<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40"><head><meta http-equiv=Content-Type content="text/html; charset=us-ascii"><meta name=Generator content="Microsoft Word 14 (filtered medium)"><style><!--
/* Font Definitions */
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
@font-face
{font-family:Tahoma;
panose-1:2 11 6 4 3 5 4 4 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0in;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Times New Roman","serif";}
a:link, span.MsoHyperlink
{mso-style-priority:99;
color:blue;
text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
{mso-style-priority:99;
color:purple;
text-decoration:underline;}
span.hoenzb
{mso-style-name:hoenzb;}
span.EmailStyle18
{mso-style-type:personal-reply;
font-family:"Calibri","sans-serif";
color:#1F497D;}
.MsoChpDefault
{mso-style-type:export-only;
font-family:"Calibri","sans-serif";}
@page WordSection1
{size:8.5in 11.0in;
margin:1.0in 1.0in 1.0in 1.0in;}
div.WordSection1
{page:WordSection1;}
--></style><!--[if gte mso 9]><xml>
<o:shapedefaults v:ext="edit" spidmax="1026" />
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext="edit">
<o:idmap v:ext="edit" data="1" />
</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'>>…</span></b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'> <b>On Behalf Of </b>John Clark<br><b>Subject:</b> Re: [ExI] underwater sprinkler, was: RE: Musical instruments in space<o:p></o:p></span></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>On Sun, Mar 31, 2013 at 12:50 AM, spike <<a href="mailto:spike@rainier66.com" target="_blank">spike@rainier66.com</a>> wrote:<o:p></o:p></p><div><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-right:0in'><p class=MsoNormal><o:p> </o:p></p><div><div><div><div><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>></span><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>>…</span><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'> Consider an S-shaped sprinkler suspended from a latex hose, underwater. Imagine water is pumped thru the sprinkler in the traditional manner at 1 ml per second, and we discover the sprinkler rotates positive pi radians. 2 ml per second rotates it 2 pi radians and so on.</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Now imagine pumping water thru it backwards.</span><o:p></o:p></p></div></div></div></div></div></div></blockquote><div><p class=MsoNormal><br><span style='color:#1F497D'>>…</span>Blowing and sucking are not symmetrical processes, that's why it's easy to tell if a film of a sprinkler is running forward or backward and why you can blow water as high as you want but no matter how powerful the pump is on the surface of the earth you can only suck water about 25 feet. In one case a pump is increasing pressure inside the narrow sprinkler nozzle causing the water to move in just one direction, perpendicular to the nozzle opening. But in the other case when the pump is decreasing pressure inside the small nozzle the water moves inside because of the outside pressure produced by the weight of the water and the air on top of it, and that pressure is coming from all directions so the water is coming through the opening from all directions too, and so no narrow beam of water is formed and no net torque is produced.<br><br> John K Clark<o:p></o:p></p></div><div><p class=MsoNormal><br><br><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Ja, agreed John however your commentary (I think) applies to steady state and integration over time torque equals zero, which is what I think you meant by “no net torque is produced.” Yet we know that increasing and decreasing flows do create a torque. Try it! Bend some copper tube, attach to a plumber’s T, some latex tube, a reversible DC motor water pump (all of which are available at the local hardware store for about 30 bucks for all of it) and try it.</span><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'><o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>But I am asking the question from the point of view of a controls engineer. Imagine you are trying to control the position of the S, and all you have is the reversible water pump. Until we can write equations to describe that motion, we cannot derive a control system. We can’t use any of those wicked cool mathematical tools we moderns have in our bag of controls magic tricks. <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>I have tried to derive those equations, and I have failed so far. But if you manage to derive the equations of motion, I can show you how to solve them and make a controls system. Then we can rig up a physical-world analog, test it to see if we know what we are doing, or if we are just a bunch of controls wannabes. {8^D If someone here manages the derivation and it turns out simple, I will be highly annoyed. But I will get over it. <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Notice the indistinguishable-from-god Richard Feynman himself mentioned the underwater sprinkler in his book Surely You’re Joking, but didn’t offer the equations of motion, or even suggest they found them. The bigshot future Nobel physicist himself immediately surrendered and went straight to physical-world analog and lab setups, which failed explosively. (Get Feynman’s book, it’s hilarious, page 52 in the Bantam edition, or if another edition, the page right before the chapter titled “Meeeeeeee!”)<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>I have half a mind to contact some mechanical engineering professors up at Stanford (or that other local school, Berk something or other) see if their students want to take up the challenge. Who would have thought, such a simple little mechanical device with only one moving part could be so educational and challenging?<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>spike<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p></div></body></html>