THE AIRSPEED INDCR WAS MALFUNCTIONING ON A PREVIOUS FLT. BFR TAKING OFF AGAIN, THE PLT WAS SEEN TO DISASSEMBLE THE PITOTTUBE AS IF THE REMOVE FOREIGN MATTER. ON THE NEXT FLT, HE BGN A HI SPD/LOW PASS OVR RWY 35. AT ABT MIDFIELD, THE ACFT ENTERED A CLIMB TO APRX 800 TO 1000 FT AGL. NR THE PEAK OF THE CLIMB, THERE WAS A REDUCTION OF PWR & THE ACFT MNVRD (TURNED LEFT, THEN RGT, AS IF TO ENTER A BASE TURN FOR RWY 17). THE LNDG GEAR WAS EXTDD AT ABT 300 TO 500 FT AGL, FLWD BY A TURN (SOUTH) TWD THE RWY. AFTER ABT 45 DEG OF TURN, THE ACFT ENTERED A STEEP DSCNT & CRASHED. AN EXAM REVEALED A RUBBER PITOT LINE, PN 35-324323, WAS DETERIORATED & LEAKED. NO OTR PREIMPACT PART FAILURE WAS FND. EXPERIMENTAL CATEGORYACFT WITH SVRL LIMITATIONS: FLTS RSTRD TO TX; EXHIBITION ONLY; PIC WAS REQUIRED TO HAVE AN INSTRUCTOR'S LOGBOOK ENDORSE-MENT OR LETTER OF AUTHORIZATION (LOA) TO OPER THE ACFT. NEITHER AN ENDORSEMENT NOR LOA WAS FND. PLT HAD ABT 1 HR IN T-34ACFT; CANNABINOIDS DETECTED IN PLT'S URINE, BUT NONE FND IN HIS BLOOD. ACFT WAS NOT EQUIPPED WITH STALL WARNING SYS.