A Water Lily
Water Lily on a Lake (Photo: ref.)

This section is meant to provide some background information on Water Engineering and it's terminology.

Fluid Statics
  1. Useful Conversions
  2. Characteristics of a Fluid
  3. Definitions
  4. Water Properties



Useful Conversions

  • gc = 32.2 ft/sec2 [lbm-ft/lbf-sec2]
  • ρwater = 1.96 slugs/ft3
  • γwater = 62.4 lb/ft3
  • 1 ft3/sec = 449 gpm
  • 1 mgd = 1.547 ft3/sec
  • 1 foot of water = 0.433 psi
  • 1 psi = 2.31 ft of water
  • 1 ft3 = 0.13368 gal
  • 101.33 kPa = 1 atm

Characteristics of a fluid:

These characteristics can be used to distinguish between liquids and gases if necessary:

  • Compressibility : Fluids are very slightly compressible. For all intents and purposes they can be considered incompressible (fill up a small water balloon and squeeze it to test this)
  • Shear Forces : Liquids (and gases) are unable to support any shear forces. They will constantly strive to find the path of least shear forces.
  • Shape & Volume : Since fluids cannot transfer shear forces, they will form to the container they reside in. Although their volume during this will be fixed (unlike a gas which will expand to fill the container a fluid's volume cannot change).
  • Pressure : the pressure in a fluid will be the same in all directions. One specific example is the pressure of a fluid transfered onto a surface will always be normal to that surface.
  • Resistance to Motion : Due to a liquids viscosity, liquids will resist an instantaneous change in velocity.

Definitions

Bernoulli's equation
The Bernoulli's Equation describes the behavior of moving fluids along a streamline.
Discharge
flow rate, usually in ft3/sec or gpm
Hydraulics
Hydraulics is a branch of science and engineering concerned with the use of liquids to perform mechanical tasks
Ideal Gas
The Ideal Gas Law - For a perfect or ideal gas the change in density is directly related to the change in temperature and pressure as expressed in the Ideal Gas Law.
Reynolds number
The Reynolds number is used for determine whether a flow is laminar or turbulent.

Properties

Density

Density (ρ) is mass per unit volume (lbm/ft3, kg/m3, slugs/ft3)

Density:

\rho = \frac{mass}{volume}

\rho_{slugs} = \frac{\rho_{lbm}}{g_c}

Using the ideal gas law, the density of gases can be found by:

\rho = \frac{p}{RT}

where:

ρ = fluid density (lbm/ft3, kg/m3, slugs/ft3)
gc = 32.2 \frac{lbm-ft}{lbf-sec^2}
p = pressure ( From pV = nRT)
R = Specific Gas Constant
T = Absolute Temperature

Specific Weight (aka Unit Weight)

Specific Weight (γ) is weight per unit volume (lb/ft3) = ρg

Density:

\gamma = \frac{weight}{volume} = \rho g = \rho* \frac{g}{g_c}

where:

ρ = fluid density (lbm/ft3, kg/m3, slugs/ft3)
g = gravitational acceleration (ft/sec2)
gc = 32.2 \frac{lbm-ft}{lbf-sec^2}

Note: In the United States specific weight is also known as density.

Specific Gravity

Specific Gravity (S) is the ratio of the weight (or mass) or a substance to the weight (or mass) of water.

S = \frac{\rho_s}{62.4} = \frac{\rho_s}{\gamma_w} = \frac{\rho_s}{\rho_w}

where the subscript s denotes of a given substance and the subscript w denotes of water.

Given S of a substance, you can easily calculate ρ and γ using the equations

\gamma_s = S*\gamma_w

\rho_s = S*\rho_w

Specific Volume

Specific Volume is the volume per unit mass (usually in ft3/lbm). Specific Volume is the reciprocal of density.

Specific Volume:

\nu = \frac{1}{\rho}

where:

ρ = fluid density (lbm/ft3, kg/m3, slugs/ft3)

Viscosity

Viscosity (υ) is a measure of a fluid's ability to resist shearing force (usually in lbf·sec/ft2). υ is a proportionality constant and is also known as absolute viscosity or dynamic viscosity. Viscosity is often given in the SI unit of Poise. To convert to English units use the relationship: 1 \frac{lb*sec}{ft^2} = 479 Poise

Viscosity:

\frac{F}{A} \propto \frac{dv}{dy}

\frac{F}{A} = \mu\frac{dv}{dy}

where:

F = Force
A = Area
y = thickness
v = velocity
μ = coefficient of viscosity

Kinematic Viscosity

Kinematic Viscosity:

\begin{eqnarray} \nu &=& \frac{\mu}{\rho} \; \; \; \mbox{ (SI)} \\ &=& \frac{\mu g_c}{\rho} \; \mbox{ (US)} \end{eqnarray}

where:

γ = kinematic viscosity (ft2/sec)
υ = dynamic viscosity (lbf·sec/ft2)
ρ = mass density (slugs/ft3)

Note: See CERM Appendix 14.A (page A-13) for a listing of water properties at various temperatures.

Absolute and Gauge Pressure

Absolute Pressure (psia) = Atmospheric Pressure + Gauge Pressure (psig)

Atmospheric Pressure changes with weather conditions and altitude though is usually assumed to be 14.7 psi at sea level. Pressures are usually given in psig, except for compressible flow.


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