Hydraulic Structures: Fourth Edition

For one unit rejection or demand, Q 0 21.7 m^3 s^1 andP 0 2.13 m. Therefore

ZmaxQ 0 /Asr11.63 m

and

K* 0 P 0 /Zmax0.183.

Upon sudden rejection, the maximum upsurge (equation (12.32)), Z*max
0.88. Therefore

Zmax0.8811.6310.23 m.

The maximum downsurge (equation (12.33)), Z*min0.7. Therefore

Zmin0.711.638.14 m.

Upon sudden demand (equation (12.34)), Z*min1.023. Therefore

Zmin1.02311.6311.9 m.

Worked Example 12.5

In a pumped-storage scheme, water is supplied to a single turbine through
a 200 m long, 2 m diameter penstock line. The power plant uses two cen-
trifugal pumps to pump water back to the upper reservoir, using the same
penstock pipeline. Basic data are as follows. Pumps (2 nos.), rated
capacity6 MW each, efficiency of pump87%, efficiency of pump
motor85%; turbine (1 no), installed capacity25 MW, efficiency of
turbine91%, efficiency of generator89%; Penstock pipeline,
length200 m, diameter2 m, Manning’s n0.015, gross head above tail-
water level115 m.
Determine

1. the maximum discharge rate per pump,


2. the maximum discharge to the turbine and


3. the overall efficiency of the system if all the water used by the
   turbine is pumped back to the upper reservoir.

Solution

PUMP DISCHARGE

The power output from the pumps

 gQ(115hf)/1000 kW

WORKED EXAMPLES 541