Trapezoidal passage sections Take a look at Figure 3. You'll notice how the pressure distribution pattern has become more uniform during the bend. Had the passage begun with a square cross-section, it would have transitioned (gradually) into the trapezoidal shape you see at the apex of the bend, up to the apex of the bend, and transitioned (again gradually) back into a square section at the passage's exit. The same would have occurred regardless of the entry and exit passage shape; e.g., circular, rectangular, and such.
Not surprisingly, gradually widening the short-side base and making the long-side base more narrow (forming the trapezoid) caused velocity pressure along both paths to become more uniform, causing the flow (wet or dry) to transition through the turn without realizing the full impact of a directional change. Both wet and dry flow conditions stand to benefit from the method.
Here's where you might want to build a test flow-box. It needn't be fancy. One way is to whittle out a wooden "plug" that's shaped like the passage you plan to evaluate. Using 2-inch-square patches of fiberglass cloth and some casting resin, wax-coat the plug and layer it with resin-impregnated patches of 'glass, randomly overlapping them to provide coverage and strength. A couple of layers are sufficient.
When the 'glass hardens, split it down its length and remove the plug, covering the cut with a few more patches of resin-soaked fiberglass cloth. Now you can attach your new "flow-box" to a mounting flange that's connectable to the bench, form a molding clay radius for an entry, and you're ready to take some measurements. Although somewhat crude, this model will help you visualize the pressure distribution relationships being described.
Using a manometer and Pitot tube for downstream flow velocity data, you can begin profiling sections through the length of the passage (see sidebar on pressure mapping). Note the similarity in velocity pressures, comparing the short- and long-side paths. Compare these same two areas at the entry and exit (assuming you are using the recommended entry radius). By adjusting the transition from square to trapezoid and back to square again, you'll be able to approach equality of pressure maps at the entry, midpoint of the bend, and exit. At that point, the flow's recognition of a directional change is minimal.
This concept is particularly applicable during conditions of wet-flow where the mechanical separation of air/fuel charges can lead to a number of consequences, virtually all of which are undesirable and include lost power and potential damage to parts. By minimizing pressure distribution differences that can lead to energy imbalance and losses in flow efficiency, it's possible to optimize volumetric efficiency and reduce problems associated with intake and exhaust flow paths.
Understand that what we're discussing is outside the intentions of what you may have heard or read about the benefits of "controlling" air or mixture motion in induction systems. This technique (sometimes referred to as "swirl" and "tumble") is more directed to exhaust emissions and fuel economy benefits, particularly at engine speed (flow rates) well below what you find in a circle track engine. Taken to extreme, these features in the inlet track can lead to poor mixture control and unwanted variations in mixture ratio as a result of excessive motion of fuel particles.
Determining the proper trapezoidal shapes Experience has shown that unless you have access to a comprehensive computational flow analysis (CFA) or comparable software package, experimental investigation is probably the best approach. Depending upon specific dimensional characteristics of the flow path change you're confronting (space limitations, abruptness of the change, and such), you'll likely find the width relationships between the upper and lower bases of a trapezoid won't become the same from passage to passage. In some cases, the smaller base width may be roughly half that of the larger, but don't expect one rule to hold for all cases.