Two of the most useful and
basic equations are

where

Dh
= Head loss in feet of flowing fluid

u = Velocity in
ft/sec

g = 32.2 ft/sec

^{2}
P = Pressure in lb/ft

^{2}
V = Specific volume
in ft

^{3}/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 = u

^{2}/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, u

^{2}/2g head is converted to PV or vice versa. We purposely change u^{2}/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 u

^{2}/2g in a form of tank blender.
Here are various recommended flows,
velocities, and pressure drops for various piping services.