Single Engine Turboprop Undifferentiated
Flight Crew Private; Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 15; Flight Crew Total 1225; Flight Crew Type 350
Situational Awareness; Time Pressure; Communication Breakdown
ATC Issue All Types; Conflict NMAC
General None Reported / Taken
Airspace Structure; Procedure
RHV is a busy training airport with two parallel runways. There were many airplanes in the pattern at the time of my departure. I requested a right turnout. I was directed to Runway 31L; which I initially thought was somewhat unusual given my right turnout request. My takeoff clearance was to depart and make my right turn 'at the freeway' (the southern boundary of the nearby SJC Class C airspace); which I presumed was to get out in front of traffic departing from the right runway; which was also turning right and staying in the pattern. Shortly after takeoff; the Tower Controller called out traffic at my 2 o'clock. I visually observed that traffic and confirmed it was no conflict; then told the Controller I was beginning my right turn. I suddenly noticed an airplane passing just below from my left to right at a very close distance. I don't recall whether my on-board traffic alerted me. But I definitely know the Tower Controller said nothing about it; either before or after it passed. Because the Controller was busy with numerous aircraft; I did not want to tie up the frequency asking about the potential conflict.So; one of these must have occurred.1) An airplane entered the Class D from the opposite direction; very close to the airport; without talking to anyone.2) The traffic departing from the right runway drifted left and passed underneath me before starting its right turn.3) I miss-identified the traffic callout by the Tower and turned over the top of departing aircraft.In this particular case; I could have refused the left runway assignment and waited for the right runway to clear. I could have sought clarification for the traffic alert from the Tower. I could have climbed steeper to more quickly get above any aircraft in the traffic pattern. I learned to be extra vigilant in situations where multiple aircraft are departing from parallel runways; especially when turning the same direction.
GA turboprop pilot reported NMAC with traffic that was unreported by a 'busy' ATC Controller at RHV.