When I half-cover a tap or hose with my thumb, why does the water suddenly spray out much faster?
This is the equation of continuity, A1v1 = A2v2.
This is the equation of continuity, A1v1 = A2v2. The same volume of water per second has to get through a smaller opening, so its speed must rise to compensate. Halving the area roughly doubles the speed. It isn't 'extra force' from your thumb — you only reduced the area, and the flow rate did the rest.
Key point
A1v1 = A2v2 — smaller cross-section means faster flow.
Common mistake
thinking your thumb adds energy or pressure to speed the water up.
Memory tip
squeeze the area → speed up the flow, at constant volume rate.
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