{"id":1424,"date":"2026-05-12T21:47:49","date_gmt":"2026-05-12T21:47:49","guid":{"rendered":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/chapter\/solution-exercise-23\/"},"modified":"2026-05-13T03:39:53","modified_gmt":"2026-05-13T03:39:53","slug":"solution-exercise-23","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/chapter\/solution-exercise-23\/","title":{"raw":"Solution Exercise 23","rendered":"Solution Exercise 23"},"content":{"raw":"
\r\n
\r\n\r\nCalculate the Piper Fractions:\r\n\r\n<\/div>\r\n<\/colgroup>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Solutes<\/strong><\/td>\r\nmeq\/L<\/strong><\/td>\r\nPiper Fractions<\/strong><\/td>\r\n<\/tr>\r\n
[latex]{Ca}_{}^{2 +}[\/latex]<\/td>\r\n4.59<\/td>\r\n4.59\/7.78 = 0.59(100) =<\/td>\r\n59%<\/strong><\/td>\r\n<\/tr>\r\n
[latex]{Mg}_{}^{2 +}[\/latex]<\/td>\r\n2.80<\/td>\r\n2.8\/7.78 = 0.36(100) =<\/td>\r\n36%<\/strong><\/td>\r\n<\/tr>\r\n
[latex]{Na}_{}^{+}[\/latex]<\/td>\r\n0.36<\/td>\r\n(0.36+0.04)\/7.78 = 0.05(100) =<\/td>\r\n5%<\/strong><\/td>\r\n<\/tr>\r\n
[latex]K_{}^{+}[\/latex]<\/td>\r\n0.04<\/td>\r\n<\/tr>\r\n
Sum cations:<\/strong><\/td>\r\n7.78 meq\/L<\/strong><\/td>\r\n<\/td>\r\n<\/tr>\r\n
[latex]{HCO}_{3}^{-}[\/latex]<\/td>\r\n5.33<\/td>\r\n5.33\/7.35 = 0.73(100) =<\/td>\r\n73%<\/strong><\/td>\r\n<\/tr>\r\n
[latex]{SO}_{4}^{2 -}[\/latex]<\/td>\r\n1.75<\/td>\r\n1.75\/7.35 = 0.24(100) =<\/td>\r\n24%<\/strong><\/td>\r\n<\/tr>\r\n
[latex]{Cl}_{}^{-}[\/latex]<\/td>\r\n0.27<\/td>\r\n0.27\/7.35 = 0.04(100) =<\/td>\r\n4%<\/strong><\/td>\r\n<\/tr>\r\n
Sum anions:<\/strong><\/td>\r\n7.35 meq\/L<\/strong><\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
\r\n\r\n\"A\r\n\r\n<\/div>\r\n
\r\n
The water is a Calcium-Magnesium-Bicarbonate type as indicated in Figure 82<\/span><\/a>. However, it is more appropriate to call it a Calcium-Bicarbonate water as Ca2+<\/sup> makes up more than 50% of all the cations.<\/blockquote>\r\n<\/div>\r\n
\r\n\r\nReturn to Exercise 23<\/strong><\/span><\/a>\u2ba5\r\n\r\n<\/div>\r\n
\r\n\r\nReturn to where text linked to Exercise 23<\/strong><\/span><\/a>\u2ba5\r\n\r\n<\/div>\r\n<\/div>","rendered":"
\n
\n

Calculate the Piper Fractions:<\/p>\n<\/div>\n\n\n\n\n\n<\/colgroup>\n\n\n\n\n\n\n\n\n\n\n\n
Solutes<\/strong><\/td>\nmeq\/L<\/strong><\/td>\nPiper Fractions<\/strong><\/td>\n<\/tr>\n
[latex]{Ca}_{}^{2 +}[\/latex]<\/td>\n4.59<\/td>\n4.59\/7.78 = 0.59(100) =<\/td>\n59%<\/strong><\/td>\n<\/tr>\n
[latex]{Mg}_{}^{2 +}[\/latex]<\/td>\n2.80<\/td>\n2.8\/7.78 = 0.36(100) =<\/td>\n36%<\/strong><\/td>\n<\/tr>\n
[latex]{Na}_{}^{+}[\/latex]<\/td>\n0.36<\/td>\n(0.36+0.04)\/7.78 = 0.05(100) =<\/td>\n5%<\/strong><\/td>\n<\/tr>\n
[latex]K_{}^{+}[\/latex]<\/td>\n0.04<\/td>\n<\/tr>\n
Sum cations:<\/strong><\/td>\n7.78 meq\/L<\/strong><\/td>\n<\/td>\n<\/tr>\n
[latex]{HCO}_{3}^{-}[\/latex]<\/td>\n5.33<\/td>\n5.33\/7.35 = 0.73(100) =<\/td>\n73%<\/strong><\/td>\n<\/tr>\n
[latex]{SO}_{4}^{2 -}[\/latex]<\/td>\n1.75<\/td>\n1.75\/7.35 = 0.24(100) =<\/td>\n24%<\/strong><\/td>\n<\/tr>\n
[latex]{Cl}_{}^{-}[\/latex]<\/td>\n0.27<\/td>\n0.27\/7.35 = 0.04(100) =<\/td>\n4%<\/strong><\/td>\n<\/tr>\n
Sum anions:<\/strong><\/td>\n7.35 meq\/L<\/strong><\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n

\"A<\/p>\n<\/div>\n

\n

The water is a Calcium-Magnesium-Bicarbonate type as indicated in Figure 82<\/span><\/a>. However, it is more appropriate to call it a Calcium-Bicarbonate water as Ca2+<\/sup> makes up more than 50% of all the cations.<\/p><\/blockquote>\n<\/div>\n

\n

Return to Exercise 23<\/strong><\/span><\/a>\u2ba5<\/p>\n<\/div>\n

\n

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