(Recasts, adds auction results, analyst comments, reverse repo volume) CHICAGO, Aug 10 (Reuters) - U.S. Treasury yields hit their highest levels since mid-July on Tuesday, rising on the long end of the curve after the U.S. Senate passed a massive infrastructure bill, while a three-year note auction produced strong results. The benchmark 10-year Treasury yield reached 1.349%, its highest since July 15, and last was up 3 basis points at 1.3473%. The 30-year bond yield, which rose as high as 1.992%, rose 2.9 basis points to 1.9895%. The 10-year yield, up for a fifth straight session on Tuesday, was set for its longest daily rising streak since late January-early February. That sharp climb took yields from 1% to 1.776% by the end of March. The $58 billion of three-year notes were sold at a high yield of 0.465% and with a bid-to-cover ratio, a gauge of demand, of an above-average 2.54. The three-year yield was last up 2.4 basis points at 0.4503%. Jim Vogel, senior rates strategist at FHN Financial, said yields rose after the U.S. Senate passed a $1 trillion infrastructure bill and opened debate on a $3.5 trillion spending plan. Light trading volume and big investment-grade corporate bond issuance so far this week were also factors, he said. "Bringing the Treasury auctions at the same time we have a lot of corporate supply tends to pressure rates higher, which would help explain why the Treasuries are cheaper, but bonds elsewhere are not." Other Treasury auctions on tap for this week include $41 billion of 10-year notes on Wednesday and $27 billion of 30-year bonds on Thursday. All eyes will be on Wednesday"s release of Consumer Price Index (CPI) data for July. Consumer prices are expected to have increased 0.5% in July after a 0.9% rise in June, according to economists polled by Reuters. They also forecast that in the 12 months through July, the index rose 5.3%, down slightly from 5.4% in June. Tony Rodriguez, head of fixed income strategy at Nuveen, said while Friday"s stronger-than-expected July employment data set some rate expectations, the inflation picture remains cloudy. "Data coming out tomorrow will obviously provide some more clarity. It"s not going to resolve the uncertainty about where inflation is heading," he said. Citing a rapidly growing U.S. economy, a few Fed officials said on Monday inflation was already at a level that could satisfy one leg of a key test for the beginning of rate hikes and that further progress on the labor front could trigger the start of tapering of the central bank"s asset purchases. Cash flowing into the Fed"s reverse repurchase agreement facility was just shy of $1 trillion at $998.6 billion on Tuesday. It reached a record high of $1.039 trillion on July 30. A closely watched part of the yield curve that measures the gap between yields on two- and 10-year Treasury notes was about less than a basis point steeper at 110.59 basis points. August 10 Tuesday 3:53PM New York / 1953 GMT Price Current Net Yield % Change (bps) Three-month bills 0.055 0.0558 0.005 Six-month bills 0.055 0.0558 0.003 Two-year note 99-199/256 0.2384 0.018 Three-year note 99-200/256 0.4503 0.024 Five-year note 99-8/256 0.8243 0.032 Seven-year note 99-40/256 1.1262 0.030 10-year note 102-136/256 1.3473 0.030 20-year bond 105-196/256 1.8986 0.029 30-year bond 108-160/256 1.9895 0.029 DOLLAR SWAP SPREADS Last (bps) Net Change (bps) U.S. 2-year dollar swap 8.50 -0.25 spread U.S. 3-year dollar swap 11.25 -0.50 spread U.S. 5-year dollar swap 8.50 -0.50 spread U.S. 10-year dollar swap 1.00 -0.25 spread U.S. 30-year dollar swap -29.50 -1.00 spread (Reporting by Dhara Ranasinghe in London and Karen Pierog in Chicago; editing by Marc Jones, Giles Elgood, Jonathan Oatis and Richard Chang) Our Standards: The Thomson Reuters Trust Principles.