Is it possible to generate electricity using a water tower? Is it possible to build a water tower that will provide enough pressure to run an electricity generator? A water pump can be used to send water up to the tower. The water pump can be powered by solar panels. Alternatively the water pump could also be powered by the electricity produced from the generator.
The water tower can hold 20,000 to 30,000 gallons of water. Could this have enough pressure to send the water down a pipe and pass it through an electric generator where it will cause a turbine to rotate and produce electricity? 
Once the water passes through the generator it can be redirected back to the water pump. The water will then be pumped back to the water tower making it a water circulation system. I would like to find out if it is physically possible to produce more power from the pressure stored in the water tower than it is required to pump it up. If solar panels are used to power the water pump, is it theoretically possible to produce more electric power using this method?
I am not familiar with any similar projects but I am looking to see if this setup will have the capacity to produce enough electricity to make it a feasible project.
 A: Yes you can use the falling water to make electricity - that's how hydroelectric dams work. But if you are using power to pump water back up then you will always use more energy to pump it up than you get back from falling down. Otherwise you have a perpetual motion machine
The only way it makes sense is if you need to pump the water up for other reasons anyway - ie you are using this as drinking water storage and just want to recover some energy - or you can use cheap electricity to pump it up and generate a smaller amount of expensive electricity when it comes back down.
These are commonly used to balance out changes in demand - see 
https://en.wikipedia.org/wiki/Pumped-storage_hydroelectricity
A: If you want to know more beyond the physics concepts, please do ask over on the new Sustainability Stack Exchange, where we can cover the physics, economics and engineering of such a question. Here I'll deal with the physics (and only touch on the other aspects in passing)
Technical feasibility
Each of the bits of the system you propose happen in real life:
Electricity is used to pump water up a tower, to create a head of water. This is used in water distribution systems around the world.
Electricity is generated by releasing water from a storage system through a turbine, converting the gravitational potential into electricity: that's a storage hydro system.
Pumped storage hydro systems combine these two mechanisms, to take cheap off-peak electricity, store it as gravitational potential, and then release it as more valuable peak electricity.
And PV panels are used to generate electricity to pump water: I and others designed and sold several systems, back in the early 1990s, that did just that, for water well in Africa. (Not an advert, I've been out of that business for 19 years now).
So, the system you propose could work, technically.
Efficiency
Note that you never get more useful energy out than you put in, there are always losses. But storage hydro is one of the largest means of storing useful energy in the world, because it's so scalable, and so efficient.
The round-trip conversion efficiency is around 80%.
Energy density
Note that the energy density is pretty low
$$ E = m{\cdot}g{\cdot}h$$
The energy stored in raising 1000kg ($1m^3$) of water by 1 metre is just $1000 \times 9.8 \times 1 = 9800 J$, or 0.0027 kWh, which isn't much at all. And that's why pumped hydro facilities tend to be mountain-scale:

In Europe alone, there's over a hundred terawatt hours of storage hydro - enough to provide electricity for Europe for about 20 days.
A: There are many ideas analogous to the water tower/turbine/pump system (minus the solar panels). One common example is a water electrolysis system which passes an electric current through water to split water molecules into hydrogen and oxygen, which is then used as a fuel in either an engine or fuel cell to produce electric power to feed the electrolysis cell. When the expectation is to produce more power in the engine than is consumed in the electrolysis cell (or more power in the turbine than is consumed by the pump), you have what is known as an "over-unity" machine. Such a device is an impossibility.
A fundamental rule of physics is conservation of energy; an over-unity machine is a violation of this rule in that it requires energy to be created out of nothing. Since no real-world device can operate at 100% efficiency, any "over-unity" scheme will in fact consume more energy than it can produce because of losses - mechanical friction, electrical resistance, etc..
When you add a solar cell to the water tower / turbine / pump scheme, what you essentially have is a solar power system employing a water tower as an energy storage device. Such a system could store collected solar energy by pumping water up into the tower, and when the sun isn't shining, the system can still produce power from the turbine. The power source (and limit of capacity) is the sunlight falling on the solar panels, not the falling water.
A: The system you describe is known as pumped storage hydro-electric generation, and is feasible and in use at some hydro plants around the world.  But
Typically, 70% to 80% of the energy used to pump water is recovered when the water flows back down;  the balance is lost in various inefficiencies; the pump/generators heat up, make noise, etc...
At Niagara Falls, for example, tourism concerns limit how much water can be diverted from the Falls for energy generation, at various times of day and at different seasons.  These amounts of water seldom coincide with the amounts of energy needed at those times.  Both the Adan Beck (Canada) and Robert Moses (US) Power plants have large reservoirs behind them. Water is pumped into them at off-hours, up to levels above the water source.  When less water is available from the Niagara River, this stored water flows back through the pumps, generating some electricity, and then through the main generators, along with the reduced, unpumped water, making more electricity. 
A: O, the age old paradigm of Free Energy!!  The quick and dirty answer to your question is yes.  You could create electricity using the potential energy of the water stored in the water tower of height (h meters).  HOWEVER, you would also have to consider the amount of energy that would be needed to pump the same volume of water to a height of h meters.  In all cases, the energy needed to pump the water  up the tower is greater than or equal to the amount of energy that would be harnessed from allowing the water to flow from said water tower. 
Free Energy comes into play when the amount of output energy is greater than the amount of input energy.  This, I promise you, will never happen with the scenario above.
Since I have disproved the Theory of Free Energy in my above statement, let me make one more.  Take the system you suggest, and completely remove the water tower.  It would be much more efficient to hook up your solar generators directly to whatever you wanted to power.  Also cheaper, water towers aren't the easiest thing in the world to build.  
A: Yes, but...
Yes, this is how pumped-storage hydroelectricity stations work. Their purpose is to consume redundant energy from the grid during off-peak period and then feed it back into the grid when there's a demand peak. About 70% energy is recovered this way.
You can go deeper™ - use solar and wind power instead of grid power and then your water tower will work like a huge rechargeable battery with the only difference that it's not chemical but uses water potential energy. Wind and solar power systems are famous for their unstable output (because solar exposure and wind speed vary over time) and so they either need backup conventional power sources or something like a battery. A water tower could work as a huge battery just fine. This also helps with serving demand peaks - if you solar/wind source provides say 10 kilowatts on average and 20 kilowatts maximum you cannot possibly drain any more that 20 kilowatts unless you have a power storage (a battery or a water tower) which can supply extra power for short periods of time.
(the but... is below)
So yes, you can use a water tower kind of as a power source but in fact it will not be a power source it will instead work as a power storage and you would need an external source to pump water up the tower.
