Question

Laplace equation for water flow in soils is given below.

$\frac{{\partial }^{2}H}{\partial x^2}+\frac{{\partial }^{2}H}{\partial y^2}+\frac{{\partial }^{2}H}{\partial z^2}=0$

Head H does not vary in y and z direction. Boundary conditions are: at x = 0, H = 5, and $\frac{dH}{dx}=-1$. What is the value of H at x = 1.2 ?

• A. 3.8

Answer 1

The correct option is A 3.8
$\frac{{\partial }^{2}H}{\partial x^2}+\frac{{\partial }^{2}H}{\partial y^2}+\frac{{\partial }^{2}H}{\partial z^2}=0$

H does not vary In y and z direction

$\therefore \frac{{\partial }^{2}H}{\partial x^2}=0$

$\Rightarrow H=(C_{1}x+C_2)$

at x = 0

H = 5

$\therefore 5=C_2$

$\therefore H=C_{1}x+5$

$and\left(\frac{dH}{dx}\right)=C_1=-1$

$\therefore H=-x+5$

at x = 1.2 m

H = (-1.2 + 5)

= 3.8 m