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So I was doing the dishes this morning using a sink wand hat can toggle between different flow speeds. The way that I've always thought of this working is using the equation of continuity:

Volume flow rate: = Area*velocity

Pressing a button on the wand decreases the cross-sectional area and correspondingly increases the flow velocity assuming that the flow rate is constant.

The issue that I'm running into is trying to simultaneously explain this with Bernoulli's equation:

P

_{1}+ pgy

_{1}+ 1/2pv

_{1}

^{2}= P

_{2}+ pgy

_{2}+ 1/2pv

_{2}

^{2}=

I'll take state 1 to be at the water reservoir or wherever the water in the pipes is pressurized and 2 to be at the outlet of the wand. I'm assuming that pressing the button on the wand does not change the pressure at the reservoir (nor at the outlet of the wand, where it is subject to atmospheric pressure).

Based on Bernoulli's equation, this would suggest that pressing the wand button should have NO effect on the flow velocity, which contradicts the result from the equation of motion. So: what am I missing here. I feel like I may be incorrect in my pressure assumption above somehow.

Thanks!

Chris