Although gravity-driven flow downwards in a vertical pipe seems simple, it gets very complicated when you get into the details. The most common example of this in everyday life is the domestic effluent drain lines (stacks) in highrise buildings. To get around the complications, the plumbing codes stipulate very safe rules of thumb for the pipe sizes, flowrates and venting requirements. In fact, you would probably get to a better design using these codes than by using a simple Darcy-Weisbach calculation.
The crux of the problem is illustrated if you calculate the pressure in the vertical drain line at exactly sea level. The pressure required is just the 0.54 m head you calculated to overcome the friction losses because the static heads in the pipe and open sea cancel each other. Now that you know that the pressure is 0.54 m at the sea level point you can start to work back up the pipe. To give this 0.54 m of head all you need is 0.54 m of water in the pipe. If the level in the pipe was more than 0.54 m then the pressure would be higher than needed and the level would drop as the excess flow caused by the higher pressure drained the pipe down to the equilibrium point of 0.54m again.
If you cannot have a level in the drain pipe of more than 0.54 m above MSL, what is above the water in the pipe? At start-up the pipe will be full of air, but with time the air will be dissolved or entrained into the water and will be removed. This could take days or even weeks. Once the air has gone the pipe must be filled with vapor, but to provide vapor the water must boil. Now you get into all sorts of problems with vibration and cavitation and you should avoid anything that could cause vacuum conditions here.
The solution is to take the same approach as the plumbing codes and to install a vent immediately after the control valve so that there is a supply of air to fill the pipe above the equilibrium water level. So now we have fixed the pressure at the downstream side of the valve at atmospheric pressure, and the pressure drop across the valve is simply the static head in the supply tank. That solves the valve sizing problem, but we still have the pipe sizing problem to contend with.
A flow of 10 m3/h in a 3" Sch 80 pipe gives a velocity of 0.65 m/s and a Froude Number of 0.76. This means that there will be a continuous entrainment of air into the falling water and air will be sucked in through the vent after the control valve. I have come across some quite serious whistles in situations like this and there is a danger of sucking debris, birds etc into the vent. In some instances entrained air can also impact the process at the discharge point, but that is probably not a problem here.
To prevent the air entrainment the Fr No must be kept below 0.31, which translates to a 5" pipe for 10 m3/h. On the other hand, the pipe below sea level will always be full of water, so from about 1 m below the sea level to the discharge point you could switch to 2" pipe (which would raise the equilibrium level in the drain pipe to 3 or 4 meters, but there is plenty of head to play with here).