Environmental Engineering Reference
In-Depth Information
Based on these sample problems, you can see that if the cross-
sectional area is decreased the velocity of the flow must be increased.
Mathematically, we can say that the velocity and cross-sectional area
are inversely proportional when the amount of flow (
q
) is constant.
Area
1
× Velocity
1
= Area
2
× Velocity
2
(3.2)
Note:
The concept just explained is extremely important in the opera-
tion of a centrifugal pump and will be discussed further later.
3.2.2 Pressure-velocity relationship
A relationship similar to that of velocity and cross-sectional area
exists for velocity and pressure. As the velocity of flow in a full pipe
increases, the pressure of the liquid decreases. This relationship is:
Pressure
1
× Velocity
1
= Pressure
2
× Velocity
2
(3.3)
Example 3.3
Problem:
If the flow in a pipe has a velocity of 3 fps and a pressure of 4 psi
and the velocity of the flow increases to 4 fps, what will the pressure be?
Solution:
P
1
×
v
1
=
P
2
×
v
2
4 psi × 3 fps =
P
2
× 4 fps
Rearranging:
4psi 3fps
4fps
×
12 psi
4
P
2
=
=
=
3psi
Again, this is another hydraulics principle that is very important to the
operation of a centrifugal pump.
3.2.3 static head
Pressure at a given point originates from the height or depth of
water above it. It is this pressure, or
head
, that gives the water energy
and causes it to flow. By definition,
static head
is the vertical distance
the liquid travels from the supply tank to the discharge point. This rela-
tionship is shown as:
Static Head (ft) = Discharge Level (ft) - Supply Level (ft)
(3.4)
In many cases, it is desirable to separate the static head into two sepa-
rate parts: (1) the portion that occurs before the pump (suction head or
suction lift), and (2) the portion that occurs after the pump (discharge
head). When this is done, the center (or datum) of the pump becomes the
reference point.
