Well, first off no such thing exists.

Second off, I doubt you could cobble up anything workable that
involved recirculating the water. The dirty water would quickly ruin
any pump capable of producing enough pressure to do what you want that
you could afford (i.e. a homeowner-grade pressure washer). Using only
clean water, it would take THOUSANDS of gallons to burn these holes in
the ground. You think your neighbors hate you now??? Wait'll you flood
their basements with muddy water.

For a mere fraction of what just the pressure washer would cost you,
you can rent a trailer-mounted power auger that an 80-year-old woman
could operate from the local big box store. They're counterbalanced so
you don't have to lift much, and the trailer takes all the jolts from
hitting rocks. They are also far more powerful than any one-man or two-
man auger.

Even in the sandy soil I have, the one-man auger is too much. Next
time I'm renting the trailer auger, or just digging the holes by hand.