.reynolds-calculator {
font-family: sans-serif;
border: 1px solid #ddd;
padding: 20px;
border-radius: 8px;
max-width: 500px;
margin: 20px auto;
background-color: #f9f9f9;
}
.reynolds-calculator h2, .reynolds-calculator h3 {
text-align: center;
color: #333;
}
.calculator-inputs {
display: grid;
grid-template-columns: 1fr;
gap: 15px;
}
.form-group {
display: flex;
flex-direction: column;
}
.form-group label {
margin-bottom: 5px;
font-weight: bold;
color: #555;
}
.form-group input[type="number"] {
padding: 10px;
border: 1px solid #ccc;
border-radius: 4px;
font-size: 1rem;
}
.form-group input[type="number"]:focus {
outline: none;
border-color: #007bff;
box-shadow: 0 0 0 0.2rem rgba(0,123,255,.25);
}
.reynolds-calculator button {
padding: 12px 20px;
background-color: #007bff;
color: white;
border: none;
border-radius: 4px;
font-size: 1.1rem;
cursor: pointer;
transition: background-color 0.2s ease;
}
.reynolds-calculator button:hover {
background-color: #0056b3;
}
.calculator-results {
margin-top: 25px;
padding-top: 20px;
border-top: 1px solid #eee;
text-align: center;
}
#reynoldsResult {
font-size: 1.8rem;
font-weight: bold;
color: #28a745;
margin-bottom: 10px;
}
#flowRegime {
font-size: 1.1rem;
color: #6c757d;
}
function calculateReynoldsNumber() {
var flowRate = parseFloat(document.getElementById("flowRate").value);
var density = parseFloat(document.getElementById("density").value);
var viscosity = parseFloat(document.getElementById("viscosity").value);
var characteristicLength = parseFloat(document.getElementById("characteristicLength").value);
var reynoldsResultDiv = document.getElementById("reynoldsResult");
var flowRegimeDiv = document.getElementById("flowRegime");
reynoldsResultDiv.innerHTML = "";
flowRegimeDiv.innerHTML = "";
if (isNaN(flowRate) || isNaN(density) || isNaN(viscosity) || isNaN(characteristicLength)) {
reynoldsResultDiv.innerHTML = "Please enter valid numbers for all fields.";
return;
}
if (viscosity <= 0 || characteristicLength <= 0 || density <= 0 || flowRate < 0) {
reynoldsResultDiv.innerHTML = "Please enter positive values for density, viscosity, and characteristic length, and a non-negative flow rate.";
return;
}
// Calculate Velocity from Flow Rate (V = Q / A, assuming A is characteristicLength^2 for simplicity in some contexts, but better to derive from specific geometry if possible. For a pipe, Area = pi*(D/2)^2. Here we'll assume characteristicLength IS the diameter and calculate area).
var area;
// Assuming characteristicLength is the diameter of a pipe for typical fluid flow calculations.
// If characteristicLength represents something else (e.g., width of a channel), this area calculation would change.
var radius = characteristicLength / 2;
area = Math.PI * radius * radius;
if (area <= 0) {
reynoldsResultDiv.innerHTML = "Characteristic Length is too small to calculate a valid area.";
return;
}
var velocity = flowRate / area;
// Calculate Reynolds Number: Re = (density * velocity * characteristicLength) / viscosity
var reynoldsNumber = (density * velocity * characteristicLength) / viscosity;
reynoldsResultDiv.innerHTML = reynoldsNumber.toFixed(2);
var flowRegimeText = "";
if (reynoldsNumber = 2300 && reynoldsNumber <= 4000) {
flowRegimeText = "Flow Regime: Transitional";
} else {
flowRegimeText = "Flow Regime: Turbulent";
}
flowRegimeDiv.innerHTML = flowRegimeText;
}
Understanding the Reynolds Number
The Reynolds number (Re) is a dimensionless quantity in fluid mechanics used to help predict flow patterns in different fluid flow situations. It is the ratio of inertial forces to viscous forces within a fluid that is subjected to relative internal movement due to different fluid velocities.
What it Means:
- Low Reynolds Number (Re < 2300): Indicates laminar flow. This is a smooth, orderly flow where fluid particles move in parallel layers without significant mixing. Think of honey slowly pouring.
- Transitional Reynolds Number (2300 <= Re <= 4000): This is an intermediate range where the flow can be unstable, exhibiting characteristics of both laminar and turbulent flow.
- High Reynolds Number (Re > 4000): Indicates turbulent flow. This is a chaotic, disordered flow with significant mixing and eddies. Think of a fast-flowing river or water gushing from a faucet.
The Formula and Its Components:
The Reynolds number is calculated using the following formula:
Re = (ρ * v * L) / μ
Where:
- Re is the Reynolds number (dimensionless).
- ρ (rho) is the density of the fluid (e.g., kg/m³). Density is a measure of mass per unit volume.
- v is the flow velocity of the fluid (e.g., m/s). This is the speed at which the fluid is moving.
- L is a characteristic linear dimension (e.g., m). For flow in a pipe, this is typically the internal diameter of the pipe. For flow over a flat plate, it might be the length of the plate in the direction of flow.
- μ (mu) is the dynamic viscosity of the fluid (e.g., Pa·s or kg/(m·s)). Dynamic viscosity measures a fluid's internal resistance to flow.
How This Calculator Works:
This calculator takes your input for volumetric flow rate, fluid density, dynamic viscosity, and a characteristic length (like pipe diameter). It first calculates the average flow velocity from the volumetric flow rate and the cross-sectional area (assuming the characteristic length is the diameter of a circular pipe). Then, it plugs these values into the Reynolds number formula to determine the numerical value of Re and categorizes the flow as laminar, transitional, or turbulent.
Example Calculation:
Let's calculate the Reynolds number for water flowing through a pipe.
- Volumetric Flow Rate (Q): 0.01 m³/s
- Fluid Density (ρ): 1000 kg/m³ (for water)
- Dynamic Viscosity (μ): 0.001 Pa·s (for water at room temperature)
- Characteristic Length (Diameter, L): 0.05 m (a 5 cm diameter pipe)
First, we find the cross-sectional area of the pipe: A = π * (D/2)² = π * (0.05/2)² ≈ 0.00196 m².
Next, we find the velocity: v = Q / A = 0.01 m³/s / 0.00196 m² ≈ 5.1 m/s.
Now, we calculate the Reynolds number: Re = (1000 kg/m³ * 5.1 m/s * 0.05 m) / 0.001 Pa·s ≈ 255,000.
With a Reynolds number of approximately 255,000, the flow is clearly in the turbulent regime.