The quantity of liquid (such as cryogenic liquidnitrogen)

Chapter 24, Problem 24.64

(choose chapter or problem)

The quantity of liquid (such as cryogenic liquidnitrogen) available in its storage tank is often monitored bya capacitive level sensor. This sensor is a vertically alignedcylindrical capacitor with outer and inner conductor radii Raand Rb, whose length spans the height of the tank. When anonconducting liquid fills the tank to a height h (< ) fromthe tanks bottom, the dielectric in the lower and upperregion between the cylindrical conductors is the liquid (^liq)and its vapor (-Kv), respectively (Fig. 24-33). (a) Determinea formula for the fraction F of the tank filled by liquid interms of the level-sensor capacitance C. [Hint: Considerthe sensor as a combination of two capacitors.] (b) Byconnecting a capacitance-measuring instrument to the levelsensor, F can be monitored. Assume the sensor dimensionsare = 2.0 m, Ra = 5.0 mm, and Rb = 4.5 mm. Forliquid nitrogen ( K \ iq = 1.4, K y = 1.0), what values of C(in pF) will correspond to the tank being completely fulland completely empty?FIGURE 24-33 64.