Question

Three soil specimens (Soil 1, Soil 2 and Soil 3), each 150 mm long and 100mm diameter are placed in series in a constant head flow set-up as shown in the figure. Suitable screens are provided at the boundaries of the specimens to keep them intact. The values of coeffcient of permeability of Soil 1, Soil 2 and Soil 3 are 0.01, 0.003 and 0.03 cm/s,

The value of h in the set-up is

• A. 0 mm
• B. 40 mm
• C. 255 mm
• D. 560 mm

Answer 1

The correct option is B 40 mm

$K_1=0.01cm/sec,K_2=0.003cm/sec,$

$K_3=0.03cm/sec$

Total head loss, h = 560 mm

Since soil specimen are connected in series, hence discharge through each soil specimen will be same.

$Q_1=Q_2=Q_3$

$K_1{A}_1{i}_1=K_2{A}_2{i}_2=K_3{A}_3{i}_3$

$K_1{A}_1\frac{h_1}{L_1}=K_2{A}_2\frac{h_2}{L_2}=K_3{A}_3\frac{h_3}{L_3}$

$K_1{h}_1=K_2{h}_2=K_3{h}_3=x$

$(\because L_1=L_2=L_3=150mm{A}_1=A_2=A_3)$

$\therefore h_1=\frac{x}{0.01},h_2=\frac{x}{0.003},h_3=\frac{x}{0.03}$

$Thus;\frac{x}{0.01}+\frac{x}{0.003}+\frac{x}{0.03}=560$

$\therefore x=1.2$

$\therefore h_1=\frac{1.2}{0.01}=120mm,$

$h_2=\frac{1.2}{0.003}=400mm,$

$h_3=\frac{1.2}{0.03}=40mm,$

Now h = 560 mm - (head loss between soil 1 & soil 2)

= 560 - $(h_1+h_2)$

= 560 - (120 + 400)

= 40 mm