# List of symbols

Symbol | Name of the symbol | Unit |
---|---|---|

$A$ | cross-sectional area of the conduit | $\mathrm{m^2}$ |

$A_1$ | 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 | $\mathrm{mm}$ |

$C_c$ | coefficient of contraction | $\mathrm{ }$ |

$F_c$ | Froude number | $\mathrm{ }$ |

$H$ | total head in the reservoir | $\mathrm{m}$ |

$H_L$ | loss of pressure on the gate | $\mathrm{m}$ |

$H_v$ | pressure on the gate | $\mathrm{m}$ |

$K_B$ | coefficient $ K_B $ | $\mathrm{ }$ |

$K_Q$ | flow coefficient | $\mathrm{ }$ |

$K_T$ | coefficient $ K_T $ | $\mathrm{ }$ |

$K_{Qmax}$ | max flow coefficient | $\mathrm{ }$ |

$L$ | pipe length behind the gate | $\mathrm{m}$ |

$P$ | 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 | $\mathrm{kN}$ |

$P_T$ | 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 | $\mathrm{m^3/s}$ |

$T$ | the water temperature | $\mathrm{°C}$ |

$W$ | force on gate | $\mathrm{kN}$ |

$a_1$ | 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 | $\mathrm{m/s^2}$ |

$h$ | gate axis position to sea level | $\mathrm{m}$ |

$h_c$ | depth of water at vena contracta | $\mathrm{m}$ |

$p$ | pressure parameter | $\mathrm{ }$ |

$p_{air}$ | under-pressure in the aerated pipeline | $\mathrm{Pa}$ |

$p_{a}$ | atmospheric pressure | $\mathrm{Pa}$ |

$r$ | radius of curvature for the rounding of the gate lip | $\mathrm{mm}$ |

$s$ | 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 | $\mathrm{m/s}$ |

$ΔP$ | water hammer | $\mathrm{m}$ |

$Δ_h$ | theoretical pressure in the gate at full opening | $\mathrm{m}$ |

$β$ | aerated coefficient | $\mathrm{ }$ |

$ζ$ | loss coefficient | $\mathrm{ }$ |

$θ$ | angle of inclination of the bottom surface of the gate | $\mathrm{°}$ |

$ρ$ | density | $\mathrm{kg/m^3}$ |

$ρ_{air}$ | air density | $\mathrm{kg/m^3}$ |

$σ$ | cavitation number | $\mathrm{ }$ |