Fluid Properties

NCEES FE Civil spec: Fluid Mechanics, B. Fluid properties. FE Reference Handbook: Fluid Mechanics chapter, fluid properties.

Every fluid mechanics calculation depends on a few properties: how heavy the fluid is, how much it resists shearing, and how it behaves at surfaces and low pressure. FE Civil questions on this section are short, but mixing up density, specific weight and the two kinds of viscosity costs points across the whole fluids section.

What the NCEES spec covers

Section B, "Fluid properties", includes density, specific weight, specific gravity, dynamic and kinematic viscosity, surface tension and capillarity, vapor pressure and compressibility (bulk modulus).

Key concepts

Density ρ is mass per volume (about 1,000 kg/m³ or 1.94 slug/ft³ for water). Specific weight γ = ρg is weight per volume (9.81 kN/m³ or 62.4 lb/ft³ for water).
Specific gravity is the ratio of a fluid's density to that of water at a reference temperature. It has no units.
Newtonian fluids have shear stress proportional to the velocity gradient. The constant is dynamic viscosity μ.
Kinematic viscosity ν = μ/ρ appears in the Reynolds number.
Viscosity and temperature. Liquid viscosity drops as temperature rises; gas viscosity rises.
Surface tension pulls liquid up a small tube (capillary rise) when the liquid wets the wall.
Vapor pressure is the pressure at which the liquid boils at a given temperature. If local pressure falls below it, cavitation occurs, a key check for pump suction lines.

Core formulas

γ = ρ g S G = \frac{ρ}{ρ _{w}} = \frac{γ}{γ _{w}} ν = \frac{μ}{ρ}

τ = μ \frac{d v}{d y} \approx μ \frac{V}{t} (thin film, linear profile)

h = \frac{4 σ cos β}{γ d} E_{v} = - \frac{Δ p}{Δ V / V}

Where it is in the FE Reference Handbook

The Fluid Mechanics chapter opens with definitions of density, specific weight, specific gravity, viscosity, surface tension and capillarity. Property tables for water at different temperatures (density, viscosity, vapor pressure) are also in that chapter, and you are expected to read them.

Worked example

A flat plate with an area of 0.50 m² slides at 2.0 m/s over a 1.5 mm film of oil (SG = 0.88). A force of 25 N is needed to keep it moving at constant speed. Find the dynamic and kinematic viscosity of the oil.

Step 1: shear stress on the plate.

τ = \frac{F}{A} = \frac{25}{0.50} = 50 Pa

Step 2: velocity gradient (assume a linear profile across the thin film):

\frac{d v}{d y} = \frac{2.0}{0.0015} = 1, 333 s^{- 1}

Step 3: viscosities.

μ = \frac{50}{1 , 333} = 0.0375 Pa \cdotp s ρ = 0.88 (1, 000) = 880 kg/m^{3} ν = \frac{0.0375}{880} = 4.26 \times 1 0^{- 5} m^{2} / s

That viscosity is about 37 times water's at room temperature, typical of a light machine oil.

Common mistakes

Using density where specific weight is needed (or the reverse), especially in US units with slugs.
Forgetting to convert film thickness from mm to m.
Mixing up dynamic viscosity (Pa·s) and kinematic viscosity (m²/s).
Assuming liquid viscosity increases with temperature.
Using the radius instead of the diameter in the capillary rise formula above.

See the oil viscosity example, and use the unit converter for viscosity and pressure units.

Practice Problems

Try these from the free PolyCalc FE Civil problem bank. Each one has a full worked solution.

A 1 m³ volume of fluid has mass 1,000 kg. What is its density? See the worked solution or practice the Fluids & Hydraulics deck
A pump draws 20 °C water from a reservoir whose surface is 3.0 m below the pump centreline. Friction loss in the suction line is 1.2 m. Atmospheric pressure is 101.3 kPa, the vapour pressure of water at 20 °C is 2.34 kPa, and the specific weight of water is 9.79 kN/m³. The net positive suction head available is most nearly: See the worked solution or practice the Fluids & Hydraulics deck
A solid sphere of diameter 0.10 m and mass 2.0 kg hangs on a light string, fully submerged in a water current flowing horizontally at 1.5 m/s. Take the sphere's drag coefficient as 0.47 and the water density as 1000 kg/m³. Including the buoyant force on the sphere, the steady-state angle the string makes with the vertical is most nearly: See the worked solution or practice the Fluids & Hydraulics deck

Related Calculators and Examples

Frequently Asked Questions

What is the difference between dynamic and kinematic viscosity?

Dynamic viscosity relates shear stress to velocity gradient and has units of Pa s. Kinematic viscosity is dynamic viscosity divided by density, with units of m^2/s, and it is used in the Reynolds number.

What is the specific weight of water?

About 9.81 kN/m^3 in SI units, or 62.4 lb/ft^3 in US units, at ordinary temperatures.

Why does vapor pressure matter for pumps?

If the pressure at the pump inlet drops below the vapor pressure of the water, vapor bubbles form and collapse, causing cavitation damage. The available net positive suction head check prevents this.

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