What just happened to my pump motor?

No. Lower is better. That's the tolerance...how far off the listed value it can actually be.
I edited my reply above. 370VAC versus 450VAC. Someone else said to match the spec's exactly, but clearly this is well out of my wheelhouse. I can change it safely enough but know nothing about capacitors and voltages.
 
It's fine. You can take a higher voltage, but not a lower one. Tolerance should be same or lower.
Critical measures are: capacitance (30uF), frequency (50/60Hz), working voltage (370VAC).
The one I linked lists 370VAC, with a max voltage of 450VAC. That basically means it's rated for a range of voltages. Your supply is around 240VAC. They spec a capacitor that can operate up to 150% of that to accomodate line surges and the like. The one I linked is good up to 450VAC, which means it will be a bit more tolerant (less "explody") with higher line surges. The one I linked also is designed to minimize the chance of explosion. These days, large electrolytics have a mechanical design that will allow them to swell, then pop an overpressure feature in the case rather than explode (still can explode, just less likely).
 
Figure out how you will secure the capacitor cover. If you can't get a waterproof seal on the capacitor cover then a new capacitor will not last.
 
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Get the 450 VAC. 340 is adequate but the 450 will give you more voltage breakdown “headroom.” The line voltage is expressed as RMS (root mean square), like square root of 2 times the RMS value to calculate peak to peak voltages on the line. At 240 VAC, peak voltages are 340 v. Get the higher voltage rated cap.
 
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The oil filled motor start* capacitor actually blew up! Cool. Like everyone has said, USUALLY this is very fixable. On AC motors the capacitor is switched in to make a phase difference for a second pole in a single pole motor (single phase) until the motor hits a certain speed. a internal centrifugal switch breaks to connection to the start winding at a certain speed, usually about 75% of the final speed. These do have limited life times and there is no doubt that it failed and was either the cause or the symptom of the motor not running when it blew across the patio! On motors with start capacitors, the motor will just sit and buzz without the start capacitor in line. This can cause one of the windings to fail. Hopefully this isn't the case in your motor. But if it does buzz that at least means that the winding isn't open. It still could be shorted but this usually takes out the breaker.

Probably once you put the new capacitor in you'll be back to the races. If not then the motor or pump will need to be replaced...sorry... Motor has to be physically compatible with the pump, it's probably worthwhile in this case to upgrade to a newer pump. Maybe splurge and get a VSP, the energy efficiency boost will help pay for itself over a couple of years.

(*Some single phase AC motors can use a run capacitor instead, or a combination of the two. Likely it's a start capacitor from the pictures and what I understand about pool pump motors.)

Sounds like you have it under control. If this is the worst thing that happens to you this week, consider yourself lucky! :)

In college, they had fluorescent light bars in the dorm bathrooms that had a switched outlet in them. We got a box of old electrolytic caps given to us that really weren't useful to build into new projects--several showed evidence of drying out and they changed value with testing.... and for several weeks there were a lot of small explosions when the lights were turned on in the restrooms.... Oh, the humanity!
 
I should add that the comments about the working voltage-- higher is better-- and sticking to the original value as practically as you can are correct. If you go too low in voltage rating the capacitor will fail prematurely. Bigger will be better until it doesn't physically fit on the motor.

As for value... that determines the amount of phase shift of the AC current to start the motor. You really need to get close to the original capacitor's value to get the right amount of magnetic shift in the motor. Now can you put in a 33uF in place of a 30uF? Likely... but you certainly can't put a 100uF in place and you'll probably have problems with 20uF or 47uF for example. This is what you need to take into account for tolerances...+/- 10% is pretty typical and should be fine for a motor. smaller is better here, but don't lose sleep over this.

You can also try an electronics supplier like Mouser and Digi-Key... you might be able to find an exact replacement there...
 
You know, owning a pool is like owning an airplane. You meet some really cool people. Thank you all for the help. I ordered the Amazon one recommended in a previous post. It’s $12, but it takes two days. I called my pool store and asked a ballpark price, and she said about $30. I totally would have walked in and bought it, but she started asking me about specs of which I gave her most, but I was driving. Then she started giving me the attitude she normally gives me, like I was imposing, and now I plan on buying and installing a SWG from someone else so I never have to buy their outdated, stale liquid chlorine again, and never give them my $2,000/year (minimum) business anymore.
 
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Thank you all. I got the new capacitor today. I ordered the one on Amazon that jedigrover recommended. The capacitor works and pump motor seems to be working fine. The only issue is that this capacitor is a little fatter than the OEM so it’s too thick for the cover, so I can’t screw it back down. Meanwhile I have the cover sitting on top and I used a bungee cord and a trash bag to cover it. But it was only $12 and now I know my pump motor is good. So tomorrow I will find another one equivalent with a slimmer form factor.
 
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So just one note for others searching for this issue in the future, one spec to not overlook is the diameter. The OEM is 1 3/4 in and that will fit into the capacitor cover on a pentair centurion pump motor like mine. Many of them come in a 50 mm diameter, which is about 2 inches and this will not fit. You need the 1 3/4 in diameter.
 
One question: is there a polarity for the two leads or do I just connect each lead to each terminal on the cap? I noticed one lead had a blue marking, and there was a blue marking on the cap, so I went with that and it worked fine. But no pos/neg markings and no red/black either.
 

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One question: is there a polarity for the two leads or do I just connect each lead to each terminal on the cap? I noticed one lead had a blue marking, and there was a blue marking on the cap, so I went with that and it worked fine. But no pos/neg markings and no red/black either.
No polarity. It’s an AC device.
 
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Even though those are electrolytic capacitors they are designed to be non-polar. Again, if you are having a problem finding a proper physically sized capacitor, you might want to look at Mouser or Digi-Key-- electronics suppliers. They both are first rate and honestly, maybe one day slower than Amazon. I am very happy it worked out for you. They might even have the same brand and type as the original.
 
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