ENERGY TRANSFER
Hydraulics or fluid dynamics has the primary influence on the geometry of a roto-dynamic pump stage—of all the engineering disciplines involved in the design of the machine. It is basic to the energy transfer or pumping process. Staging is also influenced by the other disciplines, especially in high-energy pumps. The basic energy transfer relationships need to be thoroughly understood to achieve a credible design and to understand the operation of these machines. Action of the mechanical input shaft power to effect an increase in the of energy of the pump-age is governed by the first law of thermodynamics. Realization of that energy in terms of pump pressure rise or head involves losses and the second law of thermodynamics.
The First Law of Thermodynamics
Fluid flow, whether liquid or gas, through a centrifugal pump is essentially adiabatic, heat transfer being negligible in comparison to the other forms of energy involved in the energy transfer process. (Yet, even if the process were not adiabatic, the density of a liquid is only weakly dependent on temperature.) Further, while the delivery of energy to fluid by rotating blades is inherently unsteady (varying pressure from blade to blade as viewed in an absolute reference frame), the flow across the boundaries of a control volume surrounding the pump is essentially steady, and the first law of thermodynamics for the pump can be expressed in the form of the adiabatic steady-flow energy equation as follows :
Here, shaft power Ps is transformed into fluid power, which is the mass flow rate times the change in the total enthalpy (which includes static enthalpy, velocity energy per unit mass, and potential energy due to elevation in a gravitational field that produces acceleration at rate g) from inlet to outlet of the control volume (Figure 1). When dealing with essentially incompressible liquids, the shaft power is commonly expressed in terms of “head” and mass flow rate, as in Equation:
Energy transfer in a centrifugal pump
The change in H is called the “head” _H of the pump; and, because H includes the velocity head V2/2g and the elevation head Ze at the point of interest, ΔH is often called the “total dynamic head.” _H is often abbreviated to simply “H” and is the increase in height of a column of liquid that the pump would create if the static pressure head p/ρg and the velocity head V2/2g were converted without loss into elevation head Ze at their respective locations at the inlet to and outlet from the control volume; that is, both upstream and downstream of the pump.
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