Problems And Solutions Pdf | Fluid Mechanics Dams
Suggested useful text (PDF-ready) — Fluid Mechanics: Dams — Problems & Solutions
1. Fundamental theory (concise)
- Hydrostatic pressure: p = ρ g h — explain sign convention, datum, and pressure variation with depth.
- Resultant force on a plane vertical wall: F = ρ g A y_c (where y_c is centroid depth). Line of action at ȳ = I_x / (y_c A) + y_c.
- Center of pressure formula and derivation for rectangular and triangular distributions.
- Hydrostatic thrust on an inclined plane and submerged surfaces (general integral form).
- Buoyancy and stability: Archimedes’ principle, metacentric height GM for floating structures.
- Pressure on curved surfaces: use horizontal and vertical components (horiz: same as area projection; vert: weight of fluid above projected area).
4. Example Problem 2: Inclined Upstream Face
Problem:
A dam has a vertical downstream face and an inclined upstream face with slope 1H:4V (i.e., for every 4 m vertical, it projects 1 m horizontally). Height ( H = 30 , \textm ), base width ( B = 20 , \textm ). Water depth = 30 m. Compute the horizontal and vertical components of hydrostatic force on the upstream face per meter width. Use ( \rho_w = 1000 , \textkg/m^3 ).
Locate the Lines of Action: Determine where these forces act (the "moment arm"). fluid mechanics dams problems and solutions pdf
- Bernoulli's Equation: Relates the pressure, velocity, and elevation of fluid flow.
- Hydrostatic Pressure Equation: Calculates the pressure exerted by a fluid on a surface.
- Continuity Equation: Describes the conservation of mass in fluid flow.
- Manning's Equation: Used to calculate the flow rate and velocity of water in open channels.