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 h_pump = w_pump,u/g is the useful pump head delivered to the fluid,h_turbine,e w_turbine,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 h_L 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,

h_pump,u = (z₂ – z₁) + h_L

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 .                                   

(figure 8-48)

·         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. 

---

THANK YOU

---