## Fluid

FIGURE 1 Energy transfer in a centrifugal pump

Here, shaft power Ps is transformed into fluid power, which is the mass flow rate m 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 Eq. 2:

P V2

Pg 2g e

The change in H is called the "head" AH of the pump; and, because H (Eq. 3) includes the velocity head V2/2g and the elevation head Ze at the point of interest, AH is often called the "total dynamic head." AH 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/pg and the velocity head V/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.

The Second Law of Thermodynamics: Losses and Efficiency As can be seen from Eq. 2, not all of the mechanical input energy per unit mass (that is, the shaft power per unit of mass flow rate) ends up as useful pump output energy per unit mass gAH. Rather, losses produce an internal energy increase Au (accompanied by a temperature increase) in addition to that due to any heat transfer into the control volume. This fact is due to the second law of thermodynamics and is expressed for pumps in Eq 4:

FIGURE 2 Determining component efficiencies. (This is a meridional view.)

The losses in the pump are quantified by the overall efficiency h, which must be less than unity and is expressed in Eq. 5:

It should be pointed out here that real liquids undergo some compressionâ€”which is accompanied by a reversible increase in the temperature ATc of the liquidâ€”called the "heat of compression." This portion of the actual total temperature rise AT is in addition to that arising from losses and must therefore be taken into account when determining efficiency from measurements of the temperature rise of the pumpage.1 See the discussion on this subject in Section 2.3.1.

To pinpoint the losses, it is convenient to deal with them in terms of "component efficiencies." For the typical shrouded- or closed-impeller pump shown in Figure 2, Eq. 5 can be rewritten as follows:

Noting that

H = Ideal Head one may rewrite Eq. 6 as follows:

## Renewable Energy Eco Friendly

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable.

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