How to Calculate Flow Rate of Water Tank

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Water Tank Flow Rate Calculator .wt-calculator-wrapper { max-width: 800px; margin: 0 auto; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif; color: #333; line-height: 1.6; } .wt-calc-box { background: #fdfdfd; border: 1px solid #e0e0e0; border-radius: 8px; padding: 30px; box-shadow: 0 4px 12px rgba(0,0,0,0.05); margin-bottom: 40px; } .wt-calc-title { text-align: center; color: #0056b3; margin-bottom: 25px; font-size: 24px; font-weight: 700; } .wt-form-group { margin-bottom: 20px; } .wt-label { display: block; font-weight: 600; margin-bottom: 8px; color: #444; } .wt-input { width: 100%; padding: 12px; border: 1px solid #ccc; border-radius: 4px; font-size: 16px; box-sizing: border-box; transition: border-color 0.3s; } .wt-input:focus { border-color: #0056b3; outline: none; } .wt-help-text { font-size: 12px; color: #666; margin-top: 4px; } .wt-btn { display: block; width: 100%; padding: 14px; background-color: #0056b3; color: white; border: none; border-radius: 4px; font-size: 18px; font-weight: bold; cursor: pointer; transition: background-color 0.3s; } .wt-btn:hover { background-color: #004494; } .wt-result-box { margin-top: 30px; padding: 20px; background-color: #f0f8ff; border-radius: 6px; border-left: 5px solid #0056b3; display: none; } .wt-result-item { margin-bottom: 10px; font-size: 16px; display: flex; justify-content: space-between; border-bottom: 1px solid #daeefc; padding-bottom: 5px; } .wt-result-item:last-child { border-bottom: none; } .wt-result-label { font-weight: 600; color: #333; } .wt-result-value { font-weight: 700; color: #0056b3; } .wt-article { margin-top: 50px; border-top: 1px solid #eee; padding-top: 30px; } .wt-article h2 { color: #2c3e50; margin-top: 30px; } .wt-article p { margin-bottom: 15px; text-align: justify; } .wt-article ul { margin-bottom: 20px; padding-left: 20px; } .wt-article li { margin-bottom: 8px; } @media (max-width: 600px) { .wt-calc-box { padding: 20px; } }
Water Tank Discharge Flow Calculator
Vertical distance from the water surface to the center of the outlet.
The internal diameter of the pipe or hole where water exits.
Typically 0.61 for sharp-edged orifices, 0.98 for smooth nozzles.
Exit Velocity: –
Flow Rate (Liters/minute): –
Flow Rate (Cubic m/hour): –
Time to Drain 100L (approx): –

How to Calculate the Flow Rate of a Water Tank

Calculating the flow rate of water draining from a tank is a critical task in fluid mechanics, civil engineering, and even home plumbing projects. Whether you are designing an irrigation system, managing industrial chemical tanks, or simply trying to empty a rain barrel, understanding the physics behind gravity-fed flow is essential.

The Physics: Torricelli's Law

The calculation relies primarily on Torricelli's Law. This theorem states that the speed (velocity) of a fluid flowing out of an orifice under the force of gravity is proportional to the square root of the vertical distance between the water surface and the center of the orifice.

The basic formula for velocity is:

v = √(2 · g · h)

  • v = Velocity of the fluid (m/s)
  • g = Acceleration due to gravity (9.81 m/s²)
  • h = Head of water (height in meters)

Calculating the Actual Flow Rate

While Torricelli's Law gives us the theoretical velocity, real-world scenarios involve friction and turbulence. To account for this, we use the Discharge Coefficient (Cd). We also need to account for the area of the outlet pipe.

The final formula for Flow Rate (Q) is:

Q = Cd · A · √(2 · g · h)

  • Q = Flow rate (m³/s)
  • Cd = Discharge Coefficient (0.60–0.62 for sharp edges, 0.98 for rounded)
  • A = Cross-sectional area of the orifice (m²)

Key Factors Affecting Flow Rate

  1. Water Height (Head): The higher the water level above the outlet, the greater the pressure, resulting in a faster flow rate. As the tank drains and the height decreases, the flow rate will slow down.
  2. Orifice Diameter: A larger opening allows more water to pass through. Doubling the diameter actually quadruples the area, significantly increasing flow.
  3. Orifice Shape: A smooth, rounded nozzle allows water to flow more freely (higher Cd) than a sharp-edged hole cut into a tank wall (lower Cd).

Example Calculation

Imagine you have a water tank with a water level 2 meters above the outlet. The outlet is a pipe with a 50mm diameter. Assuming a standard discharge coefficient of 0.61:

  • Velocity (v) = √(2 · 9.81 · 2) ≈ 6.26 m/s
  • Area (A) = π · (0.025)² ≈ 0.00196 m²
  • Flow Rate (Q) = 0.61 · 0.00196 · 6.26 ≈ 0.00748 m³/s

Converting this to common units, you get approximately 448 Liters per minute.

function calculateFlowRate() { // 1. Get input values var heightInput = document.getElementById("waterHead").value; var diameterInput = document.getElementById("orificeDiameter").value; var cdInput = document.getElementById("dischargeCoeff").value; // 2. Validate inputs if (heightInput === "" || diameterInput === "" || cdInput === "") { alert("Please fill in all fields (Height, Diameter, and Cd)."); return; } var h = parseFloat(heightInput); // Height in meters var d_mm = parseFloat(diameterInput); // Diameter in mm var Cd = parseFloat(cdInput); // Coefficient of Discharge var g = 9.81; // Gravity m/s^2 if (h < 0 || d_mm < 0 || Cd 0) { timeFor100L = 0.1 / flowRateM3s; } // 5. Display Results document.getElementById("resVelocity").innerText = velocity.toFixed(2) + " m/s"; document.getElementById("resLitersMin").innerText = flowRateLmin.toFixed(2) + " L/min"; document.getElementById("resCubicHour").innerText = flowRateM3h.toFixed(2) + " m³/h"; if(timeFor100L > 0 && timeFor100L = 60) { document.getElementById("resDrainTime").innerText = (timeFor100L/60).toFixed(1) + " minutes"; } else { document.getElementById("resDrainTime").innerText = "N/A"; } // Show result box document.getElementById("resultDisplay").style.display = "block"; }

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