\mathrm{m/s}$ |
| $v_j$ |
velocity in the contracted jet issuing from underneath the gate |
$\mathrm{m/s}$ |
| $v_{air}$ |
air velocity |
$\mathrm{m/s}$ |
| $v_{max}$ |
velocity before the gate |
$\mathrm{m/s}$ |
| $v̄$ |
mean air-particle speed |
$\mathrm{m/s}$ |
| $w$ |
speed of sound |
$\mathrm{m\cdot s^{-1}}$ |
| $ΔP$ |
water hammer |
$\mathrm{m}$ |
| $Δ_h$ |
theoretical pressure in the gate at full opening |
$\mathrm{m}$ |
| $α$ |
flap gate tilt angle |
$\mathrm{°}$ |
| $α_p$ |
relative pressure coefficient |
$\mathrm{K^{-1}}$ |
| $α_ν$ |
isobaric cubic expansion coefficient |
$\mathrm{K^{-1}}$ |
| $β$ |
aerated coefficient |
$\mathrm{ }$ |
| $β$ |
temperature gradient $ β $ |
$\mathrm{K\cdot m^{-1}}$ |
| $β_p$ |
isothermal stress coefficient |
$\mathrm{kg\cdot m^{-3}}$ |
| $β_s$ |
Sutherland's empirical coefficients $ β_s $ |
$\mathrm{kg\cdot m^{-1}\cdot s^{-1}\cdot K^{-1/2}}$ |
| $γ$ |
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 $ |
$\mathrm{ }$ |
| $δ$ |
reduced density |
$\mathrm{ }$ |
| $ζ$ |
loss coefficient |
$\mathrm{ }$ |
| $θ$ |
angle of inclination of the bottom surface of the gate |
$\mathrm{°}$ |
| $θ$ |
reduced temperature |
$\mathrm{ }$ |
| $θ$ |
transformed temperature |
$\mathrm{ }$ |
| $κ$ |
adiabatic index |
$\mathrm{ }$ |
| $κ_T$ |
isothermal compressibility |
$\mathrm{Pa^{-1}}$ |
| $λ$ |
thermal conductivity |
$\mathrm{W\cdot m^{-1}\cdot K^{-1}}$ |
| $μ$ |
dynamic viscosity |
$\mathrm{kg\cdot m^{-1}\cdot s^{-1}}$ |
| $ν$ |
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 |
$\mathrm{m}$ |
| $τ$ |
inverse reduced temperature |
$\mathrm{ }$ |
| $φ$ |
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 |
$\mathrm{Hz}$ |
