{"id":35,"date":"2010-04-15T20:48:52","date_gmt":"2010-04-15T18:48:52","guid":{"rendered":"http:\/\/technocktail.info\/?p=35"},"modified":"2017-07-20T01:39:02","modified_gmt":"2017-07-19T23:39:02","slug":"work-and-torque-solution","status":"publish","type":"post","link":"http:\/\/technocktail.info\/?p=35","title":{"rendered":"Work and Torque (Solution)"},"content":{"rendered":"

THIS IS A REDUNDANT POST \ud83d\ude00 \u00a0AND THE ORIGINAL POST IN MY Quantity System Blog<\/em><\/strong><\/p>\n

http:\/\/quantitysystem.wordpress.com\/2010\/04\/15\/work-and-torque-solution\/<\/a><\/p>\n

———————–<\/p>\n

I am really sorry<\/p>\n

I didn’t notice that I haven’t posted how did I solve the\u00a0dilemma\u00a0of Torque and Work Problem<\/p>\n

however the solution was there in my discussion of quantity System\u00a0http:\/\/quantitysystem.codeplex.com\/Thread\/View.aspx?ThreadId=23672<\/a><\/p>\n

and also on this post of my personal blog \u00a0http:\/\/blog.lostparticles.net\/?p=28<\/a><\/p>\n

Problem Core: Length<\/h1>\n

Simply I defined TWO Length Types<\/p>\n

Normal Length (NL)<\/h2>\n

This is the normal length that we refer to it in our daily life<\/p>\n

Radial Length (RL)<\/h2>\n

This is the radius length that have an origin point in center of circle<\/p>\n

Quantities<\/h2>\n

Work: \u00a0 \u00a0 \u00a0 Force * Normal Length<\/p>\n

Torque: \u00a0 Force * Radial Length<\/p>\n

Angle: \u00a0 \u00a0 \u00a0Normal Length \/ Radial Length<\/p>\n

In quantity system I made the L dimension as NL+RL<\/p>\n

CAN YOU SEE ANGLE<\/p>\n

I made it explicitly a quantity that is NOT dimensionless<\/p>\n

and THIS SOLVED ALL my problems of this Problem<\/p>\n

I won’t argue much let us test \ud83d\ude42<\/p>\n

Torque * Angle = Work<\/p>\n

F*RL * (NL\/RL) = \u00a0F * NL \u00a0 \u00a0<== see what I mean<\/p>\n

Torque * Angular Speed = Power<\/p>\n

F*RL * (NL\/RL*T) = F*NL\/T \u00a0 <== where T is the time.<\/p>\n

so you may wonder about Angle and Solid Angle<\/p>\n

in SI they are all dimensionless \u00a0but in Quantity System YOU CAN’T consider them like this<\/p>\n

(By the way I’ve break the checking for these two quantities to be\u00a0summable with dimensionless numbers – just to keep the\u00a0fundamentals\u00a0as it is although I am not convinced\u00a0and I may remove it in future but damn it I need support from any physics guy)<\/p>\n

ANGLE : \u00a0NL\/RL<\/p>\n

Solid Angle: \u00a0NL^2\/RL^2 \u00a0 because its area over area<\/p>\n

Frequency = \u00a01\/T<\/p>\n

Angular Velocity = (NL\/RL)\/T<\/p>\n

do you remember the conversion between RPM to frequency<\/p>\n

RPM (Revolution Per Minute) is a Angle \/ Time<\/p>\n

lets test the law<\/p>\n

Omega \u00a0= 2*pi*frequency<\/p>\n

pi: radian value which is \u00a0NL\/RL<\/p>\n

Omega = (NL\/RL) * 1\/T = (NL\/RL)\/T \u00a0 which \u00a0angular velocity<\/p>\n

Discoveries<\/h1>\n

PI value<\/h2>\n

PI<\/a> is ratio of any\u00a0circle<\/a>‘s circumference to its diameter \u00a0 \u00a0WHICH MEANS \u00a0(NL\/RL)<\/p>\n

this is the same value as the ratio of a circle’s area to the square of its radius \u00a0 \u00a0 WHICH MEANS \u00a0(NL^2\/RL^2)<\/p>\n

which corresponds to radian unit and stradian unit for angle and solid angle quantities.<\/p>\n

Reynolds Number<\/h2>\n

I am not holding back (\u00a0Reynolds number<\/a> is a dimensionless number that measure inertial forces to viscous forces)<\/p>\n

WHY we always differentiating between Flow in Pipes and Flow on Flat plate<\/p>\n

let’s see with normal length in quantity system<\/p>\n

Qs> rho = 3[Density]<\/div>\n
Density: 3 <kg\/m^3><\/div>\n
Qs> v=0.5<m\/s><\/div>\n
Speed: 0.5 <m\/s><\/div>\n
Qs> l=4<m><\/div>\n
Length: 4 m<\/div>\n
Qs> mue = 2<Pa.s><\/div>\n
Viscosity: 2 <Pa.s><\/div>\n
Qs> rho*v*l\/mue<\/div>\n
DimensionlessQuantity: 3 <kg\/m.s^2.Pa><\/div>\n

it shows it is a dimensionless quantity<\/p>\n

ok let us force my theory about flow in pipes<\/p>\n

the pipe have a diameter \u00a0and Reynolds number is calculated by rho*v*DIAMETER\/viscosity<\/p>\n

so let me add d as a diameter and solve again<\/p>\n

Qs>\u00a0d=0.5<m!><\/p>\n

RadiusLength: 0.5 m<\/p>\n

Qs> rho*v*d\/mue<\/p>\n

DerivedQuantity: 0.375 <kg\/m.s^2.Pa><\/p>\n

NOTE: Adding ‘!’ after the length unit will mark the quantity as Radial Length quantity.<\/p>\n

ERROR \u00a0it shouldn’t be DerivedQuantity at all it should be Dimensionlesss<\/p>\n

so there is another term that should be fixed. Do you know which term ???<\/p>\n

lets try the velocity \u00a0with\u00a0vr=0.5<m!\/s><\/p>\n

Qs> vr=0.5<m!\/s><\/p>\n

DerivedQuantity: 0.5 <m\/s><\/p>\n

Qs> rho*vr*d\/mue<\/p>\n

DerivedQuantity: 0.375 <kg\/m.s^2.Pa><\/p>\n

ALSO ERROR<\/p>\n

ok let us try the density<\/p>\n

Qs>\u00a0rhor = 3<kg\/m!^3><\/p>\n

DerivedQuantity: 3 <kg\/m^3><\/p>\n

Qs> rhor*v*d\/mue<\/p>\n

SolidAngle: 0.375 <kg\/m.s^2.Pa><\/p>\n

CAN YOU SEE THE SOLID ANGLE Quantity<\/p>\n

do you remember the above argue about Solid Angle is dimensionless number<\/p>\n

can I pretend now that reynolds number for pipes is CORRECT ???<\/p>\n

the new density which is kg\/m!^3<\/p>\n

This is driving me nuts<\/p>\n

<\/h2>\n

Pump Affinity Laws<\/h2>\n

Also \u00a0pump equations led to the same\u00a0SolidAngle\u00a0Quantity not\u00a0DimensionLess\u00a0one<\/p>\n

Epilogue<\/h1>\n

I’ve said what I’ve discovered till now about this problem I hope that may be someday someone explain to me or convince me that Angle is really a Dimensionless number \u00a0 after all of this and that my assumption about Torque and Work is Wrong.<\/p>\n

Qs> rho = 3[Density]Density: 3 <kg\/m^3>Qs> v=0.5<m\/s>Speed: 0.5 <m\/s>Qs> l=4<m>Length: 4 mQs> mue = 2<Pa.s>Viscosity: 2 <Pa.s>Qs> rho*v*l\/mueDimensionlessQuantity: 3 <kg\/m.s^2.Pa><\/p>\n","protected":false},"excerpt":{"rendered":"

THIS IS A REDUNDANT POST \ud83d\ude00 \u00a0AND THE ORIGINAL POST IN MY Quantity System Blog http:\/\/quantitysystem.wordpress.com\/2010\/04\/15\/work-and-torque-solution\/ ———————– I am really sorry I didn’t notice that I haven’t posted how did I solve the\u00a0dilemma\u00a0of Torque and Work Problem however the solution was there in my discussion of quantity System\u00a0http:\/\/quantitysystem.codeplex.com\/Thread\/View.aspx?ThreadId=23672 and also on this post of my […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"_links":{"self":[{"href":"http:\/\/technocktail.info\/index.php?rest_route=\/wp\/v2\/posts\/35"}],"collection":[{"href":"http:\/\/technocktail.info\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/technocktail.info\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/technocktail.info\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/technocktail.info\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=35"}],"version-history":[{"count":7,"href":"http:\/\/technocktail.info\/index.php?rest_route=\/wp\/v2\/posts\/35\/revisions"}],"predecessor-version":[{"id":52,"href":"http:\/\/technocktail.info\/index.php?rest_route=\/wp\/v2\/posts\/35\/revisions\/52"}],"wp:attachment":[{"href":"http:\/\/technocktail.info\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=35"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/technocktail.info\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=35"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/technocktail.info\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=35"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}