When I was building my house, the construction workers would eat their lunch under the double tree because it was so much cooler undert there ... have you ever looked up how much water a mature black walnut expires through its leaf canopy per hour of sunlight? It will amaze you, and is the source of the cooling at the base.
Dunno the volume of H20, but I do know that they are like swamp maples...hundreds of gallons per tree per day, as I recall.