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CivilSoil Mechanics

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For a flow net Nf = 5 and Nd = 20, the shape factor is

0.5

0.25

Correct Answer

⚙️ TE • Technical Direct FormulaCivilSoil Mechanics

Option D

0.25

Quick Summary:

Given: Number of flow channels $N_{f}$ = 5, Number of potential drops $N_{d}$ = 20

📐MAMath SolutionDirect Formula

📋 Given

Number of flow channels $N_{f}$ = 5, Number of potential drops $N_{d}$ = 20

🔢 Formula Used

S=NfNdS = \frac{N_f}{N_d}S=Nd​Nf​​

🔢 Step-by-Step Solution

Identify the given parameters

We are given the number of flow channels ( $N_f$ ) as 5 and the number of equipotential drops ( $N_d$ ) as 20.

Nf=5,Nd=20N_f = 5, N_d = 20Nf​=5,Nd​=20

Apply the shape factor formula

The shape factor ( $S$ ) of a flow net is defined as the ratio of the number of flow channels to the number of equipotential drops.

S=NfNdS = \frac{N_f}{N_d}S=Nd​Nf​​

Calculate the result

Substituting the given values into the formula: $S = \frac{5}{20} = 0.25$ .

S=0.25S = 0.25S=0.25

✅

D is correct because the shape factor is calculated as the ratio of flow channels to equipotential drops, yielding 0.25.

Core Concepts Used

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Flow Net Analysis Seepage Theory Hydraulic Conductivity

💡 EXAM TIP

The shape factor is directly used in Darcy's Law for seepage discharge calculation: $q = k H \frac{N_f}{N_d}$ , where $k$ is the coefficient of permeability and $H$ is the total hydraulic head.

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