These hydraulic calculators cover incompressible fluid mechanics (water, hydraulic oils) in pipes and tanks under steady-state conditions. The continuity equation (Q = A × v) relates volumetric flow rate, pipe cross-section, and mean velocity. Stevin's law describes hydrostatic pressure as a function of depth: p = p₀ + ρ×g×h. These calculators support preliminary sizing of plumbing systems, irrigation networks, industrial pipelines, and water tanks.
Q = V / t [m³/s] or [L/s]. Volume of fluid passing through a cross-section per unit time. In practice: Q = A × v, where A is the pipe cross-sectional area [m²] and v is the mean velocity [m/s].
Continuity equation
For incompressible fluid in steady state: Q = A₁×v₁ = A₂×v₂. As cross-section increases, velocity decreases (and vice versa). Foundation for all pipe sizing calculations.
Velocity in pipe
v = Q / A [m/s]. For circular pipe of diameter D: A = π×D²/4. Recommended velocities: domestic water supply ≈ 0.5–2 m/s; industrial piping up to 3–5 m/s depending on acceptable head loss.
Hydrostatic pressure
p = p₀ + ρ×g×h [Pa]. p₀ = pressure at free surface (typically atmospheric ≈ 101,325 Pa), ρ = fluid density [kg/m³] (water at 20°C ≈ 998 kg/m³), g = 9.81 m/s², h = depth [m]. 1 metre of water column ≈ 9,806 Pa ≈ 0.098 bar.
Reynolds number
Re = ρ×v×D/μ (dimensionless). Discriminates laminar flow (Re < 2300) from turbulent (Re > 4000). For water at 20°C with μ ≈ 10⁻³ Pa·s.
Core formulas
Q = V / t [m³/s] (flow rate from volume and time)
v = Q / A = 4Q / (π×D²) [m/s] (velocity in circular pipe)