Question

A sand sample of 35 cm^2 cross sectional area and 20 cm long was tested in a constant head permeameter. Under a head of 60 cm, the discharge was 120 mL in 6 min. The dry weight of sand used for the test was 1120 g and the specific gravity was 2.68. Determine:

a. The hydraulic conductivity in cm/sec.
b. Porosity.
c. The Darcy velocity (discharge velocity)
d. The seepage velocity.

Answer 1

Answer

given,

Area of sample = 35 cm²

Length of the sample = 20 cm

head = h  = 60 cm

discharge = 120 ml

                 = 0.33 cm³/s

time = 6 minute

dry weight of  sand = 1120 g

specific gravity, G = 2.68

a) Hydraulic conductivity

  Q = k iA

 $Q = k \dfrac{h}{L} A$

 $0.33= k \times \dfrac{60}{20}\times 35$

     k = 3.14 x 10⁻³ cm/s

b)  $G = \dfrac{weight\ of\ solid(W_s)}{volume\ of\ dry\ \times unit\ weight\ of\ water}$

   $2.68 = \dfrac{1120}{V_s \times 1}$

      V_s = 417.91 cm³

void\ ratio,e = $\dfrac{Volume\ of\ voids}{volume\ of\ solid}$

$e = \dfrac{V-V_s}{V_s}$

V = A x L = 35 x 20 = 700 cm³

$n = \dfrac{700-417.91}{417.91}$

 e = 0.675

$n = \dfrac{e}{1+e}$

$n = \dfrac{0.675}{1+0.675}$

n = 0.403

c) discharge velocity

Q = A v

0.33 = 35 x v

 v = 9.43 x 10⁻³ cm/s

d) seepage velocity

 $v_s = \dfrac{v}{n}$

 $v_s = \dfrac{9.43\times 10^{-3}}{0.403}$

 $v_s =2.34\times 10^{-2}\ cm/s$