This model represents the transition in a smooth-walled, piping system from large diameter of 16 cm to small diameter or 8 cm, together with an elevation change between pipe centerlines of 8 cm. The fluid is water and the volume flow rate is about 0.8 liter/second. Under these conditions of largish smooth pipes and smallish flow rate, the water will be a fair approximation of an ideal fluid.
Similar to the pressure depth dependence model we use imaginary surfaces to segregate volumes of fluid. Here we construct an imaginary surface in each section of pipe and consider the work done on the fluid in each region as the flow proceeds from left to right.
Since the fluid is incompressible, the volume flow rate through both large and small pipes must be the same. The large pipe is twice the diameter of the small pipe so the large section has four times the cross section area of the small section. For the volume flow rates to be the same, the velocity through the small section must be four times the velocity through the large section.
Just click on the drawing area to enable the keyboard focus in that window and use the up and down arrow keys to step forward and backward through time as the fluid flows through the pipe. The displacement of the fluid in each section of pipe, the work done in changing the velocity, the work done in changing the elevation, the total work done and model time are reported in the upper left quadrant of the drawing area. The Clear button resets the initial conditions.
The total work is in joules. If you divide that number by the model time you get joules per second, which is watts. That tells you how much power is required to maintain the flow rate through this system. I get about 0.64 watts. As you can see the bulk of the work goes into lifting the fluid.
For details on the operation of applet controls, see the Model Controls help page.