When a piping system involves a pump, the
steady-flow energy equation on a unit-mass basis is expressed as
In terms of heads as
Where hpump = wpump,u/g is the useful pump
head delivered to the fluid,hturbine,e wturbine,e/g
is the turbine head extracted from the fluid , a is the kinetic energy correction factor whose
value is about 1.05 for most (turbulent) flows encountered in practice , and hL
is the total head loss in the piping
(including the minor losses if they are significant) between points 1 and 2.
i.
The pump head is zero
if the piping system does not involve a pump
ii.
The turbine head is
zero if the system does not involve a turbine
iii.
Both are zero if the system does not
involve any mechanical work-producing or work-consuming devices
Energy equation is solved for the
required useful pump head,
hpump,u = (z2 – z1)
+ hL
Once the useful pump head is known,the
mechanical power that needs to be delivered by the pump to the fluid and the
electrical power consumed by the motor of the pump for a specified flow rate
are determined from
and
where
is the efficiency of the pump-motor combination which is the product of the pump and the motor efficiency .
· pump - motor effciency = the ratio of the net mechanical energy
delivered to the fluid by the pump to the electric energy consumed by the motor
of the pump
·
Typically ranges
between 50 and 85 percent (%)
Head loss of piping system ↑ (usually
quadratically) with the flow rate. A plot required useful pump head
as a function of flow rate is called the system (or demand) curve
- The head produced by a
pump is not a constant.
- Pump head and pump
efficiency vary with the flow rate.
- Pump manufactures
supply the variation in tabular or graphical form
(figure 8-49)
These experimentally determined
curves are called
characteristic (or
supply or
performance ) curve
·
The flow rate of a pump
↑ as the required head ↓
·
The intersection point
of the pump head curve with the vertical axis = maximum head (called the shutoff
head)
·
The intersection point
with the horizontal axis=maximum flow
rate (called the free delivery)
The efficiency
of a pump is highest at a certain combination of head and flow rate. Therefore,
a pump that can supply the required head and flow rate is not necessarily a
good choice for a piping system unless the efficiency of the pump at those
conditions is sufficiently high. The pump will operate at the point where the system
curve and the characteristic
curve intersect. This point of intersection is called operating point.
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