WEBVTT

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This is Giancoli Answers
with Mr. Dychko.

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So here's Bernoulli's equation:

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we have position 2 being the top
of the water spray

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at which point there's no
velocity of the water

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and position 1 is on the ground
where the water main is.

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And velocity 1 will also be zero

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which might be a bit surprising,

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I mean if you are thinking about the water
flowing out of the fire hose,

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it's gonna have some velocity right?

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But if that were true then the pressure
at this point...

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if the fire hose was open to the atmosphere

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then the pressure at this point would be
atmospheric pressure

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because there would be no gauge pressure.

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But since it's asking us for
the gauge pressure

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that must mean that the fire hose is close

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in which case, <i>P 1</i> is greater
than atmospheric pressure.

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So since the fire hose is close,
it's not flowing yet.

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So <i>P 2</i> is atmospheric pressure
though because

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this is when the water is up in the air,
you know, in the atmosphere

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and then we can subtract that
<i>P 2</i> from both sides.

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So we have <i>P 1</i> minus <i>P a</i>

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and this difference is gauge pressure
so gauge pressure is

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is the absolute pressure

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minus atmospheric pressure or
the amount by which

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some pressure exceeds atmospheric pressure
so that's what this difference is.

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And this equals <i>ρ</i> times <i>g</i> times
<i>y 2</i> minus <i>y 1</i>,

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factored out the <i>ρg</i> from
both of these terms

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and moved this term to the right side
which made it a minus.

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And plug and chug.

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So it's 1.00 times 10 to the 3 kilograms
per cubic meter

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times 9.8 newtons per kilogram

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times 16 meters,

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you know, <i>y 1</i> is just zero and we will
define that to be the zero point

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and we have 1.6 times 10 to the 5 pascals
has to be the gauge pressure.