Hydrostatics
Hydrostatics is the study of fluids at rest. The pressure at any point in a static fluid is given by P = ρ × g × h (or P = γ × h), where γ is the specific weight of the fluid. Pascal's principle states that pressure applied to a confined fluid is transmitted undiminished. The total hydrostatic force on a submerged surface is F = γ × h_c × A, where h_c is the depth to the centroid. The center of pressure is the point where the resultant force acts, located below the centroid.
Knowledge Check
1.A water tank has a depth of 5 m. What is the pressure at the bottom? (ρ_water = 1000 kg/m³, g = 9.81 m/s²)
2.A rectangular gate 2 m wide and 3 m high is submerged vertically in water with its top edge at the surface. What is the total hydrostatic force on the gate? (γ_water = 9.81 kN/m³)
3.What is the pressure at a depth of 10 m in seawater? (ρ_seawater = 1025 kg/m³, g = 9.81 m/s²)
4.A triangular gate (base = 2 m, height = 3 m) is submerged vertically in water with its vertex at the surface. What is the depth to the centroid (h_c)?
5.What is the specific weight (γ) of water?
6.A 3 m × 4 m rectangular gate is submerged vertically in water with its top edge at 2 m below the surface. What is the total hydrostatic force? (γ = 9.81 kN/m³)
7.Pascal's principle states that pressure applied to a confined fluid is transmitted:
8.The center of pressure on a submerged vertical rectangular plate is located:
9.A manometer measures pressure difference using a fluid column. If the height difference is 0.5 m of mercury (γ_Hg = 133 kN/m³), what is the pressure difference?
10.What is the gauge pressure at a depth of 8 m in water? (γ_water = 9.81 kN/m³)