Constant Depression Head Given Discharge And Time In Hours Calculator

Formula Used:

\[ H = \frac{Q}{\frac{2.303 \times A_{cs} \times \log\left(\frac{h_1}{h_2}\right)}{t}} \]

Discharge (Q):

m³/s

Cross-Sectional Area (A_cs):

m²

Depression Head 1 (h₁):

Depression Head 2 (h₂):

Time (t):

hours

Constant Depression Head (H):

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1. What is Constant Depression Head?

Constant Depression Head refers to the steady-state difference in water level between the water table and the water level in a well during pumping operations. It's a critical parameter in hydrogeology for determining aquifer properties and well performance.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ H = \frac{Q}{\frac{2.303 \times A_{cs} \times \log\left(\frac{h_1}{h_2}\right)}{t}} \]

Where:

\( H \) — Constant depression head (m)
\( Q \) — Discharge rate (m³/s)
\( A_{cs} \) — Cross-sectional area (m²)
\( h_1 \) — Initial depression head (m)
\( h_2 \) — Final depression head (m)
\( t \) — Time duration (hours)

Explanation: This formula calculates the constant depression head based on discharge rate, cross-sectional area, the ratio of depression heads, and time duration.

3. Importance of Constant Depression Head Calculation

Details: Calculating constant depression head is essential for well design, aquifer testing, groundwater resource management, and determining the efficiency of pumping systems in hydrogeological studies.

4. Using the Calculator

Tips: Enter discharge in m³/s, cross-sectional area in m², depression heads in meters, and time in hours. All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the logarithmic function in this formula?
A: The logarithmic function accounts for the non-linear relationship between depression head ratios and time in groundwater flow equations.

Q2: How does cross-sectional area affect constant depression head?
A: Larger cross-sectional areas typically result in smaller constant depression heads for the same discharge rate, as the flow is distributed over a larger area.

Q3: What are typical units for constant depression head?
A: Constant depression head is typically measured in meters (m), representing the height difference between water levels.

Q4: When is this calculation most commonly used?
A: This calculation is primarily used in pumping test analysis, well hydraulics, and aquifer characterization studies.

Q5: What factors can affect the accuracy of this calculation?
A: Factors include measurement precision, aquifer homogeneity, well construction details, and the assumption of constant pumping conditions.