Physics

Physics

Problem

A fire hose of internal diameter 6 cm6\,\text{cm} is fitted with a nozzle of diameter 2 cm2\,\text{cm}. If water approaches the nozzle with a speed of 3 m s−13\,\text{m\,s}^{-1}, what is the speed of water as it leaves the nozzle? a) 9 m s−19\,\text{m\,s}^{-1} b) 81 m s−181\,\text{m\,s}^{-1} c) 27 m s−127\,\text{m\,s}^{-1} d) 54 m s−154\,\text{m\,s}^{-1}
Intuitive explanation

This is a continuity problem: the same mass of water must flow through both the hose and nozzle each second, so a narrower opening forces the water to move faster. Use the principle that A1v1=A2v2A_1 v_1 = A_2 v_2 — the product of cross-sectional area and velocity stays constant along the flow. Since the nozzle's area is much smaller, the exit speed must be proportionally larger.

Intuitive explanation

This is a continuity problem: the same mass of water must flow through both the hose and nozzle each second, so a narrower opening forces the water to move faster. Use the principle that A1v1=A2v2A_1 v_1 = A_2 v_2 — the product of cross-sectional area and velocity stays constant along the flow. Since the nozzle's area is much smaller, the exit speed must be proportionally larger.

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