Here is a simple table that converts head (the height of the water above your house in this example) directly to pressure:
http://www.engineeringtoolbox.com/hydrostatic-pressure-water-d_1632.html
As an example, if the vertical height of the water (measured from the top water surface) above the pipe where it enters the house is 16 meters (52') higher, this will produce
precisely 1.6 bar, or 23 psi. If the house is two stories, you will get less pressure on the second story, because the height difference is lower.
While this would work, most people would find that pressure inadequate.
You could always add an inexpensive pump to pressurize the water from the tank to 4 or 4.5 barr in the house, regardless of the head pressure.
By the way, you could just use one pipe to the tank. Water can travel either way in that pipe depending on what's going on. If the city pipe is supplying more than you are using, the excess goes into the storage tank. If the city pipe is supplying zero, then the water flows the other way and the tank supplies water to the house. Then you just need one big pipe and a check valve on the city pipe so water can't flow from your tank into the zero pressure city pipe.
Your flow rate, on the other hand, depends on both the pressure, AND the size of the pipe. For example, a 25mm (1") pipe will allow for a far far better flow rate than a 12mm (1/2") pipe at the same pressure.