The Brake Horse Power formula shows that the BHP changes with the cube of ratios of the speeds, which is an energy savings for a small change in speed. Replacing the RPMs with the impeller diameter will follow the same rules. Decreasing the diameter of the impeller from full size does reduce the head, flow and BHP. The further away from full size diameter, the greater the drop in efficiency. The reduction in horsepower due to a lower head should offset this efficiency drop.
The BHP can be calculated from the formula BHP = Q X F X Sp Gr. / 3960 X pump efficiency. This formula can also be used to predict the operating cost. The electric motor driving the pump has an efficiency factor, so to determine the operating cost, factor in the motor by BHP X .746 / efficiency of the motor = Pump kW. (Note: With fluids other than water, the fluid's specific gravity affects the BHP.)
As a process or heating-cooling system may operate at full load for only a small portion of a given day, if the pump speed can be changed, more energy savings can be achieved (as opposed to worrying about a few +/- points on pump efficiency). Proper impeller trim, pump size and operating point are all important to best operational efficiency. It may be economical to stage different size pumps to carry the load instead of a single large pump.
The viscosity of fluids pumped influences the pump's performance and efficiency. Viscosity influences the friction loss of all the components of the system and the heat transfer rate of heat exchangers in the system. It is the responsibility of the system designer to supply the pump manufacturers with the true flow and head requirements of the system operating with fluids other than water.
Many engineering handbooks can facilitate calculating the friction loss in pipes and fittings with different fluids. The Hydraulic Institute (www.pumps.org) has an engineering data book available with information on fluids and methods for calculating losses.
Once flow, resistance (head), fluid temperature and the fluid type-and if it is a mixture of water and fluid, the concentration-are calculated, the pump manufacturer can select the properly sized pump, materials of construction and motor. The viscosity of the pumped liquid is a critical factor to consider, since it affects pump performance and horsepower required. Centrifugal pumps normally use pumping liquids with viscosities below 3,000 SSU (660 centistokes, CST). They may be used up to at least 15,000 SSU (3,300 CST). The higher the viscosity, the more significant the reduction in capacity, head and efficiency.
The effects of viscosity on performance of a centrifugal pump operating at the Best Efficiency Point can be seen in Figure 3.
In the 1960s, the Hydraulic Institute published a chart that was used to determine the performance of pumps pumping different viscosity fluids. Since its initial publication, additional data has been collected from pump manufacturers, and ANSI/HI 9.6.7-2004, The Effects of Liquid Viscosity on Rotodynamic (Centrifugal and Vertical) Pump Performance, has been published. The new guideline allows the engineer to calculate the performance of a pump more accurately.
Many factors affect a pumping system's efficiency. It is not just the pump but the whole system that has to be analyzed. Ask whether the system is steady state or cyclic, and how it operates in off-peak periods to achieve the best efficiency.