Is there a way to fill Tank 2 from Tank 1 through Gravity alone? I am a newbie in water system design but I am currently faced with the exact situation below on my land, and I need to know whether gravity alone is sufficient in order to fill Tank 2 from Tank 1, as I already experienced backflow.
Please have a look at this image:

Note: let's not worry about how Tank 1 is being filled as it probably does not matter - I just made sure I never used a pipe diameter smaller than 0.5" between Tank 1 and Tank 2.
As you can see:


*

*My water source is the overflow of Tank 1

*I have put a 1" diameter pipe in the first 'downhill' section of my path

*The second, longest section of the path is a pipe of 0.5" diameter

*The system is 'powered' through gravity alone
Questions


*

*Is there any missing variable (eg path length?) on my drawing in order to resolve this system? (What are the important variables?)

*The flow at the source (the overflow of Tank 1) can be nearly 0. How does this variable influence the system? (Can a larger flow at the source help going up the 'uphill' sections between the tanks?)

*Is the 'head' variable important at all?

*I used a bigger pipe for the first section in an attempt to 'make more weight' and create sufficient pressure to go up the small uphill that follows. Should I limit the use of that bigger pipe strictly to the downhill section, and does it actually make sense to have used a bigger pipe at all?
 A: You want to make sure your pipe is sized such that the flow, Q, out of tank 1 is greater than the flow into tank 1.  
Or, at some level, you want to know the maximum flow, Q, that the system will allow.  You can solve this kind of problem using the Bernoulli Equation for conservation of energy with the Darcy Weisbach equation to account for frictional losses equation:
$\frac{P_1}{\gamma}+z_1+\frac{v_1^2}{2 g}=\frac{P_2}{\gamma}+z_2+\frac{v_2^2}{2 g}+f\frac{L}{D}\frac{v^2}{2g}$
If we assume both tanks are under atmospheric pressure, the fluid in both tanks is not moving, and we neglect minor losses from the bends in the pipe and the change in pipe diameter then the equation reduces to:
$z_1-z_2=f\frac{L}{D}\frac{v^2}{2g}$
Where the term $z_1-z_2$ is what you're calling head.  Actually, because both tanks are full, it does not matter if the pipes are at the top or botom of the tanks, As long as both pipes are submerged the change in head (from free surface to free surface) is what's important.  so the variables we have are:


*

*$head$: the difference in water surface elevations 

*$f$:a friction factor that depends on what the pipe is made of, and how fast the fluid is moving in it,  

*$L$: the pipe length, 

*$D$: the pipe diameter,

*$v$: the fluid velocity,  

*$g$: is gravity, which is a constant


Your system is a little more complicated because we have two pipe diameters, so the equation should look like, 
$z_1-z_2=f_A\frac{L_A}{D_A}\frac{v^2}{2g}+f_B\frac{L_B}{D_B}\frac{v^2}{2g}$, although i'm going to focus on the concept here, so i'm going to stick with the simpler equation.
to find the friction factor, $f$, a moody diagram is typically used... although because you're having backflow at times, i'm going to assume your flow is low enough that we can estimate the friction factor as:
$f=\frac{64}{Re}=\frac{64 \nu}{v*D}$
where $\nu$ is the kinematic viscosity of water.
This makes the equation:
$z_1-z_2=\frac{64 \nu}{v*D}\frac{L}{D}\frac{v_A^2}{2g}$
solving for the flow rate $Q$ ($Q=V A$) gives:
$Q=\frac{\pi D^4 g (z_1-z_2)}{128 L \nu}$
So you can see that the maximum flow is strongly influenced by pipe diameter!  The bigger the pipe, the more flow from tank 1 to tank 2 will be possible.  Additionally, contracting from 1" pipe to 0.5" pipe is restricting the flow even more, do to energy losses at the connection.  Shortening the length of pipe used will also help you, but not nearly as much as increasing the pipe diameter.  Doubling the pipe diameter will give you 16 times as much flow!  The change in elevation of the free-sufrace of both tanks (head) is for sure important, but if you can't change it, that's ok. Finally, the pipe material is an important factor at higher flow rates, but maybe not for your current situation at a low flow rate.
A: *

*The main variables you're missing are those relating to energy losses to friction, such as the total surface area of the path. Why not use a straight pipe than a winding one?

*Of course the "head" is important, this is the potential difference driving the motion. If it were zero between Tank 1 and any point in the path, there would be no flow.

*Larger pipes are better.
