# PHYSICS : Homogeneous Equation

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Hi, I have learnt that in any equation where each term has the same base units, the equation is said to be homogenous or balanced. However, are ALL homogenous equations correct equations? What is the explanation to that?

Thank you very much!

Thank you very much!

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#2

In mathematics an equation is called homogenous, if its a conditional equation which contains a zero. May I ask you in which part of physics do you use a homogenous equation at the moment? perhaps I'm able to give a better answer by getting more informations.

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#3

(Original post by

Hi, I have learnt that in any equation where each term has the same base units, the equation is said to be homogenous or balanced. However, are ALL homogenous equations correct equations? What is the explanation to that?

Thank you very much!

**Phui Yeng**)Hi, I have learnt that in any equation where each term has the same base units, the equation is said to be homogenous or balanced. However, are ALL homogenous equations correct equations? What is the explanation to that?

Thank you very much!

So in

p = hdg (pressure at a depth h in a liquid of density d)

the units on the left are pressure, which is Force / area or N/m

^{2}

On the right we have h (metres) d (kg/m

^{3}) and g (m/s

^{2})

So on the left we have

Force which is defined in F=ma so the units of force are kg.m/s

^{2}

and area which is m

^{2}

Check for yourself that F/A reduces to kg.m

^{-1}.s

^{-2}

On the right you have hdg

h = m (metre)

d is kg.m

^{-3}(mass/volume)

g is m.s

^{-2}(acceleration)

Check for yourself that this also reduces to

kg.m

^{-1}.s

^{-2}

So the equation is homogeneous.

This does not mean it's correct though.

The correct equation could be, for example, p=2hdg

There is no way of knowing, purely from consideration of the units (homogeneity) that the equation is correct.

What you can say is that if the equation is

**not**homogeneous it is

**not**correct.

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#4

(Original post by

Homogeneous means that the units (dimensions of mass, length, time etc) are the same on both sides of the equation. (...)

**Stonebridge**)Homogeneous means that the units (dimensions of mass, length, time etc) are the same on both sides of the equation. (...)

Example:

1 J = 1 kg m² / s²; the units are different, but the meaning is the same. So is this an homologous equation?

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#5

(Original post by

Does apply this meaning too, if there are different units on both sides of the equation which mean the same?

Example:

1 J = 1 kg m² / s²; the units are different, but the meaning is the same. So is this an homologous equation?

**Kallisto**)Does apply this meaning too, if there are different units on both sides of the equation which mean the same?

Example:

1 J = 1 kg m² / s²; the units are different, but the meaning is the same. So is this an homologous equation?

Joule is work done and is force x distance

Force is mass x acceleration and is (kg.ms

^{-2})

So joule is (kg.ms

^{-2})m

This becomes kgm

^{2}s

^{-2}

So any equation with energy on the left has units kg.m

^{2}.s

^{-2}on

**both**sides if it's homogeneous.

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#6

(Original post by

x

**Stonebridge**)x

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#7

(Original post by

I see. Equations can be made homologous by derivating the unit on one of the sides to get the same units in equation. Right?

**Kallisto**)I see. Equations can be made homologous by derivating the unit on one of the sides to get the same units in equation. Right?

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#8

(Original post by

All true equations MUST have the same units (= combination of base units) on both sides.

**Stonebridge**)All true equations MUST have the same units (= combination of base units) on both sides.

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#9

Yes. It's possible even to derive an equation by consideration of the base units. There are examples in most physics text books.

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(Original post by

In mathematics an equation is called homogenous, if its a conditional equation which contains a zero. May I ask you in which part of physics do you use a homogenous equation at the moment? perhaps I'm able to give a better answer by getting more informations.

**Kallisto**)In mathematics an equation is called homogenous, if its a conditional equation which contains a zero. May I ask you in which part of physics do you use a homogenous equation at the moment? perhaps I'm able to give a better answer by getting more informations.

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reply

(Original post by

Homogeneous means that the units (dimensions of mass, length, time etc) are the same on both sides of the equation.

So in

p = hdg (pressure at a depth h in a liquid of density d)

the units on the left are pressure, which is Force / area or N/m

On the right we have h (metres) d (kg/m

So on the left we have

Force which is defined in F=ma so the units of force are kg.m/s

and area which is m

Check for yourself that F/A reduces to kg.m

On the right you have hdg

h = m (metre)

d is kg.m

g is m.s

Check for yourself that this also reduces to

kg.m

So the equation is homogeneous.

This does not mean it's correct though.

The correct equation could be, for example, p=2hdg

There is no way of knowing, purely from consideration of the units (homogeneity) that the equation is correct.

What you can say is that if the equation is

**Stonebridge**)Homogeneous means that the units (dimensions of mass, length, time etc) are the same on both sides of the equation.

So in

p = hdg (pressure at a depth h in a liquid of density d)

the units on the left are pressure, which is Force / area or N/m

^{2}On the right we have h (metres) d (kg/m

^{3}) and g (m/s^{2})So on the left we have

Force which is defined in F=ma so the units of force are kg.m/s

^{2}and area which is m

^{2}Check for yourself that F/A reduces to kg.m

^{-1}.s^{-2}On the right you have hdg

h = m (metre)

d is kg.m

^{-3}(mass/volume)g is m.s

^{-2}(acceleration)Check for yourself that this also reduces to

kg.m

^{-1}.s^{-2}So the equation is homogeneous.

This does not mean it's correct though.

The correct equation could be, for example, p=2hdg

There is no way of knowing, purely from consideration of the units (homogeneity) that the equation is correct.

What you can say is that if the equation is

**not**homogeneous it is**not**correct.Thank you very much, this has helped me a lot!

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