Fluid Properties
- Density: rho = m/V (mass per unit volume, kg/m^3)
- Specific weight: gamma = rho * g (weight per unit volume, N/m^3)
- Specific gravity: SG = rho_fluid / rho_water
- Dynamic viscosity: mu (Pa*s or N*s/m^2)
- Kinematic viscosity: nu = mu / rho (m^2/s)
Pressure and Hydrostatics
- Hydrostatic pressure: P = rho * g * h (pressure at depth h)
- P_abs = P_atm + P_gauge
- Manometer: P1 - P2 = rho * g * delta_h
- Force on submerged plane surface: F = gamma * h_c * A (h_c = depth of centroid)
- Buoyancy force: F_b = rho_fluid * g * V_displaced
Continuity Equation
- A1 * V1 = A2 * V2 (for incompressible flow)
- rho1 * A1 * V1 = rho2 * A2 * V2 (for compressible flow)
- Q = A * V (volume flow rate = area times velocity)
- Mass flow rate: m_dot = rho * A * V
Bernoulli Equation
- P1/(rho*g) + V1^2/(2g) + z1 = P2/(rho*g) + V2^2/(2g) + z2
- Assumptions: steady, incompressible, inviscid, along a streamline
- Each term represents: pressure head + velocity head + elevation head
- Modified Bernoulli with losses: add h_L (head loss) and h_p (pump head) terms
Reynolds Number and Pipe Flow
- Re = rho * V * D / mu = V * D / nu
- Laminar flow: Re < 2300
- Turbulent flow: Re > 4000
- Transition zone: 2300 < Re < 4000
- Darcy-Weisbach: h_f = f * (L/D) * V^2/(2g)
- Laminar friction factor: f = 64/Re
- Moody diagram for turbulent friction factor (depends on Re and relative roughness)
Open Channel Flow
- Manning's equation: V = (1/n) * R_h^(2/3) * S^(1/2) (SI units)
- Hydraulic radius: R_h = A/P (area divided by wetted perimeter)
- Froude number: Fr = V / sqrt(g * y) (y = flow depth)
- Fr < 1: subcritical flow; Fr = 1: critical; Fr > 1: supercritical