How to Calculate Gravity Flow Rate

Gravity Flow Rate Calculator

Vertical distance from water surface to exit.

Inside diameter of the outlet pipe.

Default 0.62 for sharp-edged orifices.

Calculation Results:

Theoretical Velocity: 0 m/s

Flow Rate (Liters/Sec): 0 L/s

Flow Rate (m³/Hour): 0 m³/h

Flow Rate (GPM): 0 GPM

function calculateGravityFlow() { var h = parseFloat(document.getElementById('headHeight').value); var d_mm = parseFloat(document.getElementById('pipeDiameter').value); var cd = parseFloat(document.getElementById('coeffDischarge').value); var g = 9.81; if (isNaN(h) || isNaN(d_mm) || isNaN(cd) || h <= 0 || d_mm <= 0) { alert("Please enter valid positive numbers for all fields."); return; } // Convert diameter mm to meters var d_m = d_mm / 1000; var radius = d_m / 2; var area = Math.PI * Math.pow(radius, 2); // Torricelli's Law: v = sqrt(2gh) var velocity = Math.sqrt(2 * g * h); // Flow Rate Q = Cd * A * v var flowRateM3S = cd * area * velocity; var flowRateLPS = flowRateM3S * 1000; var flowRateM3H = flowRateM3S * 3600; var flowRateGPM = flowRateLPS * 15.8503; // conversion to US Gallons per Minute document.getElementById('resVelocity').innerText = velocity.toFixed(2); document.getElementById('resLps').innerText = flowRateLPS.toFixed(3); document.getElementById('resM3h').innerText = flowRateM3H.toFixed(2); document.getElementById('resGpm').innerText = flowRateGPM.toFixed(2); document.getElementById('gravityResult').style.display = 'block'; }

Calculating the flow rate of water or other fluids under the influence of gravity is a fundamental task in civil engineering, plumbing, and irrigation. Unlike pumped systems where pressure is mechanically generated, gravity flow systems rely on "Head" — the potential energy derived from the height of the fluid source relative to its exit point.

The Core Physics: Torricelli's Law

The calculation of gravity flow typically begins with Torricelli's Law. This principle states that the speed ($v$) of efflux of a fluid through a sharp-edged hole at the bottom of a tank filled to a depth ($h$) is the same as the speed that a body would acquire in falling freely from a height ($h$).

v = √(2 * g * h)

• v = Theoretical velocity (m/s)
• g = Acceleration due to gravity (9.81 m/s²)
• h = Head height (m)

From Velocity to Flow Rate

To find the actual volume of water moving per second, we must consider the cross-sectional area of the pipe or orifice. However, in the real world, friction and turbulence reduce the efficiency of the flow. This is where the Discharge Coefficient ($C_d$) comes in.

The final formula for flow rate ($Q$) is:

Q = C_d * A * √(2 * g * h)

Where A is the cross-sectional area ($\pi * r^2$).

Step-by-Step Calculation Example

Suppose you have a rainwater harvesting tank with a 50mm (0.05m) outlet pipe located 5 meters below the water surface level. Let's calculate the flow rate using a standard coefficient of 0.62.

1. Calculate Velocity: √(2 * 9.81 * 5) = √98.1 ≈ 9.9 m/s.
2. Calculate Area: $\pi$ * (0.025)² ≈ 0.001963 m².
3. Calculate Theoretical Flow: 9.9 * 0.001963 ≈ 0.0194 m³/s.
4. Apply Discharge Coefficient: 0.0194 * 0.62 ≈ 0.012 m³/s.
5. Convert to Liters: 0.012 * 1000 = 12 Liters per second.

Factors Affecting Gravity Flow

While the calculator above provides a high-accuracy estimate for tank outlets, other factors can influence flow in longer pipe runs:

• Pipe Friction: Long horizontal pipe runs create friction loss, reducing the effective head. For long pipes, engineers use the Hazen-Williams or Manning formulas.
• Viscosity: Thick fluids (like oil) will flow significantly slower than water under the same gravitational force.
• Pipe Material: Smooth PVC pipes offer less resistance than rough, rusted iron pipes.
• Air Entrapment: Air bubbles trapped in a gravity line can create "air locks" that drastically reduce or even stop the flow.

Common Discharge Coefficients (Cd)

Opening Type	Typical Cd Value
Sharp-edged Orifice	0.61 – 0.65
Short Flush Pipe	0.80 – 0.85
Well-rounded Outlet	0.95 – 0.98