.calculator-wrapper {
font-family: sans-serif;
max-width: 600px;
margin: 20px auto;
padding: 20px;
border: 1px solid #ccc;
border-radius: 8px;
box-shadow: 0 2px 4px rgba(0, 0, 0, 0.1);
}
.calculator-inputs {
display: grid;
grid-template-columns: repeat(2, 1fr);
gap: 15px;
margin-bottom: 20px;
}
.input-group {
display: flex;
flex-direction: column;
}
.input-group label {
margin-bottom: 5px;
font-weight: bold;
font-size: 0.9em;
}
.input-group input {
padding: 8px;
border: 1px solid #ccc;
border-radius: 4px;
font-size: 1em;
}
.calculator-inputs button {
grid-column: 1 / -1;
padding: 10px 15px;
background-color: #4CAF50;
color: white;
border: none;
border-radius: 4px;
font-size: 1.1em;
cursor: pointer;
transition: background-color 0.3s ease;
}
.calculator-inputs button:hover {
background-color: #45a049;
}
.calculator-result {
margin-top: 20px;
padding: 15px;
background-color: #e9e9e9;
border-radius: 4px;
font-size: 1.1em;
text-align: center;
min-height: 40px;
display: flex;
align-items: center;
justify-content: center;
}
function calculateFlowRate() {
var pressureDrop = parseFloat(document.getElementById("pressureDrop").value);
var pipeLength = parseFloat(document.getElementById("pipeLength").value);
var pipeDiameter = parseFloat(document.getElementById("pipeDiameter").value);
var fluidViscosity = parseFloat(document.getElementById("fluidViscosity").value);
var fluidDensity = parseFloat(document.getElementById("fluidDensity").value);
var pipeRoughness = parseFloat(document.getElementById("pipeRoughness").value);
var resultElement = document.getElementById("result");
resultElement.innerHTML = "";
if (isNaN(pressureDrop) || isNaN(pipeLength) || isNaN(pipeDiameter) || isNaN(fluidViscosity) || isNaN(fluidDensity) || isNaN(pipeRoughness)) {
resultElement.innerHTML = "Please enter valid numbers for all fields.";
return;
}
if (pressureDrop <= 0 || pipeLength <= 0 || pipeDiameter <= 0 || fluidViscosity <= 0 || fluidDensity <= 0 || pipeRoughness < 0) {
resultElement.innerHTML = "Input values must be positive, except for pipe roughness which can be zero.";
return;
}
// Constants
var psi_to_Pa = 6894.76; // psi to Pascal
var ft_to_m = 0.3048; // feet to meters
var in_to_m = 0.0254; // inches to meters
var cP_to_Pa_s = 0.001; // centipoise to Pascal-second
var lb_ft3_to_kg_m3 = 16.0185; // lb/ft³ to kg/m³
// Convert inputs to SI units
var pressureDropSI = pressureDrop * psi_to_Pa;
var pipeLengthSI = pipeLength * ft_to_m;
var pipeDiameterSI = pipeDiameter * in_to_m;
var fluidViscositySI = fluidViscosity * cP_to_Pa_s;
var fluidDensitySI = fluidDensity * lb_ft3_to_m3;
var pipeRoughnessSI = pipeRoughness * in_to_m;
var pipeAreaSI = Math.PI * Math.pow(pipeDiameterSI / 2, 2);
var Re = (fluidDensitySI * 1.0) * pipeDiameterSI / fluidViscositySI; // Placeholder velocity for initial guess (e.g., 1 m/s) – this is an iterative process. For simplicity, we'll use an explicit approximation of the Colebrook equation or assume fully turbulent flow.
// For simplicity, we'll use the Darcy-Weisbach equation, but acknowledge that friction factor 'f' requires iteration or approximation.
// We'll use an approximation for the friction factor. A common one is the Swamee-Jain equation for turbulent flow.
var f; // Darcy friction factor
if (Re 0.0001) { // If roughness is significant, use a more robust approximation
f = Math.pow(-2 * Math.log10((pipeRoughnessSI / pipeDiameterSI) / 3.7 + 1.774 / (Re * Math.sqrt(f))), -2); // Re-calculate f with more accuracy
var maxIterations = 100;
var tolerance = 1e-6;
for (var i = 0; i < maxIterations; i++) {
var f_new = Math.pow(-2 * Math.log10((pipeRoughnessSI / pipeDiameterSI) / 3.7 + 2.51 / (Re * Math.sqrt(f))), -2);
if (Math.abs(f_new – f) v = Q / A
// pressureDropSI = f * (pipeLengthSI / pipeDiameterSI) * ((Q / pipeAreaSI)² / (2 * 9.81))
// pressureDropSI = f * (pipeLengthSI / pipeDiameterSI) * (Q² / (pipeAreaSI² * 2 * 9.81))
// Q² = (pressureDropSI * pipeAreaSI² * 2 * 9.81) / (f * pipeLengthSI / pipeDiameterSI)
// Q² = (pressureDropSI * pipeAreaSI² * 2 * 9.81 * pipeDiameterSI) / (f * pipeLengthSI)
// Q = sqrt((pressureDropSI * pipeAreaSI² * 2 * 9.81 * pipeDiameterSI) / (f * pipeLengthSI))
var flowRateSI = Math.sqrt((pressureDropSI * Math.pow(pipeAreaSI, 2) * 2 * 9.81 * pipeDiameterSI) / (f * pipeLengthSI));
// Convert flow rate to GPM (gallons per minute)
var m3_per_s_to_gpm = 15850.3;
var flowRateGPM = flowRateSI * m3_per_s_to_gpm;
resultElement.innerHTML = "Calculated Flow Rate: " + flowRateGPM.toFixed(2) + " GPM";
}
Understanding Pipe Flow Rate and Pressure Drop
Calculating the flow rate of a fluid through a pipe is a fundamental aspect of fluid dynamics and is crucial in many engineering applications, from water supply systems to chemical processing. The flow rate is the volume of fluid that passes a point per unit of time. Several factors influence this flow rate, and one of the most significant is the pressure drop along the pipe.
What is Pressure Drop?
As a fluid flows through a pipe, it encounters resistance from friction with the pipe walls and internal friction within the fluid itself (viscosity). This resistance causes a loss of energy, which manifests as a decrease in pressure along the length of the pipe. This pressure decrease is known as pressure drop. The longer the pipe, the rougher the pipe surface, the higher the fluid's viscosity, and the higher the flow rate, the greater the pressure drop will be.
The Darcy-Weisbach Equation
The relationship between pressure drop and flow rate is often described by the Darcy-Weisbach equation. This equation is a cornerstone of fluid mechanics for calculating pressure loss due to friction in pipes. The equation is generally expressed as:
$h_f = f \times \frac{L}{D} \times \frac{v^2}{2g}$
Where:
- $h_f$ is the head loss due to friction (in meters of fluid).
- $f$ is the Darcy friction factor (dimensionless).
- $L$ is the length of the pipe (in meters).
- $D$ is the hydraulic diameter of the pipe (in meters).
- $v$ is the average velocity of the fluid (in meters per second).
- $g$ is the acceleration due to gravity (approximately 9.81 m/s²).
The pressure drop ($\Delta P$) can be related to head loss ($h_f$) by: $\Delta P = \rho \times g \times h_f$, where $\rho$ is the fluid density.
The challenge in using the Darcy-Weisbach equation directly to find flow rate from pressure drop is that the friction factor ($f$) itself depends on the flow velocity (through the Reynolds number, Re) and the relative roughness of the pipe. For turbulent flow, calculating $f$ often requires iterative methods or approximations like the Colebrook equation or its explicit approximations (such as the Swamee-Jain equation used in this calculator).
Factors Affecting Flow Rate
- Pressure Drop: A larger pressure difference across the pipe will drive more fluid through, resulting in a higher flow rate.
- Pipe Diameter: Larger diameter pipes offer less resistance, allowing for higher flow rates at the same pressure drop.
- Pipe Length: Longer pipes mean more surface area for friction, leading to a greater pressure drop and lower flow rate for a given driving pressure.
- Fluid Viscosity: More viscous fluids are "thicker" and flow less easily, resulting in lower flow rates.
- Fluid Density: Density plays a role in the Reynolds number, which influences the friction factor, especially in turbulent flow.
- Pipe Roughness: Rougher internal pipe surfaces create more friction, increasing pressure drop and reducing flow rate.
How the Calculator Works
This calculator takes your inputs for pressure drop, pipe dimensions, and fluid properties. It then uses the Darcy-Weisbach equation, combined with an appropriate approximation for the friction factor (like the Swamee-Jain equation for turbulent flow or the laminar flow formula), to iteratively or directly calculate the flow rate. The result is typically presented in gallons per minute (GPM), a common unit for fluid flow.
Example Calculation
Let's say we have:
- Pressure Drop: 50 psi
- Pipe Length: 100 feet
- Pipe Inner Diameter: 2 inches
- Fluid Viscosity: 1 cP (like water at room temperature)
- Fluid Density: 62.4 lb/ft³ (like water)
- Pipe Absolute Roughness: 0.0005 inches (for smooth pipes)
Inputting these values into the calculator will estimate the flow rate of the fluid through the pipe. For these specific values, the calculator would output an approximate flow rate, showing how these parameters interact to determine fluid movement.