Water Tank Flow Rate Calculator

Use this calculator to determine the rate at which water flows out of a tank through an orifice or pipe at the bottom, based on Torricelli's Law.

Water Height above Outlet (meters): The depth of the water measured from the surface down to the center of the outlet hole.

Outlet/Orifice Diameter (millimeters): The internal diameter of the pipe or hole the water flows out of.

Coefficient of Discharge (Cd): Standard sharp-edged orifice is approx 0.62. A smooth rounded nozzle is approx 0.98.

function calculateWaterFlow() { var heightInput = document.getElementById('tankHeight'); var diameterInput = document.getElementById('orificeDiameter'); var cdInput = document.getElementById('dischargeCoefficient'); var resultDiv = document.getElementById('flowResult'); var h = parseFloat(heightInput.value); // Height in meters var d_mm = parseFloat(diameterInput.value); // Diameter in mm var Cd = parseFloat(cdInput.value); // Coefficient of Discharge // Validation if (isNaN(h) || h <= 0 || isNaN(d_mm) || d_mm <= 0 || isNaN(Cd) || Cd 1) { resultDiv.style.display = 'block'; resultDiv.innerHTML = 'Please enter valid positive numbers for height and diameter, and a Cd between 0 and 1.'; return; } // Constants and Unit Conversions var g = 9.81; // Acceleration due to gravity (m/s^2) var d_m = d_mm / 1000; // Convert diameter mm to meters var radius_m = d_m / 2; // Radius in meters var Area_m2 = Math.PI * radius_m * radius_m; // Area of orifice in m^2 // Calculations based on Torricelli's Law // Theoretical Velocity: v = sqrt(2gh) var theoreticalVelocity = Math.sqrt(2 * g * h); // Actual Velocity at Outlet: v_actual = Cv * sqrt(2gh) (assuming Cv roughly equals Cd for simplicity here, or just using Cd to adjust flow directly) // Actual Flow Rate (Q) = Area * Theoretical Velocity * Cd var flowRate_m3s = Area_m2 * theoreticalVelocity * Cd; // Result Unit Conversions var velocity_ms = theoreticalVelocity * Cd; // Approximation of actual velocity var flowRate_LPM = flowRate_m3s * 1000 * 60; // Convert m^3/s to Liters/minute var flowRate_m3h = flowRate_m3s * 3600; // Convert m^3/s to m^3/hour // Output Formatting resultDiv.style.display = 'block'; resultDiv.innerHTML = '

Calculation Results

' + 'Flow Rate (Liters/Minute): ' + flowRate_LPM.toFixed(2) + ' LPM' + 'Flow Rate (m³/Hour): ' + flowRate_m3h.toFixed(2) + ' m³/h' + 'Outlet Velocity: ' + velocity_ms.toFixed(2) + ' m/s' + 'Results are based on Torricelli\'s law adjusted by the discharge coefficient.'; } .calculator-container { border: 1px solid #ddd; padding: 20px; background-color: #f9f9f9; border-radius: 8px; max-width: 600px; margin: 20px auto; } .calculator-container h2 { text-align: center; color: #333; } .calc-form { margin-top: 20px; } .form-group { margin-bottom: 15px; } .form-group label { display: block; margin-bottom: 5px; font-weight: bold; } .form-group input { width: 100%; padding: 10px; border: 1px solid #ccc; border-radius: 4px; box-sizing: border-box; /* Fixes padding issues */ } .form-group small { display: block; margin-top: 5px; color: #666; font-size: 0.9em; } .calc-btn { width: 100%; padding: 12px; background-color: #0073aa; color: white; border: none; border-radius: 4px; cursor: pointer; font-size: 16px; } .calc-btn:hover { background-color: #005177; } .calc-result { margin-top: 20px; padding: 15px; background-color: #eef7fc; border-left: 5px solid #0073aa; } .calc-result h3 { margin-top: 0; color: #0073aa; } .calc-result p { font-size: 18px; margin: 10px 0; }

Understanding Water Tank Flow Rate Calculations

Knowing the rate at which water drains from a tank is crucial for various applications, ranging from agricultural irrigation systems and industrial process engineering to civil engineering tasks like designing stormwater detention tanks. The flow rate depends heavily on the gravity acting on the water and the size of the opening it flows through.

Torricelli's Law and the Physics of Draining

The fundamental principle governing free-draining tanks is **Torricelli's Law**. It states that the speed of a fluid flowing out of an orifice under the force of gravity is related to the height of the fluid above the opening. The basic formula for theoretical velocity is $v = \sqrt{2gh}$, where $g$ is the acceleration due to gravity and $h$ is the water "head" or height.

However, real-world applications must account for friction and turbulence, which reduce the actual flow. This is handled by the **Coefficient of Discharge ($C_d$)**. A standard sharp-edged hole usually has a $C_d$ around 0.60 to 0.62, meaning the actual flow is only about 60-62% of the theoretical maximum. A smooth, well-rounded nozzle will have a much higher coefficient, closer to 0.98.

Key Factors Affecting Flow Rate

Water Head (Height): This is the primary driving force. The deeper the water above the outlet, the higher the pressure at the bottom, resulting in a faster velocity and flow rate. As the tank drains and the height decreases, the flow rate will also decrease.
Orifice Diameter: The size of the opening directly dictates the cross-sectional area available for flow. Doubling the diameter quadruples the area, significantly increasing the flow rate.
Outlet Shape ($C_d$): The physical characteristics of the hole matter. Rough edges create turbulence that slows the water down, whereas smooth, tapered entries allow for more efficient flow.

Example Calculation

Let's imagine a scenario where you need to drain a large storage tank.

The water level is currently 3.0 meters above the center of the outlet valve.
The outlet pipe has an internal diameter of 75 millimeters.
It is a standard pipe connection, so we use a default discharge coefficient of 0.62.

By inputting these values into the calculator above:

Height: 3.0 m
Diameter: 75 mm
Cd: 0.62

The calculator determines that the initial flow rate will be approximately 1,257 Liters per Minute (LPM), with the water exiting at a velocity of roughly 4.75 meters per second.