Solution to Exercise 10

10) Hydraulic head controls the flow of groundwater. A sand filled column is set up as shown in the accompanying figure using a datum of 1000 m. If O=9 cm, K=5 cm, P=5 cm, S=12 cm, A=12 cm, G=5 cm, R=4 cm, M=4 cm, B=7cm, J=9cm, Q=15 cm, C=6 cm, answer the lettered items below. To answer b through d write the answer first as the letters for the relevant line segments, and then as the total value, e.g., for G+M write, 5 cm + 4 cm = 9 cm.

There are many more arrows and letters than needed to answer these questions.

10a) Which way is the water flowing?

Using the horizontal datum and the total elevation of the two water levels in the piezometers, the water is flowing from left to right as the head (as measured from the datum) is higher in the left piezometer than the right piezometer.

10b) What is the total head at the white mark labeled X relative to the 1000 m datum?

The total head at X is the elevation head (Q+C) plus the pressure head, R, Q+C+R = 9 cm + 6 cm + 4 cm = 19 cm above the datum of 1000 m.

10c) What is the elevation head at the white mark labeled Y relative to the 1000 m datum?

The elevation head at Y is (K+M) = 5 cm + 4 cm = 9 cm above the 1000 m datum.

10d) What is the pressure head at the white mark labeled X?

The pressure head at X is R, R = 4 cm