FLUID FLOW

GENERAL

Two of the most useful and basic equations are :





where:
delta h = 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 1-1 Ah 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
3. Relief valve sizing
4. Heat exchanger tube leak calculations
For a sparger consisting of a large pipe having small
holes drilled along its length, Equation 1-1 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-
1 because hole diameter is a much larger dimension than
length of travel (say ~ in. for many orifices). Orifices will
be discussed under "Metering" later 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" in this chapter.

Still more mileage can be obtained from Ah - u2/2g
when using it with Equation 1-2, 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 turbulence
and promote separation
2. Entering vacuum condensers to cut down pressure
drop
We build up PV and convert it in a controlled manner to
u2/2g in a form of tank blender. These examples are discussed
under appropriate sections.