Two of the most useful and basic equations are
Dh = Head loss in feet of flowing fluid
u = Velocity in ft/sec
g = 32.2 ft/sec2
P = Pressure in lb/ft2
V = Specific volume in ft3/lb
Z = Elevation in feet
E = Head loss due to friction in feet of flowing fluid
In Equation 1 Dh is called the “velocity head.” This expression has a wide range of utility not appreciated by many. It is used “as is” for
1. Sizing the holes in a sparger
2. Calculating leakage through a small hole
3. Sizing a restriction orifice
4. Calculating the flow with a pitot tube
With a coefficient it is used for
1. Orifice calculations
2. Relating fitting losses, etc.
For a sparger consisting of a large pipe having small holes drilled along its length Equation 1 applies directly. This is because the hole diameter and the length of fluid travel passing through the hole are similar dimensions.
An orifice on the other hand needs a coefficient in Equation 1 because hole diameter is a much larger dimension than length of travel (say 1/8 in. for many orifices). Orifices will be discussed under “Metering” in this chapter.
For compressible fluids one must be careful that when sonic or “choking” velocity is reached, further decreases in downstream pressure do not produce additional flow. This occurs at an upstream to downstream absolute pressure ratio of about 2 : 1. Critical flow due to sonic velocity has practically no application to liquids. The speed of sound in liquids is very high. See “Sonic Velocity’‘ later in this chapter.
Still more mileage can be gotten out of Ah = u2/2g when using it with Equation 2, which is the famous
Bernoulli equation. The terms are
1. The PV change
2. The kinetic energy change or “velocity head”
3. The elevation change
4. The friction loss
These contribute to the flowing head loss in a pipe. However, there are many situations where by chance, or on purpose, u2/2g head is converted to PV or vice versa. We purposely change u2/2g to PV gradually in the following situations:
1. Entering phase separator drums to cut down turbu lence and promote separation
2. Entering vacuum condensers to cut down pressuredrop
We build up PV and convert it in a controlled manner to u2/2g in a form of tank blender.
Here are various recommended flows, velocities, and pressure drops for various piping services.