Question

Water circulates around a house in a hot-water heating system. If the water is pumped at a speed of 0.50m/s through a 5.0-cm diameter pipe in the basement hat will the flow speed be in in a 2.6-cm diameter pipe on the second floor 5.0m above?

Answer 1

The law of conservation of mass says

$$v_1A_1=v_2A_2$$

Hence,

$$v_2=v_1\frac{A_1}{A_2}=\rm 0.50\: m/s\times\frac{(5.0\: cm)^2}{(2.6\: cm)^2}=1.85\: m/s$$