If c₁ = a dimensionless pressure coefficient, αh = horizontal acceleration factor, ρ = mass density of water, g = acceleration due to gravity, h = depth of the reservoir; what is the formula for the variation of horizontal hydrodynamic earthquake pressure with depth (Pe) in gravity dams ?
- APe = C₁ αh g / h
- BPe = C₁ αh / (g h)
- CPe = C₁ αh g hCorrect
- DPe = C₁ g (h + αh)
Solution
Concept
Hydrodynamic pressure on a dam (Zangar)
Formula
Pe = Cs αh ρ g h
Step-by-step solution
1. The hydrodynamic pressure at depth h is proportional to the horizontal seismic coefficient, the unit weight of water and the depth: Pe = C₁ αh ρ g h. 2. Among the options only (c) has the right dimensions (pressure) once ρ is included.
Explanation
Hydrodynamic pressure rises with depth and with the seismic coefficient, as in Zangar's formula.
Why the other options are wrong
The other options divide by h or g, or add h to αh, which is dimensionally impossible.
Shortcut
Pe = Cs αh γ h.
Common mistake
Dividing instead of multiplying by depth.
Correct answer: C) P_e = C₁ α_h g h