Piping Systems with Pumps and Turbines

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,ewturbine,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




These experimentally determined curves are calledcharacteristic (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 curveintersect. This point of intersection is called operating point.