I've seen it recommended in several places to add a tee in the pipe next to the pump used for transferring hot wort. What is the point of this / what benefits do you get? Does the tee go on the input or output side of the pump? This is the pump I'm using, and my current setup has tubing from the ball valve on the kettle directly to the input of the pump, then a ball valve on the output side of the pump, then tubing to the chiller.
Do you really mean just a tee? I guess not, since there's not much benefit, and you'll just get lots of spilled wort!
I'm guessing you mean a tee, plus an attached valve - affectionately known as a "burper valve", which can help rid trapped air from the pump. When the liquid first flows through the pump, it displaces the air, which can become trapped in the pump and prevents the pump from priming correctly. The tee plus valve provides a place for the air to collect, and can be released by opening the valve.
The tee plus valve goes on the output side, preferably oriented upwards, like this example:
(It doesn't matter if the air feed is horizontal off the tee since by that time, it's already well past the pump and won't interfere with the pump's operation.)
As well as releasing trapped air, the additional outlet is handy for taking gravity samples, during the mash, sparge and final runoff to the fermentor.
FWIW, I don't use a T on the outlet side to prime. My system isn't hard plumbed where I need it. The outlet hose I have on the pump serves as the air escape. The reason to use a venting T is when the outlet end of from the pump is connected to plumbing (or hoses) that goes into fluid. The fluid tends to create just enough back pressure that the pump doesn't prime.
I have a circular copper tube that sits in the wort above the mash, but it is submerged. When I turn on the pump and open the outlet valve from the tun the wort doesn't flow out that well and its because the end of the line is submerged. When I lift it out of the wort it primes up fine.
If I was too put a more permanent recirc setup in I'd need a T because I couldn't simply lift the hose out of the tun to clear the "back pressure".
Not much to add to mdma's very nice answer. The first time you get cavitation in your pump and lose prime, you will most definitely appreciate having the 'burper' valve to re-prime. Just open it up, let some liquid flow, then continue pumping away.
I thought I'd add a few pictures of my own tees for reference.
I used an acetal plastic gate valve on this one.
And this is a more fancy stainless setup, complete with tri-clamps so I can use the teed valve to prime, sample, reciruclate, and pump directly to my fermenter.
Also, it's much shinier.