Tropical Storm Andrea ready to pummel Florida with intense rain

(CNN) -- Tropical Storm Andrea is set to wallop Florida with torrential rainfall as it prepares to make landfall Thursday.

The first named storm of the Atlantic hurricane season made its debut Wednesday by pummeling Cuba with heavy downpours.

As of 2 a.m. ET Thursday, Andrea was 240 miles west-southwest of Tampa, Florida, and was headed north at 10 mph, the National Hurricane Center said.

The center of Andrea is expected to make landfall on the Florida Panhandle late Thursday before cutting across southern Georgia and moving up the East Coast on Friday and Saturday.

Forecasters don't expect Andrea to strengthen to a hurricane -- which would require sustained winds of at least 74 mph. But its greatest trouble will be water.

Andrea is expected to unleash 3 to 6 inches of rain over much of Florida and southeastern Georgia and as much as 8 inches in some areas. The eastern parts of North and South Carolina could see up to 4 inches of rain, the National Hurricane Center said.

"The combination of a storm surge and the tide will cause normally dry areas near the coast to be flooded by rising waters," the hurricane center said.

The Florida peninsula could also see a few tornadoes Thursday.

CNN meteorologist Ivan Cabrera contributed to this report.