Severn Trent Water say they have dealt with double the number of calls during the recent heavy downpours. Seventy percent of the calls turned out to be unnecessary. Watch Andy Bevan's full report.
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He demanded the money after placing a carrier bag containing what appeared to be a heavy object on the counter.
Closures will be in place on the Aston Expressway, Park Circus and Salford Circus. There will be some full weekend closures and diversions.
West Midlands Police have said specially trained police negotiators are speaking with the woman to try and talk her down to safety.