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

`K = 2.037*10^(-3) m/s`

`V_s = 0.0122 \ m/s`

Step-by-step 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) =
`(v)/(t)`

Q =
`(60*10^(-6) m^3)/(5)`

Q =
`12*10^(-6) m^3 /sec`

From constant head method, we use the relation K =
`((Q*L)/(A*h))` to determine the hydraulic conductivity ; we have:

`K = (12*10^(-6)*0.1)/((\pi)/(4)0.05^2*0.3)`

`K = 0.002037\\\\K = 2.037*10^(-3) m/s`

Seepage velocity
`V_s = (velocity )/(porosity)`

where; velocity =
`K*i`

=
`(2.037*10^(-3)*)((0.3)/(0.1))`

=
`6.111*10^(-3) m/s`

`V_s = (6.111*10^(-3))/(0.5)`

`V_s = 0.0122 \ m/s`