Question

To water the yard, you use a hose with a diameter of 3.1 cm. Water flows from the hose with a speed of 1.5 m/s. If you partially block the end of the hose so the effective diameter is now 0.55 cm, with what speed does water spray from the hose?

Answer 1

The continuity equation is,

$$ \begin{aligned} A_{1} v_{1} &=A_{2} v_{2} \\ \left(\frac{\pi d_{1}^{2}}{4}\right) v_{1} &=\left(\frac{\pi d_{2}^{2}}{4}\right) v_{2} \\ d_{1}^{2} v_{1} &=d_{2}^{2} v_{2} \\ (0.031 \mathrm{~m})^{2}(1.5 \mathrm{~m} / \mathrm{s}) &=(0.0055 \mathrm{~m})^{2} v_{2} \\ v_{2} &=47.65 \mathrm{~m} / \mathrm{s} \end{aligned} $$