Centrifugal pumps

Impellers

Multistage impellers

Cross section of high speed water injection pump Source: www.framo.no

Water injection unit 4 MW Source: www.framo.no

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

Affinity laws Assumptions: Geometrical similarity Velocity triangles are the same

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

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

Velocity triangles

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

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

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

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

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:

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.

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

Specific speed: This is a radial pump

We choose:

w2 c2 cm2 u2 cu2

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

w1 c1= cm1 u1

Dhub We choose: Without thickness

Thickness of the blade at the inlet w1 Cm1=6,4 m/s b1 u1

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

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