Centrifugal Pumps

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Centrifugal pumps:

Centrifugal pumps

Impellers:

Impellers

Multistage impellers:

Multistage impellers

Cross section of high speed water injection pump:

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

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

Specific speed that is used to classify pumps:

Specific speed that is used to classify pumps n q is the specific speed for a unit machine that is geometric similar to a machine with the head H q = 1 m and flow rate Q = 1 m 3 /s

Affinity laws:

Affinity laws Assumptions: Geometrical similarity Velocity triangles are the same

Exercise:

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

Exercise:

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

Velocity triangles:

Velocity triangles

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Slip angle Reduced c u2 Slip angle Slip Best efficiency point Friction loss Impulse loss

Power:

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

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

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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

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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:

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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:

Stepanoff We will show how 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

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Specific speed : This is a radial pump

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We choose:

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u 2 c 2 w 2 c u2 c m2

Thickness of the blade:

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

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u 1 w 1 c 1 = c m1

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We choose: D hub Without thickness

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Thickness of the blade at the inlet u 1 w 1 C m1 =6,4 m/s b 1

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u 2 =44,3 m/s c 2 w 2 c m2 =4,87m/s b 2 =22,5 o c u2

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u 2 =44,3 m/s c 2 w 2 c m2 =4,87m/s c u2

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