I have also felt that the Durand and Marquez-Lucero equation generates rather high flow rates but it is for a very specific situation that is rarely encountered in process plant design. This equation is for open ended pipes discharging freely into the space above the liquid level in a tank or pond. It is far more usual to find pipes that discharge into a tank below the surface level, or are kept full and hydraulically sealed by control systems.
And even when you do have a situation where the end of the pipe is not hydrulically sealed and does discharge above the liquid surface it would be unusual to require the pipe to be running full. So I have to agree with Bobby Strain that it is not something we come across often.
I can recall only one instance where I have seen that it was relevant and important. And although Bobby says he has never seen such a situation I think it is probably because his good pipe designing skills did not allow him to get into this bad predicament!
I was asked to trouble shoot a situation similar to that shown in the attached sketch. These are not the real numbers - it was too long ago for me to remember them exactly but I have set up a similar situation to illustrate the principle.
Tank 1 overflows at a rate of 35 m3/h through 63 m of 100 NB HDPE pipe to the free space above the liquid in Tank 2. The run from A to B is 50 m long and is horizontal. Section B-C drops vertically for 3 m. The final 10 m from C to D is horizontal. The design engineer had calculated that the friction loss would be 980 mm of water column and since the actual difference was 3 m it was believed to be a safe design. In practice Tank 1 overflowed and the line was not able to cope with the 35 m3/h flow.
As I said, Bobby would never design something like this and all of the experienced engineers reading this have already spotted the mistake. For the sake of any inexperienced engineers I will show how the Durand/Marquez-Lucero equation can explain the problem. This equation (and the table prepared by ryn376) gives the sealing flow for a 4" (100 NB) pipe as 335 USgpm (75 m3/h). This indicates that the horizontal section from C to D will not run perfectly full at 35 m3/h - although it would be more than 75% full according to Ankur's table. It does not matter how full it is - as long as there is a continuous air layer above the water it means that the pressure at C is the same as at D.
If the horizontal section from C to D is not full then the vertical section from B to C is even less likely to be full. And if there is a continuous air portion in the vertical section it means that the pressure at B is the same as at C. So we come to the conclusion that the pressure at B (or just below B ) is atmospheric. If we calculate the pressure drop from A to B (including the entrance and acceleration effects) we see that it is almost 1 m of water column and since the pressure recovery the design engineer expected to get from the drop between B and C does not exist the only way to get this head is to increase the level in Tank 1 and that is why it was overflowing.
So. even if we do not use this equation to design pipe systems that we actually build, it is useful in enabling us to avoid design mistakes. It may be that the equation predicts values on the high side, but I believe that pipes designed this way will definitely be full.