There is a general rule of thumb that says your tank should be close to the size of your pump (22 gallon tank for 22 GPM pump). The main reason behind this rule is to keep the hydraulic oil from getting too hot. The pump can get pretty hot and the hydraulic oil takes on a lot of this heat as is circulated. If your oil circulates too quickly, it will not have enough time to cool down.
For a typical hydraulic system, you need to keep the temperature below 150 degrees Fahrenheit. Any hotter and it will start to damage the seals in the pump and valves. However, the optimum operating temperature is around 120 degrees so you want it to warm up somewhat.
I think my tank is a 12 or 15 gallon size. I have thermometer in the tank so I can watch it. I found out that on a hot summer day here in central Texas, I get 30 to 45 minutes before the oil gets too hot. So I have to take a break and let it cool down. Since then, I’ve added a hydraulic oil cooler with an electric fan that is controlled by a thermostat. It’s much like a small transmission oil cooler only it’s made for hydraulic applications and is matched to handle the 22GPM flow of my system. I got the 12VDC fan at a hot rod shop. The thermostat is mounted in the tank to measure the oil temperature directly. It turns the fan on at 130 and off at 120.
I did most of my shopping at Northern Hydraulics which has now changed their name to Northern Tool. They carry a decent line of pumps, mounting brackets, couplers, cylinders, etc. The oil cooler came from Graingers. I had my hoses custom made at a local hydraulic hose shop. I had them connectorized at one end only and cut a bit long. From there, I dressed them in and marked the end of the hose. I then took the hoses back to the hose shop and had them connectorize the remaining end.
Hydraulics are a lot of fun.