1. Centrifugal pumps

3. Impellers

4. Multistage impellers

5. Cross section of high speed water injection pump
Source:

6. Water injection unit
4 MW
Source:

7. Specific speed that is used to classify pumps
nq is the specific speed for a unit machine that is geometric similar to a machine with the head Hq = 1 m and flow rate Q = 1 m3/s

9. Affinity laws Assumptions: Geometrical similarity
Velocity triangles are the same

10. Exercise
Find the flow rate, head and power for a centrifugal pump that has increased its speed
Given data:
hh = 80 % P1 = 123 kW n1 = 1000 rpm H1 = 100 m
n2 = 1100 rpm Q1 = 1 m3/s

11. Exercise
Find the flow rate, head and power for a centrifugal pump impeller that has reduced its diameter
Given data:
hh = 80 % P1 = 123 kW D1 = 0,5 m H1 = 100 m
D2 = 0,45 m Q1 = 1 m3/s

12. Velocity triangles

14. Reduced cu2
Slip angle
Friction loss
Slip angle
Impulse loss
Slip
Best efficiency point

15. Power
Where:
M = torque [Nm]
w = angular velocity [rad/s]

16. In order to get a better understanding of the different velocities that represent the head we rewrite the Euler’s pump equation

17. Euler’s pump equation
Pressure head due to change of peripheral velocity
Pressure head due to change of absolute velocity
Pressure head due to change of relative velocity

18. Rothalpy
Using the Bernoulli’s equation upstream and downstream a pump one can express the theoretical head:
The theoretical head can also be expressed as:
Setting these two expression for the theoretical head together we can rewrite the equation:

19. Rothalpy The rothalpy can be written as:
This equation is called the Bernoulli’s equation for incompressible flow in a rotating coordinate system, or the rothalpy equation.

20. Stepanoff
We will show how a centrifugal pump is designed using Stepanoff’s empirical coefficients.
Example: H = 100 m
Q = 0,5 m3/s
n = 1000 rpm
b2 = 22,5 o

21. Specific speed:
This is a radial pump

22. We choose:

23. w2 c2
cm2 u2
cu2

24. Thickness of the blade
Until now, we have not considered the thickness of the blade. The meridonial velocity will change because of this thickness.
We choose: s2 = 0,005 m
z = 5

25. w1
c1= cm1 u1

26. Dhub
We choose:
Without thickness

27. Thickness of the blade at the inletw1
Cm1=6,4 m/s b1 u1

28. w2 c2
cm2=4,87m/s
b2=22,5o
u2=44,3 m/s
cu2

29. w2 c2
cm2=4,87m/s
u2=44,3 m/s
cu2