So you will forgive me if I don't understand the details, but I will try to help.
The depth of your pond creates pressure at the entrance to your pipe. You can determine that pressure with p=rho*g*h. That pressure drives the fluid flow and overcomes all losses through your pipe system. You will have an entrance loss, major losses (pressure drop along straight lengths of pipe), and minor losses (pressure drop due to those 45s). Each loss is a function of fluid velocity. It sounds like you also have an altitude change while in the pipe, so that needs to be included as well. So you basically write out a conservation of energy equation and the only unknown in the equation is the fluid velocity.
The calculation is sometimes referred to as the bernoulli equation with head loss. This website explains it reasonably well and has a few examples which seems relevant to your situation.
The Bernoulli Equation
Calculating the actual head loss terms is not explained well on that site, but you can find it via google. The units can be a little tricky to get right, because everyone writes the bernoulli equation differently and so the appropriate units on the loss terms must match whatever units you need. Also, there will be a friction factor (f) to be determined. It is simply a function of the pipe type (smooth in your case) and the Reynolds number (Re= rho*V*D/mu). There are correlations to calculate directly, but if you only need a few values, using something called the Moody Diagram is probably the easiest way to estimate f.
It is turning out to be harder to explain than it would be to actually calculate it. If you tell me the water depth, all the pipe geometries, and the altitude change between the pipe entrance and exit, I can try to calculate it for you if you want.