Chapter 7, Problem 7.1P

(a)

To determine

State whether the statement “pressure head decreases along the flow line” is true or false.

Answer to Problem 7.1P

The given statement is $\underset{\_}{\text{False}}$.

Explanation of Solution

Express Bernoulli’s equation as follows:

$\frac{P}{\rho g}+\frac{V^2}{2g}+z=H=\text{Constant along streamline}$

This equation clearly says that the pressure head is constant along the flow lines.

Thus, the given statement is $\underset{\_}{\text{False}}$.

(b)

To determine

State whether the statement “pressure head is the same along an equipotential line” is true or false.

Answer to Problem 7.1P

The given statement is $\underset{\_}{\text{False}}$.

Explanation of Solution

Calculate the total head (h) using the relation.

$h=\frac{P}{{\gamma }_w}+z$

Here, $\frac{P}{{\gamma }_w}$ is the pressure head and z is the elevation head.

From the above equation, it is clear that if there is an increase in the water pressure then it increases depth along the equipotential line. Therefore, pressure is not at the same level along the equipotential line.

Thus, the given statement is $\underset{\_}{\text{False}}$.

(c)

To determine

State whether the statement “flow lines and equipotential lines are not perpendicular to each other in anisotropic soils” is true or false.

Answer to Problem 7.1P

The given statement is $\underset{\_}{\text{True}}$.

Explanation of Solution

Express the equation of continuity for two dimensional flow as follows:

$k_x\frac{{\partial }^{2}h}{\partial x^2}+k_z\frac{{\partial }^{2}h}{\partial z^2}=0$

The hydraulic conductivity in the horizontal and vertical directions for anisotropic soils is not equal.

$k_x\ne k_z$

The above equation denotes the two families of curves that do not meet at $90°$. Transformed sections are utilized to draw the flow nets of an anisotropic soils. The equipotential lines and flow lines are orthogonal. These two lines are not right angle to each other while they are drawn in true sections.

Thus, the given statement is $\underset{\_}{\text{True}}$.

(d)

To determine

State whether the statement “water level rises to 4.5 m in a standpipe piezometer, the pore water pressure is equal to $44.1{\text{kN/m}}^{\text{2}}$” is true or false.

Answer to Problem 7.1P

The given statement is $\underset{\_}{\text{True}}$.

Explanation of Solution

Calculate the pore water pressure $\left(p_s\right)$ using the relation.

$p_s={\gamma }_w{h}_w$

Here, ${\gamma }_w$ is the unit weight of water and $h_w$ is the depth of water.

Take the unit weight of the water as $9.81{\text{kN/m}}^{\text{3}}$.

Substitute $9.81\text{kN}/{\text{m}}^{\text{3}}$ for ${\gamma }_w$ and 4.5 m for $h_w$.

$\begin{array}{c}{p}_s=9.81\times 4.5\\ =44.1\text{kN}/{\text{m}}^{\text{2}}\end{array}$

The pore water pressure at 4.5 m of water level rise is $44.1\text{kN}/{\text{m}}^{\text{2}}$.

Thus, the given statement is $\underset{\_}{\text{True}}$.

(e)

To determine

State whether the statement “size of the square flow element is the same at all locations within the flow net” is true or false.

Answer to Problem 7.1P

The given statement is $\underset{\_}{\text{False}}$.

Explanation of Solution

While drawing the flow net, the smooth curves are followed by right angle intersection on the intermediate flow lines and equipotential lines.

The curvilinear square grid is the space which is accurately between the pair of flow lines and equipotential lines. Therefore, the size of the square element is varied in the flow net.

Thus, the given statement is $\underset{\_}{\text{False}}$.