I want to measure the density in different layers of a suspension. To do this I want to place pressure sensors at different heights. Let's assume that the sensors are not by orders of magnitude more exact than neccessary (because I want to detect small differences in density, like 1% over heights of 1m or smaller, and maybe I'm on a budget for the sonsors). The idea would be to place the sensors on a vertical pole with a known distance between two. The pole will be placed in the liquid and not be moved vertically during the measurements. Possibly I will use two sensors at each height.
Now, I know that - labeling the sensors downward, 0 at the top - that $(p_1-p_0)+(p_2-p_1)=p_2-p_0$ Now my questions are, how do I use this fact to combine the readings into a coherent, exact picture and how do I calculate the actual error of my result?
Here's my approach:
- Set up linear equations for the "true" pressures that follow the relation given above.
- find - numerically, with some equation solver - the tupel of "true" pressures that satisfy the linear equations and have the least mean square deviation from the measured pressures
Is this approach basically correct? How would I calculate the error of the true pressure from the error of my sensors?