[Requin]

Just for simplicity lets assume a made flush is the nuts, I know its not exact but whatever. We called 30 on turn, pot after call is 112. So we need to make about 40 bucks on average to make calling the turn profitable with a FD. If villain calls our 80$ bet 1/2 the time when we have a flush we come out ahead. If villain calls 1/2 the time when we bluff we come out ahead also. So playing a flush this way and playing a bluff this way can both be profitable lines.
Edit: I just realized I forgot to factor in the lost money from turn call for bluff profitability, but it doesn't cost us 30$ on turn, it costs us less in the long run since we have a straight draw and will get paid sometimes... I'm not a math guy so I'm won't get further into it, but it can certainly be the case that playing this hand this way and playing a flush this way can both be profitable.