Question

A cylindrical soil sample, 7.3 cm in diameter and 16.8 cm in height, is tested in a constant-head permeability apparatus. A constant head of 75 cm is maintained during the test. After 1 minute of testing, a total of 945.7 gm of water was collected. The temperature was 20 oC. The void ratio of the soil was 0.43. Calculate the following:

1. The hydraulic gradient

2. The flow rate

3. The discharge velocity

4. The seepage force per unit volume

5. The coefficient of permeability

Answer 1

GIVEN;

Diameter of sample, D=7.3 cm

Height/Length of sample, L=16.8 cm =0.168 m

Weight of water collected in 1 minute, W= 945.7gm =0.9457 kg

Constant head, H= 75 cm 0.75 m

Time, t= 1 Minute = 60 sec

Void ratio, e=0.43

Solution:

Cross sectional area of sample, A= (D²)/4

A=( x7.3x7.3)/4

A= 41.85 cm²

A= 0.004185 m²

Volume of water collected in time t, Q= (Weight of water)/(Density of water)

Q= 0.9457/1000 m³

Q=0.0009457 m³

(i) Hydraulic gradient, i=H/L

i= 75/16.8

i=4.464

(ii) The flow rate , q= kiA

k= (QL)/(tHA)

i=H/L

q=(QL/tHA)x(H/L)xA

q=Q/t

q=0.0009457/60

q= 1.58x10^-5 m³/s

(iii) Discharge velocity, V= ki = q/A

V= (1.58x10^-5)/ (0.004185)

V= 3.78x10^-3 m/s

(iv) Seepage force per unit volume F_s= i_w

F_s= (H_w)/L

F_s= (0.75x9.81)/0.168

Fs= 43.79 KN

(v) The coefficient of permeability , k= (QL)/(tHA)

k= V/i

k= (3.78x10^-3)/4.464

k=8.14x10^-4 m/s