Tun Geometry and Flow Potential
The biggest factor for determining how uniformly the grainbed is rinsed is the distribution of the drains. Experimentation and computer analysis have shown that the fluid flow velocity at any location in the grainbed during lautering is a function of the depth and the straight-line distance to the drain. What does this mean? Let's look at Figure 167.
Figure 167 - Lauter tun cross sections showing flow directions.
Figure 167 shows a cross section of the grainbed being lautered by one pipe running up the middle. The lines surrounding the drain show regions of equal flow potential, i.e. pressure. Look at the gradient line with a relative value of  in figures 168-173 to better illustrate the differences between the different configurations. The arrows in figure 167 show how the flow is vectored toward the drain by these pressure gradients. Notice how the flow is concentrated toward the center of the tun, leaving the areas at the corners with very low flow velocities. Colored dye studies showed this same result. During the lauter, single drain systems did not adequately rinse the grain in the corners while the center was so thoroughly rinsed that tannin extraction was likely. Under some conditions and layouts, it is possible that only 2/3 of the total grainbed would be adequately sparged, resulting is a low total extraction, and of that 2/3, a significant percentage may have been over-sparged, possibly resulting in tannin extraction and astringency.
I should point out that this is an extreme scenario. Many brewers use single pipe systems (most notably the JSP Easymasher) and produce consistently fine beer. What this section hopes to illustrate is that by understanding how flow through the grainbed works, you can take the guesswork out of designing an efficient tun.
Figure 168 - Grainbed depth comparison.
There are two ways to improve the uniformity of the flow: increase the depth of the grainbed or add more drains. Increasing the depth of the grainbed (see Figure 168) puts more of the grain higher up in the regions of flatter gradients. Adding more pipes and spacing them efficiently (see Figures 169-173) also flattens out the pressure gradients and make the flow through the grainbed more uniform.
Look at Figures 168, 169, and 170. Comparing these figures shows how increasing the spacing between two pipes from 2 to 4 to 6 inches moves the  gradient off the bottom, up the sides of the tun, and dips it down in the middle. The 4 inch spacing illustrates the guideline of having the distance to the walls be half of the pipe spacing and is clearly the most balanced with respect to the gradients. Adding additional pipes, as in figures 172 and 173, and maintaining the spacing guideline improves the gradients even further. Experimentation has shown that the maximum effective drainage radius for a 1/2 dia. pipe is about 3 inches, equating to a maximum suggested pipe spacing of 6 inches.
Figure 169: 2 drains spaced 2 inches apart. Note that the flow is concentrated towards the center and away from the walls, similar to a single pipe system.
Figure 170: 2 drains spaced 4 inches apart. Note that the distance to the walls is 2 inches or half of the drain spacing.
Figure 171: 2 drains spaced at 6 inches apart. Note that the flow has be vectored away from the center and is concentrated near the walls.
Figure 172: 3 drains. Compare the gradients here to those of figure 170.
Figure 173: 4 drains. Compare the gradients here to those of figure 170 and 172.