AP Physics 2: 1.2 Changes and Conservation Laws

AP Physics 2: 1.2 Changes and Conservation Laws. What should the water velocity be when the sludge is cleared?

APAP Physics 2
AP Physics 2Changes and Conservation Laws
LanguageEnglish Language
Science Practice 3Engaging in scientific questioning
Test PrepAP Physics 2

Transcript

00:24

water flow measurements, in one spot a 20 centimeter thick layer of sludge has [sludge in the sewer pipe]

00:30

narrowed to 2.0 meters diameter pipe take a look at this diagram right

00:35

there yeah it shows that the sludge so we're going to call it politely goes

00:40

completely around the pipe the water velocity at this point is 10 meters per

00:45

second well based on this information what should the water velocity be when

00:48

the sludge is cleared and here the potential answers.....So sewer sludge is

00:56

really really gross and we're just going to move right ahead because we don't [Man slipping in sewer sludge]

00:59

even want to think about it we've never been so happy to do math before.. Solve

01:03

this well we'll use the fluid continuity equation that equation states that the

01:08

product of the cross-sectional area of the pipe and the fluids velocity at one

01:12

portion of a pipe equals the product of area and velocity at a second portion of

01:18

the same pipe this is a function of the conservation of mass well basically if a [A garden hose pipe]

01:24

volume X of fluid enters one portion of a pipe the same volume has to exit

01:29

that same portion as a pipe narrows the velocity of the fluid increases as [Girl squirts boy with a water pipe]

01:35

anyone who has ever put a thumb over the end of the garden hose can attest and if

01:39

the pipe broadens well the velocity slows.. in this question we're not given [Dimensions of a pipe]

01:44

the area but we're given the diameter and super genius types like us know that

01:49

the area of a circle equals pi times one half of the diameter squared well we can

01:55

plug that in on both sides of the equation and we can simplify it by

01:59

cancelling out PI from both sides so the pipe was originally two meters but due [pipe's diameter measurements]

02:04

to the twenty centimeters of sludge the diameter is reduced by forty centimeters

02:09

since the layer of sludge encircles the pipe and now we're getting a little

02:13

queasy from all this sludge talk, but we know that the current diameter is 1.6

02:18

meters and since we know that the current velocity is 10 meters per second

02:22

we plug those numbers in and we can solve for V sub 2 ...well V sub 2 equals V [Hand places V sub 2]

02:27

sub 1 times d sub 1 squared over d sub 2 squared, which means it equals 10 meters

02:34

per second times 1.6 meters squared over 2 meters squaresd, well simplifying the

02:40

division helps us find that the post-sludge cleaning velocity is 6.4

02:44

meters per second making B) the right answer... Now that we're finally done

02:48

talking about sewer sludge we want to take a shower so we can feel clean again [Man runs away from sewer sludge and takes a shower]

02:52

we'll try not to think about where all that water goes is it runs down the [water running down a drain]

02:58

drain