Question

A soil sample 90 mm high and 6000 mm2 in cross section was subjected to a falling head permeability test. The head fell from 500 mm to 300 mm in 1500 s. The permeability of the soil was 2.4x10-3 mm/s.

Determine the diameter of the stand pipe. (in mm)

Answer 1

the diameter of the stand pipe is 24.456mm

Step-by-step explanation:

Given that:

Height of the soil sample = 90 mm

Cross section area of the soil sample = 6000 m²

The head fell from 500 mm to 300 mm

i,e

`H_1 = 500 \ mm`

`H_2 = 300 \ mm`

Time = 1500 s

The permeability of the soil (K) was 2.4x10⁻³ mm/s.

The objective is to determine the diameter of the stand pipe. (in mm)

Using the formula :

`K = ((2.303 )*a*L)/(A*t) log((H_1)/(H_2))`

`2.4*10^(-3)= ((2.303 )*a*(90))/((6000 )*(1500 )) log((500)/(300 ))`

`2.4*10^(-3)= ((207.27 *a))/(9000000) *0.22185`

`2.4*10^(-3)*9000000= (207.27 *a)}*0.22185`

21600 = 45.983 a

a = 21600/45.983

a = 469.74 mm

Recall thar:

a = π/4 (d²)

So;

469.74 = 0.7854 ((d²)

d² = 469.74/0.7854

d² = 598.09

d = √598.09

d = 24.456 mm

Hence ; the diameter of the stand pipe is 24.456mm