640-381: Principles and
Applications of Sensors
Problem Sheet 1:
9. The capacitance of cylinder of height H
partially immersed in liquid is:
C = 2 p e 0 [ H - h (1 - k ) ]
/ ln b /a
Here b is the outer diameter of the cylinder, a is the inner diameter, k is the dielectric constant
of the liquid in which the cylinder is immersed and h is the level to which the
cylinder is immersed in the liquid (ie h=0 is completely out of the water, h=H
is completely immersed.
a) If h = 2 cm, H = 20 cm, e 0 = 8.85 10 -12 C 2 /Nm 2, a = 1 mm,
b = 2 mm, k (water) = 78.5, what is the capacitance of the cylinder?
b) How different
is it to the value when the sensor is out of the
water?
c) The sensor is
to be used to measure the height of fluid. Discuss the performance of this sensor for this purpose. Is the
transfer function linear? Is the sensitivity the same regardless of the fluid
height. Give an expression for the sensitivity.
d) Is the sensor performance independent of what fluid it is immersed in? For example, how sensitive would this coaxial level sensor if it were used to detect the level of transformer oil [k(oil)= 4.5)] instead of water.