Water enters a typical garden hose of diameter 0.016 m with a velocity of 3 m/s. Calculate the exit velocity of water from the garden hose w

Question

Water enters a typical garden hose of diameter 0.016 m with a velocity of 3 m/s. Calculate the exit velocity of water from the garden hose when a nozzle of diameter 0.0050 m) is attached to the end of the hose in units of m/s.

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Ben Gia 4 years 2021-08-12T07:06:19+00:00 1 Answers 17 views 0

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  1. sori
    0
    2021-08-12T07:07:52+00:00
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    Answer:

    v₂ = 306.12 m/s

    Explanation:

    We know that the volume flow rate of the water or any in-compressible liquid remains constant throughout motion. Therefore, from continuity equation, we know that:

    A₁v₁ = A₂v₂

    where,

    A₁ = Area of entrance pipe = πd₁²/4 = π(0.016 m)²/4 = 0.0002 m²

    v₁ = entrance velocity = 3 m/s

    A₂ = Area of nozzle = πd₂²/4 = π(0.005 m)²/4 = 0.0000196 m²

    v₂ = exit velocity = ?

    Therefore,

    (0.0002 m²)(3 m/s) = (0.0000196 m²)v₂

    v₂ = (0.006 m³/s)/(0.0000196 m²)

    v₂ = 306.12 m/s

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