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A typical garden hose has an inner diameter of 5/8". Let's say you connect it to a faucet and the water comes out of the hose with a speed of 7.0 feet per second. If you then put your thumb over the end of the hose so the opening is only a circle 0.25" across, with what speed will the water stream out now?

Respuesta :

budwilkins
Since speed (v) is in ft/sec, let's convert our diameters from inches to feet:
1) 5/8in = 0.625in
0.625in × 1ft/12in = 0.0521ft
2) 0.25in × 1ft/12in = 0.021ft
Equation:
[tex]v = 4q \div ( {d}^{2} \pi) \: where \: q = flow \\ v = velocity \: (speed) \: and \: \\ d = diameter \: of \: pipe \: or \: hose \\ and \: \pi = 3.142[/tex]
[tex]we \: can \: only \: assume \:that \\ flow \: (q) \:stays \: same \: since \: it \\ isnt \: impeded \: by \: anything \\ thus \:it \: (q)\: stays \: the \: same \: \\ so \: 4q \: can \: be \: removed \: from \: \\ the \: equation[/tex]
[tex]then \: we \: can \: assume \: that \: only \\ v \: and \: d \: change \: leading \:us \: to > > \\ (v1 \times {d1}^{2} \pi) = (v2 \times {d2}^{2}\pi) [/tex]
[tex]both \: \pi \: will \: cancel \: each \: other \: out \: \\ as \: constants \:since \: one \: is \: on \\ each \: side \: of \: the \: = [/tex]

[tex](v1 \times {d1}^{2}) = (v2 \ \times {d2}^{2}) \\ (7.0 \times {0.052}^{2}) = (v2 \times {0.021}^{2}) \\ divide \: both \: sides \: by \: {0.021}^{2} \\ to \: solve \: for \: v2 > > [/tex]
[tex]v2 = (7.0)( {0.052}^{2} ) \div ( {0.021}^{2}) \\ v2 = (7.0)(.0027) \div (.00043) \\ v2 = 44 \: feet \: per \: second[/tex]
new velocity coming out of the hose then is
44 ft/sec
Cricetus

The speed of the water will be "43.75 ft/sec".

According to the question,

Initially inner diameter,

  • 5/8 inch or 0.052 ft

Final diameter,

  • 0.25 inch or 0.0208 ft

By continuity equation, we get

→ [tex]Area1\times Velocity1=Area2\times Velocity2[/tex]

By substituting the values, we get

→ [tex]pi\times (\frac{0.052}{2} )^2\times 7= pi\times (\frac{0.0208}{2} )^2\times Velocity[/tex]

→             [tex]Velocity = 43.75 \ ft/sec[/tex] (speed)

Thus the above answer is correct.

Learn more:

https://brainly.com/question/3877231

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