Ibu's and effects of adding water post boil

[Aschecte]

How would adding top up water effect the Ibu's of the beer. A specific example is that I had done a 8 gallon boil which I calculated at 64 Ibu's and 1.069 post boil based on beersmith calculation for a 5.5 gallon batch. I had a very bad brew day and only ended up with 3.75 gallons of useable wort so I topped of with 1.75 gallons of fresh water. I understand how to calculate my dillution for the SG but what about my Ibu's as I'm sure that is effected as well.

Is this formula possibly correct ?

(Ibu's x wot collected) + (fresh water addded) / total volume of fermenter
(64 x 3.75 ) + (1.75 ) / 5.5
240 + 1.75 = 241.75 / 5.5 = 44 Ibu's

I'm really winging that formula but am I on track or can someone tell me a way to calculate this problem.

 

[ajdelange]

If you indeed have 64 IBU wort have 64 units of bittering in 3.75 gal of wort you would have (approximately) 64 mg/L isomerized bittering principle for a total of 64 mg/L * 3.75 gal * 3.78 liter/gal. Diluting to 5.5 gal would result in 64 mg/L * 3.75 gal * 3.78 liter/gal / (5.5*3.75) or 64*3.75/5.5. But you calculated the hops charge such that you got the 64 IBU based on 5.5 gal implying total bittering of 64 mg/L * 5.5 gal * 3.78 liter/gal. Dividing the total bittering by 5.5 * 3.75 shows that the bittering is unchanged.

The only problem here is that if you boil the hops in more concentrated wort the hops utilization goes down and you probably have, therefore, extracted less than 64 IBU's. Calculated bittering levels are little more than WAGs anyway so I wouldn't worry about it. Call it 64.

 

[dnr]

So this was a bit confusing to look at and I am curious to find out. I've heard it said that you can probably only extract 100 bittering units/gallon of plain water. So if I boil hops in 2 gallons of plain water, adding LME at 15 minutes to flameout. Expecting a 77 IBU, what's my maths for adding 3.5 gallons?
I'm trying to figure out the best way to accomplish this with two 8qt pots for boiling.

 

[VirginiaHops1]

Can't you just put your batch size after top off into the software and let it do the math. I top off a little at the end of my all-grain batches, due to kettle size limitations. I basically can't put enough water into my kettle at beginning of boil to hit my post boil target so I have to just top off a little at the end.
Anyways, I just put in my ending batch size(after top off) which is 4.5 gallons into the software(3.5 for you) and I'm assuming it gets me a fairly accurate IBU calculation, especially considering they're just rough estimates anyways. I don't think you'd need to do any extra math yourself.

 

[Yooper]

So this was a bit confusing to look at and I am curious to find out. I've heard it said that you can probably only extract 100 bittering units/gallon of plain water. So if I boil hops in 2 gallons of plain water, adding LME at 15 minutes to flameout. Expecting a 77 IBU, what's my maths for adding 3.5 gallons?
I'm trying to figure out the best way to accomplish this with two 8qt pots for boiling.

You'd be very fortunate if you could extract 100 IBUs- that would be absolute max, best case scenario. It's more likely in the 80s.
So if you end up with 2.5 gallons of 85 IBUs, and add 2.5 gallons of 0 IBUs, you'd be looking at about 43 IBUs.

Topping off works great for many beers, but with heavily hopped beers is not ideal. If you're going to need to top off, I'd suggest getting some hop extract for bittering so that you're not limited to 50 IBU beers.