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The correct answer is that neglecting viscosity, there is no net torque on the sprinkler arms during operation, so overall the sprinkler will not rotate, neglecting any initial jerks. The incoming water imparts momentum on the sprinkler arms, which is counteracted by the pressure difference between the surrounding water and the point of contact. Since the water's momentum is due to the pressure gradient in the first place, it must balance (this can be calculated explicitly). But since real water is slightly viscous, the effect of the pressure gradient will be slightly greater than that of the incoming water's momentum. For most ordinary situations, it shouldn't be enough to overcome the friction between the arm and the pivot.

The problem can also be restated in terms of angular momentum. To do so correctly, one should keep in mind that in forward operation, the force moving the water is on the pivot, while in reverse operation, the force originates externally.

Oh! I'm sorry. Your post was hiding behind ZigguratII's signature pic; I was a bit blind. My apologies and congratulations--you had the right idea, although one critique would be that you've provided no reason as to why the momentum and pressure gradient balance.

I don't think that you can reverse a sprinkler eek

The whole point is that the garden hose provides all the kinetic force necessary to allow the sprinkler to rotate.

You would have to attach a vacuum or fan (with the right polarity) to the bottom which made it suck in water, or somehow magically reverse the function of your garden hose.

Which ever the case, any sprinkler with a vacuum or a fan attached most likely doesn't spin relative to the water coming from a water hose. So I must say that it would do nothing, or that it's impossible.