Question

The velocity of glycerin in a 5 cm diameter pipe is 1.6 m/s. Find the velocity in a
3 cm diameter pipe which connects with it, both pipes flowing full.

Answer 1

By the definition of the Law of Continuity, we have:

$$A_1v_1=A_2v_2,$$ $$v_2=\dfrac{A_1v_1}{A_2},$$ $$v_2=\dfrac{\dfrac{\pi(0.05\ m)^2}{4}\cdot 1.6\ \dfrac{m}{s}}{\dfrac{\pi(0.03\ m)^2}{4}}=4.4\ \dfrac{m}{s}.$$

Answer:

$v_2=4.4\ \dfrac{m}{s}.$