Fluid properties
A fluid is a substance that deforms continuously under any shear stress, however small. Liquids and gases are both fluids. Civil engineers deal mostly with water, sometimes with air (wind loads, ventilation of tunnels) and with slurries, sewage and fresh concrete, which behave in more complex ways.
Density ρ is mass per unit volume, about 1 000 kg/m³ for water; specific weight γ = ρ g, about 9.81 kN/m³; and specific gravity compares a substance with water. Viscosity measures resistance to shear: Newton's law of viscosity says shear stress equals dynamic viscosity μ times the velocity gradient. Kinematic viscosity ν = μ / ρ appears in the Reynolds number. Water's viscosity falls markedly as it warms, which affects settling tanks and pipe friction. Fluids that follow Newton's law are Newtonian; others, such as fresh concrete, drilling muds and sludge, are non-Newtonian and need a yield stress or variable viscosity to describe them.
Surface tension makes water rise in thin tubes and in fine soils, causing capillary rise above the water table. Compressibility, described by the bulk modulus (about 2.1 GPa for water), is negligible in most hydraulics but important in water hammer. Vapour pressure matters at pump inlets and siphons: if pressure falls to vapour pressure, water boils at ambient temperature, cavities form and collapse, and cavitation damages pumps, spillways and valves.
Write down the temperature with any viscosity value; it can change by a factor of two between cold and warm water.
ρ_water ≈ 1 000 kg/m³; γ = ρ g ≈ 9.81 kN/m³Newton: τ = μ du/dy; ν = μ / ρCapillary rise: h = 4 σ cos θ / (γ d)Bulk modulus: K = −dp / (dV/V)
Problem. Find the capillary rise of water in a glass tube of 1 mm diameter (σ = 0.073 N/m, θ = 0) and in a silt with an equivalent pore size of 0.02 mm.
- h = 4 × 0.073 / (9 810 × 0.001) = 0.0298 m ≈ 30 mm for the tube.
- For 0.02 mm: h = 4 × 0.073 / (9 810 × 0.00002) = 1.49 m.
- So capillary water can rise well over a metre in silts, which affects frost heave, damp walls and pavement subgrades.
Answer. About 30 mm in the tube; about 1.5 m in the silt
Quick quiz
1What makes a fluid different from a solid?
It deforms continuously under any shear stress.
2How does water viscosity change with temperature?
It decreases as temperature rises.
3What is cavitation?
Formation and collapse of vapour bubbles where pressure drops to vapour pressure.
References and further reading
Standard texts, listed in no order of merit. We do not copy text, figures, tables or solved problems from any book; our explanations and examples are original.
- P. N. Modi, S. M. Seth, Hydraulics and Fluid Mechanics including Hydraulic Machines, Standard Book House, latest edition.
- V. T. Chow, Open-Channel Hydraulics, McGraw Hill, 1959.
- K. Subramanya, Flow in Open Channels, McGraw Hill Education (India), latest edition.
Free and official sources
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