CHAPTER 1  >  ACTIVITIES  >  PROBLEMS  >  PROBLEM 3
Elastance and capacitance of a beaker
Water is filled into a large glass beaker and the pressure of the water at the bottom of the tank is measured (see the table on the right).
In the accompanying data sheet (see the file => Pressure_Volume.xls), volume and pressure data for the beaker is reported.
Dimensions of beaker: Bottom radius: 13.0 cm; radius at a height of 10.3 cm: 6.62 cm.

a. Convert the values in the table to standard SI units. Determine the pressure difference with respect to the lowest value (empty container). Plot the pressure difference as a function of volume (this is called the hydraulic capacitive characteristic).
b. Roughly determine the values of the elastance of the system for the smallest and the largest quantities of water in the beaker.
c. Use the data sheet to determine the elastance of the system as a function of volume. Then plot the elastance as a function of capacitive pressure difference. Plot the result.
d. Determine the capacitance of the system as a function of capacitive pressure difference. Plot the result.
e. Use the data on the dimensions of the beaker, and the theoretical expression for the capacitance of a liquid in an open tank to determine the capacitance for some heights in the tank. Compare these results to the results obtained in the previous question (d).



V / ml
p / mbar
0
978.0
1000
979.7
1500
980.9
2000
982.2
2500
983.8
3000
985.6
3300
986.8
3500
987.7
3600
988.1