Question

A sample of sand, 5cm in diameter and 10 cm long, was prepared at a porosity of 50% in a constant head apparatus. The total head was kept constant at 30 cm and the amount of water collected in 5 seconds was 60 cm3. The test temperature was 17oC. Calculate the hydraulic conductivity and the seepage velocity at 20 oC.

Answer 1

Answer:

$K = 2.037*10^{-3} m/s$

$V_s = 0.0122 \ m/s$

Explanation:

Given that;

diameter (d) = 10cm/2 = 0.1m/2 = 0.05 m

length (l) = 10 cm = 0.1 m

porosity = 50%

height (h) = 30 cm = 0.3 m

time (t) = 5 s

volume (v) = 60 cm³ = 60 × 10⁻⁶ m³

Q (flow rate) = $\frac{v}{t}$

Q = $\frac{60*10^{-6} m^3}{5}$

Q = $12*10^{-6} m^3 /sec$

From constant head method, we use the relation K = $(\frac{Q*L}{A*h})$ to determine the hydraulic conductivity ; we have:

$K = \frac{12*10^{-6}*0.1}{\frac{\pi}{4}0.05^2*0.3}$

$K = 0.002037\\\\K = 2.037*10^{-3} m/s$

Seepage velocity $V_s = \frac{velocity }{porosity}$

where; velocity = $K*i$

=$(2.037*10^{-3}*)(\frac{0.3}{0.1})$

= $6.111*10^{-3} m/s$

$V_s = \frac{6.111*10^{-3}}{0.5}$

$V_s = 0.0122 \ m/s$