The discussion revolves around converting a differential equation related to air pressure, expressed in terms of height in kilometers, into a form that uses meters. The original poster attempts to manipulate the equation dp/dh = -0.13*p to achieve this conversion.
Some participants have offered insights into the dimensional analysis of the constant 0.13, suggesting that it has a dimension of L-1. There is an ongoing exploration of how to properly convert this constant to maintain dimensional consistency when changing units from kilometers to meters.
There is a noted confusion regarding the units and dimensions involved in the conversion process, as well as the implications of these conversions on the differential equation being discussed.
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.Poetria said: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 said: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?
Right number, wrong dimension.Poetria said:Oh dear, I understand what's wrong.
0.00013 meters
Right.Poetria said:Of course:
0.00013 meters^-1
Thank you very much. :)