AP Physics 2: 1.2 Changes and Conservation Laws
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AP Physics 2: 1.2 Changes and Conservation Laws. What should the water velocity be when the sludge is cleared?
AP | AP Physics 2 |
AP Physics 2 | Changes and Conservation Laws |
Language | English Language |
Science Practice 3 | Engaging in scientific questioning |
Test Prep | AP Physics 2 |
Transcript
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