Each system configuration will be unique, so there is no way to know exactly how many pumps you are going to need. A very simple arrangement may only need one, to bring water from the fish tank up to the plant beds. Gravity can be used to let the water from through the growing medium and back into the fish tank. Additional pumps are going to be needed if you are using settling tanks, and to supply multiple grow beds. Gravity can be a big help if you can arrange things so that water can naturally flow "downhill" as often as possible.
The simplest arrangement is that you use a pump to move a portion of water from your fish tank, so that it flows into your growing bed. From there, you would either pump the water back into the fish tank or have it naturally flow back into the tank (a sloping grow bed will help with this design). After a certain amount of time, the pump will have to run again and reflood the grow bed. This is the basic ebb and flow design, and it will require 1 or 2 pumps. If you can't have it flow naturally back into the tank, then a 2nd pump may be required to empty out the grow bed.
If you have a deep water system, you will still need just one pump on average. The cycling process is a little less critical because the tank of water under your plants stays basically full at all times. Water is pumped from the fish tank into the plant tank to keep the flow of fresh nutrients going, and the plant tank then overflows on its own back into the fish tank. Unlike the on/off nature of ebb and flow, the water levels for the fish stay constant through the entire process.
A system with a sump tank may not necessarily need an extra pump since the water usually flows via gravity from the fish tank to the sump, leaving you the need for still just one pump.
Small aquarium pumps aren't going to cut it either. You'll need reliable pumps that can move many gallons of water relatively quickly. The specs you need to focus on are the obvious gallons per hour rating, but also the "head height" (which refers to the distance vertically that you are moving water). Each model of pump should provide both details. Basically, a pump may move 640 gallons per hour through level pipes, but then only 390 gph to a height of 5 feet. Do some measuring around your tanks and grow beds before you buy a pump or you might not have the water-moving power you need.
An aquaponics system isn't going to run for a full hour at a time either, so figure that into your calculations. To use the above pump as an example, it would take an hour to move 640 gallons. If you need to move that much water in just 15 minutes, you'll need a bigger pump.
Pumps designed for ponds are often use, though there are many models designed specifically for aquaponics that can handle these loads. Costs can run from $50 to beyond $300. For a new small system, the pump should cost you under $150.
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