ABSTRACT
Using the numerical values given above and the lumped element values derived from Fig. 4-9, the reference computed the desired transfer function as:
(4-64) Using the same physical parameter values but the distributed-parameter method, this transfer function was:
Figure 4-24 shows the amplitude ratio and phase angle curves for both Jumped and distributed models, together with the values actually measured in the Jab test. The
Although our discussion has involved only one specific example, the basic concepts will carry over to all fluid systems. Once we have a formula for the velocity of propagation and choose the highest frequency of interest, we can pick a size and number of lumps which will give good accuracy up to that frequency, using the "10 lumps per wavelength" guideline. Higher operating frequencies require more and smaller lumps. If you are asking yourself, "Why use lumped models when distributed are available?", remember that the lumped models can be solved easily for the time response to any form of input and they also allow easy simulation with standard software such as our SIMULINK. The distributed models offer none of these important features, even though they are more accurate representations of the physical facts.
