WEBVTT

00:00:00.000 --> 00:00:02.840
This is Giancoli Answers
with Mr. Dychko.

00:00:03.840 --> 00:00:08.040
If the volume rate of blood flow is
reduced by a factor of 65 percent

00:00:08.040 --> 00:00:13.820
that means <i>Q 2</i> minus <i>Q 1</i> over <i>Q 1</i>
equals negative 0.65;

00:00:14.260 --> 00:00:16.680
negative means that there is a reduction

00:00:16.780 --> 00:00:20.680
and the 0.65 is the factor by which
it's been reduced

00:00:20.680 --> 00:00:22.560
and we change the percent to
a decimal there.

00:00:22.660 --> 00:00:29.020
So <i>Q 2</i> is negative 0.65 times <i>Q 1</i> and
then add <i>Q 1</i> to both sides as well

00:00:29.020 --> 00:00:32.460
and you get this and that's 0.35<i>Q 1</i>.

00:00:32.560 --> 00:00:35.060
So <i>Q 2</i> is 0.35 times <i>Q 1</i>.

00:00:35.200 --> 00:00:38.780
So here we have <i>Q 2</i> with
Poiseuille's equation

00:00:38.780 --> 00:00:41.020
so we have <i>π</i> times <i>R 2</i>
to the power of 4 times

00:00:41.020 --> 00:00:44.840
the pressure difference divided by
8 times the viscosity times <i>l</i>

00:00:44.980 --> 00:00:47.180
and then that equals 0.35

00:00:47.180 --> 00:00:51.040
times the same stuff with <i>R 1</i> to
the power of 4 instead of <i>R 2</i>

00:00:51.140 --> 00:00:52.760
and every term is the same

00:00:52.760 --> 00:00:55.100
or every factor I should say is the same

00:00:55.160 --> 00:00:57.160
they cancel on both sides with
the exception of

00:00:57.160 --> 00:01:01.800
<i>R 2</i> to the power of 4 equals 0.35
times <i>R 1</i> to the power of 4.

00:01:02.200 --> 00:01:05.040
So 8<i>ηl</i> cancels everywhere,

00:01:05.160 --> 00:01:07.620
the change in pressure is
the same everywhere,

00:01:07.620 --> 00:01:08.820
<i>π</i> is the same everywhere.

00:01:09.000 --> 00:01:14.140
So to get <i>R 2</i>, take both sides
to the power of one-quarter

00:01:14.240 --> 00:01:16.300
so <i>R 1</i> to the power of
one-quarter is <i>R 1</i>

00:01:16.300 --> 00:01:20.760
and then 0.35 to the power of one-quarter
is 0.7692.

00:01:21.000 --> 00:01:26.120
So the radius in the second case is 0.7692
times the radius in the first case.

00:01:26.240 --> 00:01:28.800
So the factor by which the radius
has been reduced

00:01:28.860 --> 00:01:33.280
is the difference in radii divided by
the original radii

00:01:33.380 --> 00:01:36.940
and so that's <i>R 1</i> minus 0.7692<i>R 1</i>—

00:01:37.060 --> 00:01:39.020
because that's what we just
discovered <i>R 2</i> is—

00:01:39.140 --> 00:01:41.200
and that's divided by <i>R 1</i> and that gives

00:01:41.880 --> 00:01:46.240
well, the <i>R 1</i>'s cancel so that's 1 minus
0.7692 is just 0.23.

00:01:46.320 --> 00:01:50.140
So the radius has been reduced
by about 23 percent.