Water Nozzles

摘要

The following type of nozzle problem is found in some introductory-level physics textbooks.1"3 The (average) flow speed of water through and out a hose with a cross-sectional areaylH is vH. If a nozzle with an exit area AH is attached to the hose, what is the speed v^ of the water out of it? The books simply apply the continuity equation AHvu = ANvN to the nozzle to obtain AN = (Au/AN)vH. This solution is not correct because it does not take account of the fact that attaching the nozzle to the hose reduces the flow speed in it. So the books' values of AN must always be too high, sometimes by large amounts. It should not seem surprising that it takes more time to fill a watering can with a garden hose when there is a nozzle at the end of it than when there isn't. This paper will explain how a water nozzle actually works, and for a situation with a simple water source, the correct flow speed from a nozzle will be derived.