Chapter 6, Problem 6.1P

(a)

To determine

State whether the statement "seepage velocity is always greater than the discharge velocity" is true or false.

Answer to Problem 6.1P

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

Explanation of Solution

Express the derived equation to relay seepage velocity $\left(v_s\right)$ and discharge velocity (v) as follows:

$q=vA=v_s{A}_s$

Here, q is the flow rate, v is the discharge velocity, A is the gross cross sectional area, $v_s$ is the seepage velocity, and $A_s$ is the area of void in the cross section of the specimen.

Seepage velocity is based upon the void space of the soil and simultaneously the discharge velocity is based upon the gross sectional area of the soil. Therefore, this directly means that the seepage velocity is greater than the discharge velocity.

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

(b)

To determine

State whether the statement "hydraulic conductivity of a sandy soil is greater than that of a clayey soil" is true or false.

Answer to Problem 6.1P

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

Explanation of Solution

The hydraulic conductivity (k) for clayey soils varies for different types and the k value for Silty clay is $\left(1\times {10}^{-5}-1\times {10}^{-3}\right)\text{cm}/\text{s}$ and for clay is $<1\times {10}^{-6}\text{cm}/\text{s}$.

The hydraulic conductivity (k) for sandy soils varies from $0.00\text{1}–\text{1}\text{cm}/\text{s}$.

Based on the above values, hydraulic conductivity (k) for sandy soil is greater than the clayey soil.

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

(c)

To determine

State whether the statement “hydraulic conductivity is same for water and oil in a porous medium” is true or false.

Answer to Problem 6.1P

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

Explanation of Solution

For each time, the hydraulic conductivity contains the unit of length and this represent that there is a fluid flow which is a property of porous medium. However, the viscous fluid like oil moves slowly through sand when compared to water. From the above comparison, it means that the flow of water and oil differs in the hydraulic conductivity of the porous medium.

Hence, the given statement is $\underset{\_}{\text{false}}$.

(d)

To determine

State whether the statement “pressure head is proportional to the pore water pressure” is true or false.

Answer to Problem 6.1P

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

Explanation of Solution

Write the pressure head equation $\left(h_w\right)$ as follows:

$h_w=\frac{u}{{\gamma }_w}+z$

Here, u is the pore water pressure, ${\gamma }_w$ is the unit weight of water, and z is the elevation head.

The above equation shows that the pressure head $\left(h_w\right)$ is directly proportional to pore water pressure (u).

Hence, the given statement is $\underset{\_}{\text{true}}$.

(d)

To determine

State whether the statement “magnitude of pressure head depends on the selected datum” is true or false.

Answer to Problem 6.1P

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

Explanation of Solution

Write the pressure head equation $\left(h_w\right)$ as follows:

$h_w=\frac{u}{{\gamma }_w}+z$

From the above equation, it is clear that the pressure head magnitude depends upon the datum plane. However, the pressure head magnitude does not depend upon the selected datum.

Hence, the given statement is $\underset{\_}{\text{false}}$.