CHAPTER 1

ACTIVITIES  > PROBLEMS  >  PROBLEM 15

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15

A model of a windkessel pump

The windkessel pump was invented for fire fighting purposes. The hand operated pumps worked intermittently. By placing a storage vessel (windkessel) between the pump and the hose, the flow could be made much smoother. (Windkessel functions can be found in different examples in nature and engineering. Example: Heart and aorta.)

Data is given in graphical form for a particular example. The pump increases the pressure difference at fixed intervalls (graph on the left, red curve). The resulting pressure of the liquid at the bottom of the tank (blue curve) is smoother and at an intermediate level.

The flow leaving the pump (when the pressure of the pump is greater than the fluid pressure in the tank) is strongly pulsed (like the pressure difference established by the pump).

1. Sketch a system dynamics model diagram that represents the windkessel pump system.

2. Write down the equations relevant for the model. Assume flows to be turbulent.

3. Estimate as carefully as possible the quantity of liquid transferred by the pump. Determine the average flow.

4. Use the average flow and the average pressure difference across the hose to estimate the turbulent flow factor for the hose in the model.

5. Use the change of pressure in the tank to estimate the capacitance of the tank.

6. Sketch the flow through the hose as a function of time. Compare to the flow from the pump.

                       
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