Is pressure linear?

[tursiops]

I guess this is pedantic and probably unnecessary, but there is no way "pressure is linear." That is because it has not been said with respect to what else is changing. What linearity means (this is a definition, not an opinion) is that, if you plot pressure against something else, the plot is a straight line, not a curve. It is the straight line that is linear, not the pressure. So, if you believe PV=nRT (ideal gas law) for example, then plotting P against T gives a straight line. For you calculus buffs, dP/dT=nR/V, all constants, just a number, the slope of the straight line. But if you were to plot P against depth, you'd only get a straight line if temperature and salinity are constant. And if you plot pressure in your cylinder against time, it is not linear, because depth and temperature and breathing rate (and probably other stuff too!) can change the pressure, not just time.

 

[Steelyeyes]

For the purposes of scuba diving, with the accuracy of the devices used to measure it...and therefore for all practical purposes, pressure is linear.

 

[D_Fresh]

Tursiops is certainly correct. Temperature and salinity do affect pressure:depth, and salinity changes with depth (but only on the scale of outside of diving range), which further complicates things.

But, for all practical diving applications, any difference in values are so small that they're meaningless (except for cylinder gas pressure, which is greatly influenced by temperature). So I concur that in any diving application, pressure of the water column above can be assumed to be linear in relation to depth within dive range.

From the conceptual aspect, it's pretty cool. I hadn't looked too deeply into the math behind it until this thread. Thanks OP and everyone else, really got the gears a-turnin!

Edit to add link if anyone is interested:
Standard Salinity Profile - Windows to the Universe

 

[tursiops]

pressure is linear

See post #11. Linear with respect to what?

 

[tursiops]

pressure can be assumed to be linear

See post #11. Linear with respect to what?

 

[D_Fresh]

See post #11. Linear with respect to what?

Fair point, I fixed my statement in italics.