Mechanical Properties of Fluids - Quick Revision
Fluid statics
- Pressure P = F/A (Pa); a fluid at rest exerts pressure perpendicular to any surface, equal in all directions at a point (Pascal).
- P = P0 + h rho g (increases with depth); gauge pressure = P - atmospheric.
- Pascal's law: pressure applied to an enclosed fluid is transmitted undiminished -> hydraulic lift/brakes, F2 = F1 (A2/A1).
- Archimedes: upthrust = weight of displaced fluid = V rho g; floating bodies displace their own weight.
Fluid dynamics
- Equation of continuity A1v1 = A2v2 (mass conservation, incompressible).
- Bernoulli: P + (1/2)rho v^2 + rho g h = constant along a streamline (energy conservation, ideal flow). Faster flow -> lower pressure (aerofoil lift, atomiser, Venturi).
- Torricelli: efflux speed v = sqrt(2gh).
Viscosity
- Viscous force F = eta A (dv/dx); eta = coefficient of viscosity (Pa s).
- Stokes: F = 6 pi eta r v; a sphere reaches terminal velocity vt = 2 r^2 (rho-sigma) g / (9 eta).
- Reynolds number Re = rho v D / eta predicts laminar (<1000) vs turbulent (>2000) flow.
Surface tension
- Surface tension S = force per unit length = surface energy per unit area (N/m); arises from net inward cohesive force on surface molecules.
- Angle of contact decides wetting; excess pressure = 2S/R (drop), 4S/R (soap bubble).
- Capillary rise h = 2S cos(theta)/(r rho g).