I would like to measure the pressure inside the car ( by a pressure sensor or the altimeter). If we consider that the temperature inside the car is constant, do the car's velocity or acceleration affect the pressure measurements?
Thank you
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3 Answers
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This is really a comment to the two existing answers from Phoenix87 and Pranav.
I agree entirely with their comments on acceleration. However if the car is not air tight, i.e. if air can flow in and out of the car, then there will be an effect of velocity as well. For example if there are small apertures in the car we'd expect the pressure inside to fall with increasing velocity due to Bernoulli's principle. If there is greater airflow through the car then the pressure inside is likely to vary in a complex way due to turbulent air flows.
If we can treat the car interior as a sealed volume then this isn't a consideration and, as Phoenix87 and Pranav say, we need only consider the pressure gradients caused by aceleration.
answered Feb 24, 2015 at 9:13
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Yes. Air has mass, and anything with mass has inertia. Due to these inertial effects, the air in a car will be redistributed as you would expect any other object with mass to move in a non-inertial frame. See Why does a helium filled ballon move forward in a car when the car is accelerating?
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By the equivalence principle you can take into considerations the effects of gravity on pressure for instance. Then it is known that pressure depends on altitude (although this dependence is not simple due to many other factors). The general relation for the pressure gradient is $$\nabla p=\rho\mathbf g$$ where $\mathbf g$ is the gravitational acceleration, but by the above argument it could be any acceleration field. It follows that at constant velocity the pressure remains constant.
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$\begingroup$ Do you not think that a horizontal velocity would increase the air density at the back of the car, and hence increase the pressure there? $\endgroup$ Commented Feb 24, 2015 at 9:03
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2$\begingroup$ @HritikNarayan: constant velocity means the acceleration is zero, and therefore $\nabla P = 0$ and the pressure is the same everywhere. $\endgroup$ Commented Feb 24, 2015 at 9:05
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1$\begingroup$ Just to be pedantic, the horizontal component of the acceleration would be zero, hence the pressure remains constant on horizontal surfaces. A helium balloon would still float upward in this case, as confirmed by experience. $\endgroup$ Commented Feb 24, 2015 at 9:10