1. Pumpturbines

2. Turbine mode 1 3 4 2 5
1-2:
2-3:
3-4:
4-5:

3. Turbine mode 1 3 4 2 5

4. Pump mode 1 3 4 2 5
5-4:
4-3:
3-2:
2-1:

5. Pump mode 1 3 4 2 5

6. Pump versus turbine mode1 3 4 2 5

7. Euler’s equation for pump and turbine1 2

8. Specific energy turbine mode: Ent = g·Hnt
Specific energy pump mode: Ept = g·Hnp
Static pressure (Q=0): Hst
Theoretic head (turbine mode): Htt
Theoretic head (pump mode): Htp
Hnt< Hst because of the head loss
Hnp> Hst because of the head loss

9. We assume:
Frictionless flow
Hnt = Hnp
No swirl at the outlet (turbine mode)
Cu2 = 0
For the turbine the Euler equation can be written as:
For the pump:

10. We assumes that:
Speed is the same in both turbine and pump mode (u1 is the same for both pump and turbine)
From the equations we can derive:
This means:

11. For a pump turbine the following yields:
Hnt < Hnp
We can not achieve no swirl condition in both turbine and pump mode on the low pressure side (inlet of the pump and outlet of the turbine)
The equation above show that the pump turbine has to be designed for a higher head than the theoretical head.
The pump will be designed with the assumption: u1 = 0,95

13. Bajina Basta, Yugoslavia
D0 = 5,6 m
De = 4,7 m
Di = 2,2 m
B0 = 0,31 m
Turbine mode:
*Q = 61,8 m3/s
*H = 554 m
*P = 294 MW
Pump mode:
*Q = 41,8 m3/s
*H = 602 m
*P = 281 MW

15. Mount Hope