Centrifugal pumps Impellers Multistage impellers Cross section of

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Centrifugal pumps

Centrifugal pumps

Impellers

Impellers

Multistage impellers

Multistage impellers

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

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

Water injection unit 4 MW 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

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 m 3/s

Affinity laws Assumptions: Geometrical similarity Velocity triangles are the same

Affinity laws Assumptions: Geometrical similarity Velocity triangles are the same

Exercise • Find the flow rate, head and power for a centrifugal pump that

Exercise • Find the flow rate, head and power for a centrifugal pump that has increased its speed • Given data: hh = 80 % n 1 = 1000 rpm n 2 = 1100 rpm P 1 = 123 k. W H 1 = 100 m Q 1 = 1 m 3/s

Exercise • Find the flow rate, head and power for a centrifugal pump impeller

Exercise • Find the flow rate, head and power for a centrifugal pump impeller that has reduced its diameter • Given data: hh = 80 % D 1 = 0, 5 m D 2 = 0, 45 m P 1 = 123 k. W H 1 = 100 m Q 1 = 1 m 3/s

Velocity triangles

Velocity triangles

Reduced cu 2 Slip angle Friction loss Slip angle Impulse loss Slip Best efficiency

Reduced cu 2 Slip angle Friction loss Slip angle Impulse loss Slip Best efficiency point

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

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

In order to get a better understanding of the different velocities that represent the

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

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 theoretical

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

Rothalpy The rothalpy can be written as: This equation is called the Bernoulli’s 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 a centrifugal pump is designed using Stepanoff’s empirical coefficients. Example:

Stepanoff We will show a centrifugal pump is designed using Stepanoff’s empirical coefficients. Example: H = 100 m Q = 0, 5 m 3/s n = 1000 rpm b 2 = 22, 5 o

Specific speed: This is a radial pump

Specific speed: This is a radial pump

We choose:

We choose:

w 2 u 2 cm 2 cu 2

w 2 u 2 cm 2 cu 2

Thickness of the blade Until now, we have not considered the thickness of the

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: s 2 = 0, 005 m z = 5

w 1 u 1 c 1= cm 1

w 1 u 1 c 1= cm 1

Dhub We choose: Without thickness

Dhub We choose: Without thickness

Thickness of the blade at the inlet w 1 u 1 b 1 Cm

Thickness of the blade at the inlet w 1 u 1 b 1 Cm 1=6, 4 m/s

w 2 cm 2=4, 87 m/s b 2=22, 5 o u 2=44, 3 m/s

w 2 cm 2=4, 87 m/s b 2=22, 5 o u 2=44, 3 m/s cu 2

w 2 cm 2=4, 87 m/s u 2=44, 3 m/s cu 2

w 2 cm 2=4, 87 m/s u 2=44, 3 m/s cu 2