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### Wind Mill Powered Piston Pumps Design Equation and Calculator

Wind Mill Powered Piston Pumps Design Equation and Calculator

Positive displacement piston pumps are used in most of the commercial wind pumps. Constructional features of such a system are shown in Fig. 1. The system consists of a high solidity multi-vane wind rotor, drive shaft, crank, connecting rod and a reciprocating pump. Rotary motion of the windmill rotor is translated to reciprocating motion of the connecting rod by the crank. The connecting rod operates the pump’s piston up and down through the cylinder during its strokes. Two check valves, both opening upwards, are fitted on the piston and the bottom of the pump. These valves allow the flow only in upward. direction.

Wind driven piston pump Figure 1

When the connecting rod drives the piston in the upward direction, the piston valve is closed and thus the water column above the piston is lifted up, until it is delivered out through the discharge line. At the same time, suction is created below the piston, which causes the suction valve to open and thus fresh water
from the well enter into the space below. During the downward stroke, the piston valve is opened and the suction valve is closed. The water collected below the piston thus enters into the space above, through the piston valve. These cycles are repeated resulting in pulsating sinusoidal water discharge from the system.

The volume of water discharged during one delivery stroke is given by the product of inner area of the cylinder and the height through which the water column is displaced during a stroke. Thus, if d is the inner diameter of the pump cylinder and s is the stroke length (distance between the extreme lower and upper positions of the piston) then, theoretically the volume of water pumped per discharge stroke is given by

Eq. 1
Vs = π · d2 · s / 4

Eq. 2
s = 2 · r

where r is the crank length. As the pump delivers one discharge per revolution of the wind rotor, the discharge is given by

Eq. 3
Q = ηv · Vs · d2 · r · N / 2

where ηv is the volumetric efficiency of the pump and N is the rotational speed of the driving wind rotor. Usually, the volumetric efficiency of piston pumps is quite impressive, typically higher than 90%. The power requirement of the pump (P ) for a discharge Q may be estimated by

Eq. 4
PH = ρw · g · Q · h / ηp

where ρw is the density of water, g is the gravitational constant, h is the total head against which the pump delivers water an ηp is the pump efficiency. Density of water, under standard ambient conditions, can be taken as 1000 kg/m3. The pumping head includes the suction head, delivery head as well as the frictional head. Similarly, the pump efficiency takes care of various efficiencies involved in converting the mechanical shaft power to hydraulic power.

Limitations of wind driven piston pumps

Mechanical coupling of a piston pump with wind rotor makes the system simple and cost effective. Many of such pumps are installed at different parts of the world. However, the field performances of these units are not encouraging.

The major reasons are:

• hysteresis behavior of the system due to its high starting torque demand
• mismatch between the characteristics of the rotor and the pump