Solution Exercise 4

The freshwater head can be calculated using h_{f}=z_{i}+(h_{i}-z_{i})\frac{\rho _{i}}{\rho _{f}}, which gives (noting that zi = 100 − 60 = 40 m):

1. h_{f,1}=40+(100.4-40)\frac{1010}{1000}=101\;\textrm{m}
h_{f,2}=40+(100-40)\frac{1020}{1000}=101.2\;\textrm{m}

The freshwater head is higher at piezometer 2 than at piezometer 1, so the flow is from piezometer 2 to 1. This is opposite to what one would conclude from uncorrected hydraulic head measurements.

2. The specific discharge follows from

q_{x}=-K_{f}\frac{\Delta h_{f}}{\Delta x}=-10\times \frac{101.2-101}{200}=-0.01\;\textrm{m}\;\textrm{d}^{-1}

which is a negative number because flow is in the direction of declining head.

Return to Exercise 4

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Variable-Density Groundwater Flow Copyright © 2022 by Vincent E.A. Post and Craig T. Simmons. All Rights Reserved.