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

Answer:

the diameter of the stand pipe is 24.456mm

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 :

$K = \dfrac{(2.303 )*a*L}{A*t} log(\dfrac{H_1}{H_2})$

$2.4*10^{-3}= \dfrac{(2.303 )*a*(90)}{(6000 )*(1500 )} log(\dfrac{500}{300 })$

$2.4*10^{-3}= \dfrac{(207.27 *a)}{9000000} *0.22185$

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

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