The efficiency of the Plunger pumps is determined by the following physical quantities:
– Flow rate
The flow rate is the volume pumped in the unit of time and can be split into a theoretical Flow Rate Qt (the flow rate which can theoretically be supplied by the pump) and an actual flow rate Qe (the flow rate actually supplied by the pump). The Flow Rates are normally expressed by the unit of measurement l/min (metric system) or gpm (system used in English-speaking countries). The Flow Rate Qt is calculated according to the following formula (valid for metric units):
D [mm] = piston diameter
e [mm] = pump shaft eccentricity
n [rpm] = rotation speed
From the above figures in metric units, the flow rate in English speaking country units can be obtained with the formula:
The ratio between the two flow rates, theoretical and actual, defines the volumetric efficiency ηv of the pump:
The flow rate figures shown in the catalogue efficiency are those of the theoretical flow rate Qt, i.e., with volumetric efficiency ηv = 1.
The flow rate of positive-displacement plunger pumps is proportionate to the rotation speed and tends to be independent from the delivery pressure, while tending however to decrease with the increase of the latter. The pressure is the maximum value which can exist in the pump head in operating conditions. It must be pointed out here that positive-displacement plunger pumps do not intrinsically develop pressure during their movement, but move the liquid by virtue of their construction characteristics as described in the previous chapter. If however, downstream of the pump, in the delivery circuit, there is an obstacle (e.g., a nozzle), the pressure needed to enable the pump flow to cross the encountered obstacle is generated in the pump head. The delivery circuit must therefore feature a maximum pressure valve which prevents the occurrence of a pressure above the maximum pressure, set on the basis of the pump resistance characteristics. In fact, if the above obstacle were to form a complete blockage (e.g., total closing of the delivery circuit), the pressure would increase exponentially with consequent breakage of the head. If an adjustable by-pass valve is fitted, furthermore, a determinate pressure value can be set according to operating needs. Pressure is indicated in metric units, in bar, in MPa and in English-speaking country units in PSI. The relations between the above units of measurement are the following:
The effective power Nu of a pump is the energy provided to the pumped liquid in the unit of time, while the absorbed power Na is the energy in the unit of time which the pump requires from its energy source (electric, thermal, hydraulic motor, etc.) to perform the required pumping operation. The units of measurement used to express the Power are kW, CV and HP.
The effective power Nu is calculated with the formula:
The ratios between the other power units of measurement are as follows:
The absorbed power is tied to effective power with the ratio:
wherein ηt is the total efficiency of the pump produced by the three efficiencies ηv (volumetric), ηm (mechanical) and ηi (hydraulic). The volumetric efficiency ηv normally takes on values between 0.85 to 0.95. Lower values occur in pumps with higher pressures and higher rotation speeds, while higher values occur in pumps with lower pressures and lower rotation speeds.
Hydraulic efficiency ηi expresses the losses for resistances opposing the flow through the head and for high pressures typical of plunger pumps, and has values close to the unit. Mechanical efficiency ηm expresses the power drops in the mechanical-kinematic part: values are normally around 0.94÷0.96. On the basis of the above, the total efficiency ηt therefore takes on the lowest values (0.78÷0.80) in plunger pumps with higher pressures and higher rotation speeds and the highest values (0.90÷0.92) in plunger pumps with lower pressures and lower rotation speeds. The power values shown in the catalogue efficiencies are those of the absorbed power Na. The absorbed power in positive-displacement plunger pumps, with constant rotation speed (and therefore with constant flow rate) is proportionate to pressure.