AP Physics 2: 1.2 Changes and Conservation Laws

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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]

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

drain