Air Pressure Conversion: Units to Meters

[Poetria]

Homework Statement

[/B]
dp/dh = -.13*p h in kilometers

I should convert it into meters2. The attempt at a solution

I thought it would be enough to multiply -0.13 by 1000. :(

dp/dh = -130*p but it is wrong.

 

[kuruman]

The statement of the problem is not clear. What are you trying to do, what does the formula that you posted represent and what are the units for this number 0.13?

 

[Poetria]

dp/dh=-0.13*p
dp/dx = ??

p - air pressure in kg/cm^2

h - height in km
I should convert h in km into x in meters.

What is the differential equation for p if altitude is measured in meters x instead of kilometers h?

 

[haruspex]

dp/dh=-0.13*p
dp/dx = ??

p - air pressure in kg/cm^2

h - height in km
I should convert h in km into x in meters.

What is the differential equation for p if altitude is measured in meters x instead of kilometers h?

From the equation given, you can deduce that the constant 0.13 has dimension L^-1. Since we are told the distance unit is km, we can say it is 0.13km^-1.
To convert to m, we need to multiply km^-1 by unity in the form of a constant with units km/m. What would that be?

 

[Poetria]

From the equation given, you can deduce that the constant 0.13 has dimension L^-1. Since we are told the distance unit is km, we can say it is 0.13km^-1.
To convert to m, we need to multiply km^-1 by unity in the form of a constant with units km/m. What would that be?

Oh dear, I understand what's wrong.

0.00013 meters

 

[haruspex]

Oh dear, I understand what's wrong.

0.00013 meters

Right number, wrong dimension.

 

[Poetria]

Of course:

0.00013 meters^-1

Thank you very much. :)

 

[haruspex]

Of course:

0.00013 meters^-1

Thank you very much. :)

Right.