| $A$
| 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 | $\mathrm{m}$
|
| $H$
| 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 | $\mathrm{m}$
|
| $K_B$
| coefficient $ K_B $ | $\mathrm{ }$
|
| $K_Q$
| flow coefficient | $\mathrm{ }$
|
| $K_T$
| coefficient $ K_T $ | $\mathrm{ }$
|
| $L$
| pipe length behind the gate | $\mathrm{m}$
|
| $M$
| air molar mass at sea level | $\mathrm{kg\cdot kmol^{-1}}$
|
| $N_A$
| Avogadro constant | $\mathrm{kmol^{-1}}$
|
| $P$
| downpull force | $\mathrm{kN}$
|
| $P_1$
| 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 | $\mathrm{Pa}$
|
| $P_{u}$
| 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 | $\mathrm{m^3/s}$
|
| $R$
| specific gas constant | $\mathrm{J\cdot K^{-1}\cdot kg^{-1}}$
|
| $R^*$
| universal gas constant | $\mathrm{J\cdot K^{-1}\cdot kmol^{-1}}$
|
| $S$
| Sutherland's empirical coefficients $ S $ | $\mathrm{K}$
|
| $T$
| temperature $ T $ | $\mathrm{K}$
|
| $T$
| the water temperature | $\mathrm{°C}$
|
| $T_b$
| lower limit temperature | $\mathrm{K}$
|
| $W$
| force on gate | $\mathrm{kN}$
|
| $a$
| 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 | $\mathrm{mm}$
|
| $c_{ef}$
| effective closing time factor | $\mathrm{ }$
|
| $d$
| 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 | $\mathrm{m/s^2}$
|
| $h$
| height above sea level | $\mathrm{m}$
|
| $h_c$
| depth of water at vena contracta | $\mathrm{m}$
|
| $l$
| mean free path of air particles | $\mathrm{m}$
|
| $n$
| air number density | $\mathrm{m^{-3}}$
|
| $p$
| pressure parameter | $\mathrm{ }$
|
| $p_b$
| lower limit pressure | $\mathrm{Pa}$
|
| $p_{air}$
| under-pressure in the aerated pipeline | $\mathrm{Pa}$
|
| $p_{air}$
| atmospheric pressure air | $\mathrm{Pa}$
|
| $r$
| radius of curvature for the rounding of the gate lip | $\mathrm{mm}$
|
| $r$
| nominal earth's radius | $\mathrm{m}$
|
| $s$
| gate opening | $\mathrm{mm}$
|
| $s/s_0$
| gate position | $\mathrm{ }$
|
| $s_0$
| conduit height immediately upstream from the gate | $\mathrm{mm}$
|
| $s_s$
| gate sealing height | $\mathrm{mm}$
|
| $t$
| closing time | $\mathrm{s}$
|
| $v$
| 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 | $\mathrm{m/s}$
|
| $ΔP$
| water hammer | $\mathrm{m}$
|
| $Δ_h$
| theoretical pressure in the gate at full opening | $\mathrm{m}$
|
| $β$
| aerated coefficient | $\mathrm{ }$
|
| $β$
| temperature gradient $ β $ | $\mathrm{K\cdot m^{-1}}$
|
| $β_s$
| Sutherland's empirical coefficients $ β_s $ | $\mathrm{kg\cdot m^{-1}\cdot s^{-1}\cdot K^{-1/2}}$
|
| $γ_{air}$
| specific weight air | $\mathrm{kg\cdot m^{-2}\cdot s^{-2}}$
|
| $ζ$
| loss coefficient | $\mathrm{ }$
|
| $θ$
| angle of inclination of the bottom surface of the gate | $\mathrm{°}$
|
| $θ$
| transformed temperature | $\mathrm{ }$
|
| $κ$
| adiabatic index | $\mathrm{ }$
|
| $λ$
| thermal conductivity | $\mathrm{W\cdot m^{-1}\cdot K^{-1}}$
|
| $μ$
| dynamic viscosity | $\mathrm{kg\cdot m^{-1}\cdot s^{-1}}$
|
| $ν$
| kinematic viscosity | $\mathrm{m^2\cdot s^{-1}}$
|
| $ρ$
| density | $\mathrm{kg/m^3}$
|
| $ρ_{air}$
| density air | $\mathrm{kg/m^3}$
|
| $σ$
| cavitation number | $\mathrm{ }$
|
| $σ$
| effective collision diameter of an air molecule | $\mathrm{m}$
|
| $ω$
| air-particle collision frequency | $\mathrm{Hz}$
|
