When a wet dog shakes it self ` people standing nearby tend to wet. Why deos the water fly outward from the dog in this way?

It is a combination of centripetal force (moves skin a circle) just lagging behind the muscle wave, and also how surface tension holds and releases water. Astonishingly in under 5 seconds they will have shook off nearly 3/4 of the water in their coat. My Borzois definitely needed to be avoided when wet... I`d get very wet indeed if the shaking wasn`t spotted soon enough!