When a garden hose with an output diameter of 20 mm is directed straight upward, the stream of water rises to a height of 0.13m . You then u

Question

When a garden hose with an output diameter of 20 mm is directed straight upward, the stream of water rises to a height of 0.13m . You then use your thumb to partially cover the output opening so that its diameter is reduced to 10 mm.

Part A

How high does the water rise now? Ignore drag and assume that the smaller opening you create with your thumb is circular.

Express your answer with the appropriate units

h=

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Neala 3 years 2021-09-04T09:37:51+00:00 1 Answers 16 views 0

Answers ( )

  1. thachthao
    0
    2021-09-04T09:38:53+00:00
    Reply

    Answer: h = 0.52m

    Explanation:

    Using the equation of out flow;

    A1 × V1 = A2 ×V2

    Where A1 = area of the first nozzle

    A2 = area of the second nozzle

    V1= velocity of flow out from the first nozzle

    V2 = velocity of flow out from 2nd nozzle

    But AV= area of nozzle × velocity of water = volume of water per second(m³/s).

    Now we can set A×V = Area of nozzle × height of rise.

    Henceb A1× h1 = A2 × h2 ( note the time cancel on both sides)

    D1 = 20mm= 0.02m; h1 = 0.13m

    D2 = 10mm = 0.01m; h2= ?

    h2 = π(D1/2)²× h1 /π(D2/2)²

    h2 = (0.02/2)² × 0.13/(0.01/2)²

    = (0.01)² ×0.13 /(0.005)²

    = 1.3 × 10^-5/(5 × 10^-3)²

    = 1.3 × 10^-5/25 × 10^-6

    = (1.3/25) 10^-5 × 10^6

    = 0.052× 10

    = 0.52m

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