Elsewhere in the UK, rivers burst their banks, sometimes trapping drivers, after the torrential downpours on Thursday.
A Met Office amber weather warning, the second-highest, was in place until 9pm covering an area that included Aberdeen, Stonehaven, Montrose and the eastern Cairngorms.
Forecasters warned communities could be cut off, homes and businesses flooded and there was a "danger to life from fast-flowing or deep flood water". Parts of the Grampians and Cairngorms could expect to have more than 150mm of rain with areas around Inverurie, Brechin and Ballater particularly badly affected.
A yellow warning from Kelso in the Borders up the east coast of Scotland to Banff was also in place on Friday. It had been due to expire at 6pm but was extended to midnight because the rainfall was slower to ease than predicted.
In Angus, all schools in Brechin, Montrose and Kirriemuir were closed due to localised flooding as well as more than a dozen others.
Aberdeenshire council reported 11 power cuts and said some roads were impassable. It advised people to avoid travel if possible.
Network Rail Scotland said the line between Aberdeen and Dundee was closed as it dealt with "flooding at multiple sites along the route" while the line between Aberdeen and Inverness was closed at Dyce and at Huntly.
The east coast mainline was closed for a time between Dunbar and Reston but later reopened. In Edinburgh, cars were trapped and abandoned at the flooded junction of a busy road.
The Scottish Environment Protection Agency on Friday had in place five severe flood warnings, 28 flood warnings and nine flood alerts.
The disruption came after a band of rain hit the south-west coast of England on Wednesday evening before travelling north-east over two days, accompanied by cooler temperatures in a change to the previous unseasonably warm weather.
In England, which was hit by torrential rain on Thursday, there were nine flood warnings in place and 69 flood alerts. The warnings included the River Ouse at York, which broke its banks on Friday morning.
In the village of Alfriston in East Sussex, a refuse lorry and its crew were trapped by a severely flooded road.
Newcastle, Sunderland, Gateshead and Doncaster were among places in England facing travel disruptions to rail networks, metro lines, roads and bus services.
Stephen Dixon, a spokesperson for the Met Office, said the rain would slowly peter out by Friday evening but temperatures would drop overnight, as low as -4C in Northern Ireland. Saturday was expected to be clear, followed by more rain on Sunday.
"That sets up what is really the theme of the next week, which is continued wet and windy weather for much of the UK," he said.
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