Head difference between Headwater and Tail Water given Quantity of Seepage in Length of Dam Calculator

Head Difference Formula:

\[ H_L = \frac{Q \times N}{B \times k \times L} \]

Quantity of Seepage:

m³/s

Equipotential Lines:

Number of Beds:

Coefficient of Permeability:

m/s

Length of Dam:

Head Difference (m):

1. What is Head Difference Calculator?

Definition: This calculator estimates the head difference between headwater and tailwater based on seepage quantity, equipotential lines, number of beds, soil permeability, and dam length.

Purpose: It helps hydraulic engineers determine the pressure difference across a dam structure due to seepage.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ H_L = \frac{Q \times N}{B \times k \times L} \]

Where:

\( H_L \) — Head difference (meters)
\( Q \) — Quantity of seepage (m³/s)
\( N \) — Number of equipotential lines
\( B \) — Number of beds
\( k \) — Coefficient of permeability of soil (m/s)
\( L \) — Length of dam (m)

Explanation: The seepage quantity multiplied by equipotential lines is divided by the product of beds, permeability, and dam length.

3. Importance of Head Difference Calculation

Details: Proper head difference estimation ensures dam stability, seepage control, and structural integrity assessment.

4. Using the Calculator

Tips: Enter all required values with ±5% accuracy. Default permeability is 0.1 m/s (typical for sandy soil).

5. Frequently Asked Questions (FAQ)

Q1: What affects the coefficient of permeability?
A: Soil type, grain size, porosity, and degree of saturation significantly influence permeability.

Q2: How do I determine equipotential lines?
A: These are determined from flow net analysis of the dam cross-section.

Q3: Why is head difference important?
A: It helps evaluate uplift pressure and potential piping failure in dams.

Q4: What's a typical permeability value for clay?
A: Clay typically has permeability around 10⁻⁸ to 10⁻¹⁰ m/s.

Q5: Does this include safety factors?
A: No, engineers should apply appropriate safety factors to the calculated value.