Fluid Properties
Understanding fundamental fluid properties is essential for fluid mechanics analysis:
- Density (rho): mass per unit volume (kg/m^3). Water at 4 C: 1000 kg/m^3
- Specific weight (gamma): weight per unit volume, gamma = rho*g
- Specific gravity: ratio of fluid density to water density at 4 C
- Viscosity (mu): resistance to shear deformation. Water at 20 C: 1.002 x 10^-3 Pa*s
- Kinematic viscosity: nu = mu/rho (m^2/s)
- Surface tension: force per unit length at a fluid interface
- Bulk modulus: E_v = -delta_P / (delta_V/V), resistance to compression
Hydrostatic Pressure
In a static fluid, pressure increases linearly with depth:
- P = P0 + rho*g*h (pressure at depth h below surface)
- Pressure is the same at all points on a horizontal plane in a connected fluid
- Pascal's law: pressure applied to an enclosed fluid is transmitted equally in all directions
- Manometers: measure pressure differences using columns of fluid
- Gauge pressure: P_gauge = P_abs - P_atm
Forces on Submerged Surfaces
- Force on a flat surface: F = gamma * h_c * A (h_c = vertical distance to centroid)
- Center of pressure (below centroid): y_cp = y_c + I_c/(y_c*A)
- Buoyancy (Archimedes): F_b = rho_fluid * g * V_submerged
- Stability of floating bodies depends on the metacentric height
Fluid Flow Fundamentals
- Continuity: A1*V1 = A2*V2 for steady, incompressible flow
- Bernoulli equation: P/(rho*g) + V^2/(2*g) + z = constant along a streamline
- Assumptions: steady, incompressible, inviscid flow along a streamline
- Energy equation (with losses): includes pump head (h_p), turbine head (h_t), and head loss (h_L)
Pipe Flow
- Reynolds number: Re = rho*V*D/mu = V*D/nu
- Laminar (Re < 2300): fully developed velocity profile is parabolic
- Turbulent (Re > 4000): flatter velocity profile, higher friction losses
- Darcy-Weisbach: h_f = f*(L/D)*V^2/(2*g) (major head loss)
- Minor losses: h_m = K*V^2/(2*g) (valves, elbows, entrances, exits)
- Laminar friction factor: f = 64/Re
- Turbulent: use Moody diagram or Colebrook equation
Dimensional Analysis
- Buckingham Pi theorem: number of dimensionless groups = number of variables minus number of fundamental dimensions
- Common dimensionless numbers: Reynolds (Re), Froude (Fr), Mach (Ma), Weber (We)
- Dynamic similarity: model and prototype share the same dimensionless parameters
- Useful for scaling experiments and model testing