Hi Clark,

This sounds like a Control problem, where you need to derive the Transfer Function using Laplace transform and then evaluate the System Response. Can you put up the block diagram?

(1) Understanding the fluid system

In analyzing systems involving fluid flow, you find it necessary to divide flow regimes into laminar flow and turbulent flow, according to the magnitude of the Reynolds number. If the Reynolds number is greater than about 3000 to 4000, then the flow is turbulent. The flow is laminar if the Reynolds number is less than about 2000. In the laminar case, fluid flow occurs in streamlines with no turbulence. Systems involving laminar flow may be represented by linear differential equations.

(2) Modeling via Differential Equations

Anyway, you can make a model of the rate of dispensing pressure simple enough to understand only by making simplifying assumptions and lumping together effects that may or may not belong together, by deriving the relations among the rates of change of the variables of interest using differential equations.

Once you’ve built the model, you should compare predictions of the model with data from the system. If the model and the system agree, then you gain confidence that the assumptions you made in creating the model are reasonable, and you can use the model to make predictions. If the system and the model disagree, then you must study and improve your assumptions. In either case, you'll learn more about the system by comparing it to the model.

The types of predictions that are reasonable depend on your assumptions. If your model is based on precise rules such as Navier–Stokes equations, then you can use the model to make very accurate quantitative predictions. If the assumptions are less precise or if the model is a simplified version of the system, then precise quantitative predictions would be silly. For your info, Navier–Stokes equations are a set of differential equations which describe the motion of a fluid.

(3) Numerical Methods

If the analytical approach fails, numerical methods provide quantitative information about solutions even if you cannot find their formulas. There is also the advantage that most of the work can be done by computers. The disadvantage is that you obtain only approximations, not precise solutions. If you remain aware of this fact and are prudent, numerical methods become powerful tools for estimating the rate of dispensing pressure.

I don't sense any technical difficulty if you can sketch a good & simple fluid flow diagram. It helps to make the problem more transparent. A picture is worth a thousand words. By the way, what is your discipline? Mechanical Engineering? Are you taking or teaching the Fluid Mechanics course now?