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Flow net discharge, 200 cc/day

Short answer

Using q = kh(Nf/Nd), with q=200 cm³/day, Nf=5, Nd=10, h=250 cm, permeability k = (q/h)(Nd/Nf) = 1.6 cm/day ≈ 1.85×10⁻⁵ cm/s.

The discharge through the pervious soil is 200 cc/day. The flow net shows 5 flow channels and 10 equipotential drops. If the net head causing the flow is 2.5 m, calculate the permeability of the soil.

q=k h NfNdq = k\,h\,\frac{N_f}{N_d}

Given

q=200q = 200 cm³/day (per unit width, taken as 1 cm), Nf=5N_f = 5, Nd=10N_d = 10, h=2.5h = 2.5 m =250= 250 cm.

Calculation

k=qh⋅NdNf=200250×105=1.6 cm/dayk = \frac{q}{h}\cdot\frac{N_d}{N_f} = \frac{200}{250} \times \frac{10}{5} = 1.6\ \text{cm/day} k=1.686400=1.85×10−5 cm/sk = \frac{1.6}{86400} = 1.85\times10^{-5}\ \text{cm/s}

Answer: k=1.6k = 1.6 cm/day ≈1.85×10−5\approx 1.85\times10^{-5} cm/s.

✓ Answer checked by Claude Opus 5.5 (high effort)

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