Qestion about pressure transducer

[fatima_ib89]

i have to install a pressure transducer to convert the pressure value to volume, but its not the problem, the shape of the water tank , the water tank like cylinder but the base is concave to the bottom, how can i do that ? please
thank you all

 

[RTW69]

A diagram with dimensions would be helpful. Try to solve the problem so we can see where to help.

 

[fatima_ib89]

First, thank you for reply
i want to measure the volume of water in the tank by using TECSIS pressure transducer with built in microcontroller and analoge output from it between 4-20mA , by using this equation P=g*h*density, i can get analoge output which indicate the volume, of course after set the microcontroller ,but the shape of the tank like cylinder and concave to the bottom-see the attachment-this means that i have two equation of the volume, what can i use with the transducer to solve this problem?

 

[RTW69]

I would refresh your memory regarding applications of triple integrals in calculus. You have a shape that looks like a hemisphere, you are trying to find its volume bounded by a plane at different heights measured from the bottom of the hemisphere. My "Mathematical handbook of Formulas and Tables" shows the volume of a Spherical cap of Radius r and Height h to be:

V=1/3*pi*h^2(3r-h)

The volume of a Right Circular cylinder of radius r and Height h is:

V=pi*r^2*h

You have two equations for Volume vs height, one for the sphere and another for the cylinder

 

[fatima_ib89]

you are extremely right, but for example when the pressure equal 2 bar the output current will be 6 mA,
from this equation P=density*h*g i can get P=density*g*(volume/Pi*r^2) this is for cylinder
so i can set the microcontroller in the transducer to give me indication of volume instead of current
ex:
P= 1000*9.8*(volume/Pi*r^2)....for pure water so the volume = p*(pi*r^2)/1000*9.8
for 1m reduis
volume = p*3.14/1000*9.8...when pressure=2 bar
volume = 64 m^3, and the transdcucer should give me 6mA but i can set the microcontroler
(proportional control) to give me for example 0.64

 

[fatima_ib89]

continue...
this is all equation for cylinder, but there is a spherical cap shap as u said , is there any method to switch the transducer and separate the volume indication between this two shapes ..i hope u get it other wise i would have a mistake in my delivery ..thank you