Vision systems that can provide a linear measurement back to a PLC?

[theColonel26]

Pressure sensor at a fixed depth combined with level sensor giving the top of the lighter fluid?

How would that work? what does the math look like for that?

 

[Steve Bailey]

Pressure in a tank of water increases at a rate of 0.43 PSI per foot of depth. Call that Rw. The pressure due to the oil increases at a rate proportional to its specific gravity, so for an oil with a specific gravity of 0.8 pressure increases at a rate of (0.8 * 0.43) PSI per foot of depth. Call that Ro.

Call the depth of the water Dw. Call the depth of the oil Do.

Total pressure = (Ro * Do) + (Rw * Dw).

The level sensor gives you the elevation of the surface. Your pressure sensor is mounted at a fixed elevation so you know the total depth of the liquid in the tank.

Total Depth = Do + Dw

That's two equations in two unknowns (Do and Dw).

 

[drbitboy]

Pressure in a tank of water increases at a rate of 0.43 PSI per foot of depth. Call that Rw. The pressure due to the oil increases at a rate proportional to its specific gravity, so for an oil with a specific gravity of 0.8 pressure increases at a rate of (0.8 * 0.43) PSI per foot of depth. Call that Ro.

Call the depth of the water Dw. Call the depth of the oil Do.

Total pressure = (Ro * Do) + (Rw * Dw).

The level sensor gives you the elevation of the surface. Your pressure sensor is mounted at a fixed elevation so you know the total depth of the liquid in the tank.

Total Depth = Do + Dw

That's two equations in two unknowns (Do and Dw).

N.B. I. Implicit in Steve's formulae is that the locations of the bottom reference for [Total Depth] and of the lower tap for [Total Pressure] must be at the same elevation (or corrected to same).


N.B. II. This method is sensitive to the knowledge of specific gravity of the oil, any errors in the level distance and pressure measurements, and possibly the temperature of the fluids; that said, the 1/4" accuracy requirement might be achievable, although I would not be surprised to see negative Do values calculated in the running system. The best approach would probably be to calibrate the system once it is in place.

Divide the PSI pressure measurement by 0.43 so both equations will be in feet.

DHead = Differential Head = [Differential Pressure] / 0.43 = (SGo * Do) + (SGw * Dw)
DDepth = Differential Depth = Do + Dw

Dw = DDepth - Do

DHead = (0.8 * Do) + (1.0 * Dw) 
DHead = (0.8 * Do) + (1.0 * (DDepth - Do))
DHead = (0.8 * Do) + DDepth - Do
DHead = DDepth + ((0.8 - 1.0) * Do)
Dhead = DDepth - (0.2 * Do)
 
(DHead - DDepth) = - 0.2 * Do

Do = (DDepth - DHead) / 0.2

More generally,

Do = (DDepth - DHead) / (1.0 - SGo)

SGi = Specific Gravity of [fluid i] i.e. density of [fluid i] as a fraction of the density of water, so

• SGo = SGoil = 0.8
• SGw = SGwater = 1.0