Static & Dynamic Water Level Calculator

ANA›Life Services Authority›National Calculator Authority›Static & Dynamic Water Level Calculator

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Static & Dynamic Water Level Calculator

Calculate the static water level (SWL), dynamic water level (DWL), and drawdown in a pumping well using field measurements and the Theis or Cooper-Jacob method.

### Well & Aquifer Parameters

Static Water Level, SWL (m below ground)

Pumping Rate, Q (m³/day)

Transmissivity, T (m²/day)

Storativity, S (dimensionless)

Radial Distance from Pumping Well, r (m)

Pumping Time, t (days)

### Optional: Observed Field Data

Observed Water Level During Pumping (m below ground)

Aquifer Thickness, b (m) — for specific capacity

Calculate

Results will appear here.

function staWellFunction(u) { // Theis well function W(u) approximated by series expansion // W(u) = -0.5772 - ln(u) + u - u²/(2·2!) + u³/(3·3!) - ... // Valid for u 5) { // For large u, W(u) is negligibly small return 0.0; }

// Series: W(u) = -gamma - ln(u) + sum_{n=1}^{inf} (-1)^(n+1) * u^n / (n * n!) const gamma = 0.5772156649; let sum = 0; let term = 0; let uPow = u; let factorial = 1; for (let n = 1; n 0."); if (isNaN(T) || T 0."); if (isNaN(S) || S 1) errors.push("Storativity S must be between 0 and 1."); if (isNaN(r) || r 0."); if (isNaN(t) || t 0.");

if (errors.length > 0) { resultDiv.innerHTML = 'Input Errors:' + errors.map(e => '').join('') + ''; return; }

// ── Theis Method ────────────────────────────────────────────── // u = r² S / (4 T t) const u = (r * r * S) / (4 * T * t);

// W(u) = Theis well function const Wu = staWellFunction(u);

// Drawdown: s = Q / (4πT) × W(u) const drawdown_theis = (Q / (4 * Math.PI * T)) * Wu;

// Dynamic Water Level (depth below ground) const dwl_theis = swl + drawdown_theis;

// ── Cooper-Jacob Approximation (valid when u 0) ? Q / drawdown_theis : null;

// ── Hydraulic Conductivity ──────────────────────────────────── // K = T / b let K = null; if (!isNaN(b) && b > 0) { K = T / b; }

// ── Observed Drawdown (if provided) ────────────────────────── let obsDrawdown = null; let residual = null; if (!isNaN(obsWL) && obsWL > 0) { obsDrawdown = obsWL - swl; residual = obsDrawdown - drawdown_theis; }

// ── Format output ───────────────────────────────────────────── const fmt = (v, d=3) => isNaN(v) || v === null ? "N/A" : v.toFixed(d); const fmtSci = (v) => (v !== null && !isNaN(v)) ? v.toExponential(4) : "N/A";

let html = '### Results '; html += 'ParameterValueUnit'; html += 'Static Water Level (SWL)' + fmt(swl,2) + 'm below ground'; html += 'Theis Parameter u' + fmtSci(u) + 'dimensionless'; html += 'Well Function W(u)' + fmt(Wu,5) + 'dimensionless'; html += 'Drawdown s (Theis)' + fmt(drawdown_theis,3) + 'm'; html += 'Dynamic Water Level (Theis)' + fmt(dwl_theis,3) + 'm below ground';

if (cj_valid) { html += 'Drawdown s (Cooper-Jacob)' + fmt(drawdown_cj,3) + 'm'; html += 'Dynamic Water Level (Cooper-Jacob)' + fmt(dwl_cj,3) + 'm below ground'; } else { html += 'Cooper-Jacob approximation not valid (u = ' + fmtSci(u) + ' ≥ 0.05). Use Theis result.'; }

if (specificCapacity !== null) { html += 'Specific Capacity (Q/s)' + fmt(specificCapacity,2) + 'm³/day/m'; } if (K !== null) { html += 'Hydraulic Conductivity K' + fmt(K,4) + 'm/day'; } if (obsDrawdown !== null) { html += 'Observed Drawdown' + fmt(obsDrawdown,3) + 'm'; html += 'Residual (Observed − Theis)' + fmt(residual,3) + 'm'; }

html += '';

// Interpretation html += 'Interpretation:'; if (drawdown_theis 20) html += ''; if (u = 0.05) html += ''; if (specificCapacity && specificCapacity ';

resultDiv.innerHTML = html; }

#### Formulas Used

Theis (1935) — Transient Radial Flow:

s = Q / (4πT) × W(u)

where u = r²S / (4Tt)

W(u) = −γ − ln(u) + u − u²/(2·2!) + u³/(3·3!) − ⋯    (Euler–Mascheroni γ = 0.5772)

Cooper-Jacob (1946) — valid when u < 0.05:

s = (2.303Q / 4πT) × log₁₀(2.25Tt / r²S)

Dynamic Water Level: DWL = SWL + s  (depth below ground surface)

Specific Capacity: Sc = Q / s  (m³/day per m of drawdown)

Hydraulic Conductivity: K = T / b

#### Assumptions & References

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