Improved Fuel
Economy with " Controllable Variable Flow " 

Euler Equations The principle Euler turbine equations apply also to this centrifugal coolant pump application which takes advantage of varying inlet swirl vectors. The geometry and notation used to develop the speed triangles for such a typical pump are shown in figure 1. Using the vector notations shown in figures 1 and 2 and applying the conservation of momentum relationship between torque and the moment of momentum applied to a fixed control volume enclosing the impeller in the tangential direction, the Euler turbine equations can be expressed to describe the theoretical head, a simplified form of which is represented as follows: H = ( u_{2 }x V_{t2 }±_{ } u_{1} x V_{t1 } ) closed 

Velocity Vectors The angles α_{1} and α_{2} shown in figures 1 and 2 express the tangential components of the absolute velocity vectors, V_{t1} and V_{t2} . The inlet component V_{t1} , written as V_{t1} = V_{1} cos α_{1} describes the amount and direction of inlet preswirl. Figure 2 shows the entry speed vector triangles for three cases. The triangles in figure 2 show the relative effect of the inlet angle α_{1 }on the entry vector V_{t1} . So, the magnitude of α_{1} denotes the effect of the inlet preswirl (or prerotation) on the Head, and Velocity vector product which is proportional to Flow. For example when α_{1} = 90 degrees (no preswirl), V_{t1} = zero. Similarly for α_{1} < 90° the sign is negative, effectively reducing the pump Flow and Head output, and conversely for α_{1} > 90° the pump Head (and Flow) output is increased. The resulting impact of pump performance is shown in figure 3, which depicts several different pump performance characteristics for variable inlet guide vane positions. 

Hydraulic Principles  Figure 2 

Variable Performance Range  Figure 3 

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