A dam has been constructed across a river over a permeable stratum of soil of limited thickness. The head of water on the upstream side is 18 m and on the downstream side is 8 m. The flow net constructed across the dam gives Nf as 6 and Nd as 12. If the equivalent coefficient of permeability is 1·28 × 10⁻³ cm/s, what is the quantity of seepage per unit length of the section per cm length of dam ?
- A0·64 × 10⁻³ cm³/s
- B0·64 cm³/sCorrect
- C2·56 × 10⁻³ cm³/s
- D2·56 cm³/s
Solution
Concept
Seepage discharge per unit length
Formula
q = k H Nf / Nd
Step-by-step solution
1. H = 18 − 8 = 10 m = 1000 cm. 2. q = 1.28 × 10⁻³ × 1000 × 6/12 = 0.64 cm³/s per cm length of the dam.
Explanation
The seepage per unit length equals the permeability times the head loss times the ratio of flow channels to potential drops.
Why the other options are wrong
The ×10⁻³ options forget to convert 10 m into 1000 cm, and 2.56 results from using Nf/Nd = 2.
Shortcut
q = k H (Nf/Nd) with H in cm.
Common mistake
Using H = 10 without converting to cm.
Correct answer: B) 0·64 cm³/s