Applied Mathematics and Sciences: An International Journal (MathSJ ), Vol. 2, No. 2, June 2015 height
h x, t
________________________________________________________________________________ x (m)
t=0
t=0.4
t=0.8
t=1.2
t=1.6
t=1.8
t=2
t=2.8
t=3.2
t=4
(days) (days)
(days)
(days)
(days)
(days)
(days)
(days)
(days)
(days)
0 0.458 0.833 1.125 1.333 1.458 1.5
0.3998 0.6544 0.8627 1.0247 1.1405 1.2100 1.2331
0.4715 0.6798 0.8503 0.9829 1.0776 1.1344 1.1533
0.4715 0.6623 0.8153 0.9304 1.0076 1.0469 1.0483
0.5285 0.6922 0.8261 0.9303 1.0047 1.0494 1.0642
0.5400 0.6928 0.8178 0.9150 0.9844 1.0261 1.0400
0.5665 0.6871 0.7858 0.8625 0.9174 0.9503 0.9612
0.5725 0.6817 0.7710 0.8404 0.8900 0.9198 0.9297
t=4.2
t=4.3
t=4.3 (days) (days)
(days) 0 0.5 1 1.5 2 2.5 3
0.2694 0.5968 0.8646 1.073 1.2218 1.3111 1.3409
0.5772 0.6689 0.7439 0.8022 0.8439 0.8689 0.8772
0.5774 0.6655 0.7376 0.7937 0.8338 0.8578 0.8658
0.5773 0.6638 0.7345 0.7896 0.8289 0.8525 0.8603
Table 3.Numerical values of water head in an unconfined horizontal aquifer for different time t at distance x = 0 , 0.5 , 1,…, 3. height
h x, t
________________________________________________________________________________________________________ t x=0 x=0.5 x=1 x=1.5 x=2 x=2.5 x=3 0 0.2694 0.3998 0.4715 0.5139 0.5400 0.5564 0.5665 0.5725 0.5758 0.5772 0.5773
1.4
0.4583 0.5968 0.6544 0.6798 0.6902 0.6928 0.6912 0.6871 0.6817 0.6755 0.6689 0.6655
0.8333 0.8647 0.8627 0.8503 0.8344 0.8178 0.8015 0.7858 0.7710 0.7570 0.7439 0.7376
1.125 1.073 1.0248 0.9829 0.9466 0.9150 0.8872 0.8625 0.8404 0.8204 0.8022 0.7937
1.3333 1.2218 1.1405 1.0776 1.0267 0.9845 0.9485 0.9174 0.8900 0.8657 0.8439 0.8338
1.4583 1.3111 1.2100 1.1344 1.0748 1.0261 0.9853 0.9503 0.9198 0.8929 0.8689 0.8578
1.5 1.3409 1.2331 1.1533 1.0908 1.0400 0.9975 0.9612 0.9297 0.9019 0.8772 0.8658
EXACT HPTM
1.2
1 height h(x ,t )
0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4 4.2
0.8
0.6
0.4
0.2
0 0
0.5
1
1.5 Distance x
2
2.5
3
Figure 3.Graph of Exact and HPTM solution for height of water table vs distance x.
9
