Selena uses a garden hose to fill a bucket of water. the water enters the house through a faucet with a 6.0-cm diameter. the speed of the water at the faucet is 5 m/s. if the faucet and the nozzle are at the same height, and the water leaves the nozzle with a speed of 20 m/s, what is the diameter of the nozzle?

the diameter of the nozzle = 3 cm

Explanation:

let the diameter of nozzle be x cm.

then, area of cross-section at nozzle =

nozzle with a speed of 20 m/s, and  speed of the water at the faucet is 5 m/s.

area of cross section at faucet = = 9π

now , area×velocity has to be constant (since area×velocity gives volume flow rate which should be same at both ends).  

therefore

5×9π = 20×π×x^2/4

=>45 = 5×x^2

=>9 = x^2

=> x = 3 cm (as 3^2 =9)

therefore, the diameter of the nozzle = 3 cm

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