I flop the nut straight and bet hard, but 3 to a flush falls on the turn. Should I have bet the turn? With my bet on the flop it's very unlikely to be a flush draw.

Poker Room skin
No Limit Holdem Ring game
Blinds: $0.15/$0.25
10 players
Converter

Pre-flop: (10 players) Hero is BB with :as :js
UTG folds, UTG+1 calls, 5 folds, Button calls, SB calls, Hero checks.

Flop: :kh :10h :qc ($1, 4 players)
SB bets $1, Hero raises to $4, UTG+1 calls, 2 folds.

Turn: :ah ($10, 2 players)
Hero checks, UTG+1 checks.

River: :9c ($10, 2 players)

Hero?

Rest in white
Hero bets $4, UTG+1 calls.

Results:
Opp shows K 10
Hero wins: $18