# Work and Torque (Solution)

I am really sorry

I didn’t notice that I haven’t posted how did I solve the dilemma of Torque and Work Problem

however the solution was there in my discussion of quantity System http://quantitysystem.codeplex.com/Thread/View.aspx?ThreadId=23672

and also on this post of my personal blog http://blog.lostparticles.net/?p=28

# Problem Core: Length

Simply I defined TWO Length Types

## Normal Length (NL)

This is the normal length that we refer to it in our daily life

## Radial Length (RL)

This is the radius length that have an origin point in center of circle

## Quantities

Work: Force * Normal Length

Torque: Force * Radial Length

Angle: Normal Length / Radial Length

In quantity system I made the L dimension as NL+RL

CAN YOU SEE ANGLE

I made it explicitly a quantity that is NOT dimensionless

and THIS SOLVED ALL my problems of this Problem

I won’t argue much let us test 🙂

Torque * Angle = Work

F*RL * (NL/RL) = F * NL <== see what I mean

Torque * Angular Speed = Power

F*RL * (NL/RL*T) = F*NL/T <== where T is the time.

so you may wonder about Angle and Solid Angle

in SI they are all dimensionless but in Quantity System YOU CAN’T consider them like this

(By the way I’ve break the checking for these two quantities to be summable with dimensionless numbers – just to keep the fundamentals as it is although I am not convinced and I may remove it in future but damn it I need support from any physics guy)

ANGLE : NL/RL

Solid Angle: NL^2/RL^2 because its area over area

Frequency = 1/T

Angular Velocity = (NL/RL)/T

do you remember the conversion between RPM to frequency

RPM (Revolution Per Minute) is a Angle / Time

lets test the law

Omega = 2*pi*frequency

pi: radian value which is NL/RL

Omega = (NL/RL) * 1/T = (NL/RL)/T which angular velocity

# Discoveries

## PI value

PI is ratio of any circle‘s circumference to its diameter WHICH MEANS (NL/RL)

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

which corresponds to radian unit and stradian unit for angle and solid angle quantities.

## Reynolds Number

I am not holding back ( Reynolds number is a dimensionless number that measure inertial forces to viscous forces)

WHY we always differentiating between Flow in Pipes and Flow on Flat plate

let’s see with normal length in quantity system

it shows it is a dimensionless quantity

ok let us force my theory about flow in pipes

the pipe have a diameter and Reynolds number is calculated by rho*v*DIAMETER/viscosity

so let me add d as a diameter and solve again

Qs> d=0.5<m!>

RadiusLength: 0.5 m

Qs> rho*v*d/mue

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

NOTE: Adding ‘!’ after the length unit will mark the quantity as Radial Length quantity.

ERROR it shouldn’t be DerivedQuantity at all it should be Dimensionlesss

so there is another term that should be fixed. Do you know which term ???

lets try the velocity with vr=0.5<m!/s>

Qs> vr=0.5<m!/s>

DerivedQuantity: 0.5 <m/s>

Qs> rho*vr*d/mue

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

ALSO ERROR

ok let us try the density

Qs> rhor = 3<kg/m!^3>

DerivedQuantity: 3 <kg/m^3>

Qs> rhor*v*d/mue

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

CAN YOU SEE THE SOLID ANGLE Quantity

do you remember the above argue about Solid Angle is dimensionless number

can I pretend now that reynolds number for pipes is CORRECT ???

the new density which is kg/m!^3

This is driving me nuts

## Pump Affinity Laws

Also pump equations led to the same SolidAngle Quantity not DimensionLess one

# Epilogue

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 after all of this and that my assumption about Torque and Work is Wrong.

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