Fluids, in general cover a large variety subjects and make up a huge component of the possible PE exam questions. Common subject matter that is often encountered on the exam includes:

FLUID PROPERTIES

SPECIFIC WEIGHT

Specific weight is a fundamental definition which can show up in many types of fluid problems. Specific weight and density are easily confused and are very similar. The difference is in the name. Specific weight is a weight (in other words a force) whereas density is an expression of mass. Knowing which one to use in a given problem can be determined by checking the units required to correctly solve the problem. Typically, specific weight for a fluid is denoted by the gamma symbol and is defined as:

An easy way to remember this relationship is to think of Newton�s 2nd law: F=ma. In this case, the density is the mass (rho) which is being acted on by the acceleration due to gravity (G).
Specific weight for a gas can be calculated from the ideal gas law:

Note for the above equation to be true, the correct form of gas constant must be used. In this case R=1545 lbf-ft/(lbmole-R) when p is expressed in [lb/ft2], V is [ft3], T is [R] and M is the molar mass of the gas [lb/lbmole].

At standard temperatures, specific weight for water is 62.4 [lb/ft3] and 9.8 [kN/m3]. Common specific weights that may appear on the exam are:

SPECIFIC GRAVITY

Specific gravity is a measure of how much heavier or lighter a fluid is to a known reference fluid. For liquids the reference is water and for gases the reference is air. Specific gravity is expressed as the ratio of the densities or specific weights of the working fluid over the reference fluid:

HEAD

Fluid or hydraulic head for the purposes of the PE exam shows up in three major forms excluding head losses which will be covered later in this section:

Static head, otherwise known as pressure head as the name implies is a measure of static energy of a fluid. The best way to visualize this concept is with a column of liquid. At a given pressure, the fluid will rise up the column until the weight of the fluid over a unit area equals the corresponding pressure:

In this figure, you can intuitively tell that as the pressure P goes up, the height of the corresponding liquid column will increase as well. The relationship for this effect is:

Velocity head can be described as the energy of a fluid due to its motion. As such static fluids have no velocity head. Velocity head can be described as:

Where V is the velocity of the fluid and g is the local gravitational constant.

Elevation head is the easiest to determine as it simply the vertical height of a given continuous volume of fluid. Note the geometrical configuration, length, or overall volume of a fluid does not necessarily contribute to a fluids elevation head, just the vertical height.



HEAD LOSSES

There two major sources of head loss. The first is Friction Head which is a measure of losses in a closed volume (typically a pipe network) due to friction between the moving fluid and the surrounding surface. The second is sometimes referred to as component losses or minor losses which are losses due to common piping components like bends, valves, and orifice plates.

Friction losses are proportional to the speed of the fluid, the affected length of the closed volume, and the surface conditions the fluid is in contact with. Depending on whether the fluid flow is laminar or turbulent, the method to determine the friction head is different.

Flow characteristics (i.e. laminar or turbulent flow) are determined by the Reynolds number. The Reynolds number is a dimensionless parameter that is a ratio of inertial forces in the fluid to viscous forces:

Where ρ is the fluid density, V is velocity, L is the effective length of fluid travel, and ν is the fluid kinematic viscosity. The units for these values should all cancel when put in Equation F.1-7. Laminar flow is defined as Re < 2000, transitional flow is 2000 < Re < 4000, and fully turbulent flow is Re > 4000. Reynolds number is used with a Moody chart to determine the friction factor-f which can ultimately be used to determine friction head loss via the Darcy Weisbach correlation shown in Equation F.1-8.

Figure F1-3 shows a typical Moody chart from which the friction factor f can be obtained.

Friction factors can be obtained from the Moody chart when surface roughness is known. Common values of surface roughness (ε) are shown in Table F.1-1:

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