10 / CHAPTER 01
Fluid properties and pressure
Define density, viscosity, compressibility, and pressure for a fluid model.
ANCHOR EQUATION
Fluid density
In symbols: ρ = m/V
Density connects a fluid’s mass to the volume it occupies.
Fluid properties set the scale of response
Density measures mass per volume; viscosity measures resistance to velocity gradients; compressibility measures how density changes with pressure. Pressure is normal force per area and can vary even when a fluid is motionless.
Start with definitions and units
Density is ρ = m/V in kg/m³. Pressure is p = F_n/A in Pa. Dynamic viscosity μ has units Pa·s because shear stress τ = μ du/dy. Kinematic viscosity ν = μ/ρ has units m²/s and compares momentum diffusion with bulk motion.
A 2 L sample of water with mass 1.98 kg has ρ = 1.98/0.002 = 990 kg/m³. A 100 N normal force over 0.01 m² gives p = 10,000 Pa, or 10 kPa.
Property values depend on state
Water density and viscosity change with temperature; air is strongly compressible; a fluid can be Newtonian or not. Use absolute or gauge pressure consistently and state the reference pressure.
Work it: For water at 20°C, use ρ = 998 kg/m³ and μ = 1.00 mPa·s to calculate ν. Compare with a glycerin-like fluid μ = 1 Pa·s at the same density.