Analysis of Centrifugal Pumps (continued)

Summary: The principles of conservation of mass, angular momentum, and energy apply

directly to the analysis of centrifugal pumps. The table below details the kinematics involved

and lists each of these principles for steady, uniform flow. Let 1 denote the fluid entering the

leading edge of the vane and 2 denote the fluid exiting the trailing edge of the vane.

Kinematics	V = U + W Note: Vector addition. Construction of the velocity diagram is a key step in the analysis. Two constructions are necessary: One diagram for the entrance to the vane and one for the exit of the vane V = absolute velocity of the fluid U = absolute velocity of the impeller taken at the entrance to the vane and at the exit of the vane W = velocity of the fluid with respect to the vane on the impeller Note: For an ideal pump the W doesn't change along the vane. It is the same for the inlet and for the exit on the vane.
Conservation of Mass	dm/dt |1 = dm/dt |2 or ρA1V1r = ρ A2 V2r (slugs/sec or kg/sec) Let r1 denote the entrance radius of the vane with height b1 Let r2 denote the exit radius of the vane with height b2 V1r is the radial component of the absolute fluid velocity at 1 V2r is the radial component of the absolute fluid velocity at 2 Entrance (1) means the leading edge of the vane and exit (2) means the trailing edge of the vane. Where: A1 = 2π r1 b1 and A2 = 2π r2 b2
Conservation of Angular Momentum (Torque or Shaft Power) Tz ω = P	ρ Q [( r2 Vt2 ] = Tz (ft lb) or (N m) Note: Vt1 = 0 ρ Qω[( r2 Vt2 ] = P (ft lb/sec) or (Nm/sec)

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