| 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} |
