Flowel

Meet Flowel, a garden hose who sprays faster when her nozzle narrows.

For a liquid that cannot be squeezed, the same volume must pass every point of a pipe each second. That volume flow rate is the cross-sectional area times the speed, so where the pipe narrows, the liquid speeds up, and where it widens, it slows down.

Suppose water moves at 1.5 m/s in a hose 2.0 cm across and leaves through a nozzle 1.0 cm across. Halving the diameter makes the area four times smaller, so the water leaves four times faster, at 6.0 m/s. Putting your thumb over the end of a hose does the same thing.

Rivers show it too: the water runs faster through narrow, shallow sections and slower where the river is wide and deep.

In your body, blood leaving the heart flows quickly through the aorta. It then divides into billions of capillaries whose total cross-sectional area is far bigger, so it slows right down there, giving time for oxygen and nutrients to pass into the tissues. The equation is a statement of conservation of mass.