WEBVTT
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This is Giancoli Answers
with Mr. Dychko.
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The volume rate of flow of blood
through this needle is gonna be
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π times radius of the needle
to the power of 4 times
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the pressure difference between
the top of the IV bag
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and the person's blood pressure—
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that's an important point there that I'm gonna
elaborate on in a second—
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and that's divided by 8 times
the viscosity of blood
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times the length of the needle.
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So pressure two is gonna be
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the pressure of the patient's blood
in their arm
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so that's gonna be...
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we are told that it's 78 torr above
atmospheric pressure
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so it's P a plus 78 torr.
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P 1 is the pressure due to
the column of blood
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from the bag to the needle
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so this is the pressure in the needle
and this is the pressure in the arm
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and the needle pressure is gonna be
atmospheric pressure plus
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the pressure due to the height of
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the column of blood from
the needle to the bag.
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So substituting each of these in,
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we have P 1 is gonna be P a plus
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density of blood times g times
height of the bag
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minus the pressure in the patient's arm
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which is atmospheric pressure plus 78 torr.
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So this pressure difference then is gonna be
ρgh minus 78 torr
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and then we have to solve this for h
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so we'll multiply both sides by
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8ηl over πR to the power of 4
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and we end up with this line here
after you switch the sides around
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and then add 78 torr to both sides
and then divide by ρ and g
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and you get the height is 1 over density
times g times 8ηlQ over
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πR to the power of 4 plus 78 torr
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and then plug in some numbers
taking care to convert units
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and this diameter should be divided by
2 to get radius.
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So we have 1 over 1.05 times 10 to the 3
kilograms per cubic meter
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times 9.8 newtons per kilogram
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and then—you can see what it looks like
in the calculator too—
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times 8 times 4 times 10 to the minus
3 pascal seconds—
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viscosity of blood—times 25 times
10 to the minus 3 meters—
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length of the needle—
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times 2.0 centimeters cubed per minute
is the volume rate of flow
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which we have to convert into
cubic meters per second
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so times by 1 meter for every
100 centimeters cubed
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and then multiply by 1 minute for
every 60 seconds...
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(what just happened there...
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there we go!)
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and then divide all that by π
times the diameter over 2
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so that's 0.80 times 10 to the minus
3 meters over 2
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all that to the power of 4
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and then add 78 torr converted
into pascals by
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multiplying by 133 pascals per torr
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and all of this works out to 1.04
which is about 1.0 meters
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and that's the required height
of the IV bag.