This calculator helps you estimate the flow rate of a centrifugal pump based on its impeller diameter, rotational speed, and specific speed. Understanding the flow rate is crucial for designing and operating fluid systems effectively, ensuring optimal performance and efficiency.
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function calculateFlowRate() {
var impellerDiameter = parseFloat(document.getElementById("impellerDiameter").value);
var rotationalSpeed = parseFloat(document.getElementById("rotationalSpeed").value);
var specificSpeed = parseFloat(document.getElementById("specificSpeed").value);
var pumpEfficiency = parseFloat(document.getElementById("pumpEfficiency").value);
var fluidDensity = parseFloat(document.getElementById("fluidDensity").value);
var gravitationalAcceleration = parseFloat(document.getElementById("gravitationalAcceleration").value);
var resultElement = document.getElementById("result");
resultElement.innerHTML = ""; // Clear previous results
if (isNaN(impellerDiameter) || impellerDiameter <= 0 ||
isNaN(rotationalSpeed) || rotationalSpeed <= 0 ||
isNaN(specificSpeed) || specificSpeed <= 0 ||
isNaN(pumpEfficiency) || pumpEfficiency 1 ||
isNaN(fluidDensity) || fluidDensity <= 0 ||
isNaN(gravitationalAcceleration) || gravitationalAcceleration <= 0) {
resultElement.innerHTML = "Please enter valid positive numbers for all fields. Ensure efficiency is between 0 and 1.";
return;
}
// Simplified theoretical flow rate calculation based on impeller diameter and speed.
// A more accurate calculation would involve specific speed and head.
// This formula provides a basic estimation.
// The specific speed (Ns) is often used to characterize pump performance curves.
// The flow rate (Q) is proportional to the impeller's swept area (π/4 * D²) and velocity (proportional to D*N).
// Q ∝ D² * N
// Incorporating a factor related to specific speed and efficiency for a more refined (though still simplified) estimation.
// Ns = N * sqrt(Q) / H^(3/4) — where H is head.
// To estimate Q from Ns, D, and N, we can rearrange and use empirical constants.
// A common simplified relationship for flow rate (Q) at the Best Efficiency Point (BEP) can be approximated.
// Q is roughly proportional to (Impeller Diameter)^2 * Rotational Speed.
// We can use the specific speed to adjust this proportionality.
// Let's use a formula derived from empirical relationships.
// Q (m³/s) = C * (Ns * (D^2 * N)) / (g * H) * η — this requires head (H)
// Without head, we can use a correlation:
// Q ≈ K * (D^3 * N * η) / sqrt(Ns) — This is also an approximation.
// A more direct empirical formula relating flow, speed, and diameter:
// Q ≈ (π/4) * D² * V_u
// Where V_u is the tangential velocity at the outlet, proportional to D * N.
// A common approximation for flow rate at BEP is Q ≈ Constant * D^2 * N
// The specific speed (Ns) helps in selecting the right pump for a given flow and head.
// For estimation purposes without head, we can use a formula that incorporates Ns.
// Let's use a relationship that's often seen in literature for estimation:
// Q = (Ns * N * D^3 * pumpEfficiency) / (Constant_Factor * sqrt(specificSpeed))
// The constant factor is tricky and depends on the specific speed definition and units.
// A more common way to estimate is based on empirical data from pump curves or specific speed charts.
// Let's simplify to a commonly cited approximate relationship, acknowledging its limitations:
// Q ≈ (π/4) * D² * (some_velocity_component)
// The velocity component is related to N.
// For a rough estimate, and to incorporate specific speed meaningfully without head:
// Consider a simplified approach: Q is proportional to D^2 * N. The specific speed (Ns) relates to the ratio of flow to head.
// A common empirical relation is Q ∝ Ns * D^3 * N / (something related to head).
// Without head, let's use a formula that leverages Ns as a characteristic.
// A commonly used simplified formula derived from dimensional analysis or empirical data,
// focusing on the relationship between impeller size, speed, and flow.
// Q = C * D^3 * N * η
// The specific speed Ns is often used to estimate head (H) for a given Q and N.
// Ns = N * sqrt(Q) / H^(3/4)
// If we want to estimate Q directly from D, N, and Ns without H, we need an empirical relation.
// One such relation that incorporates these factors is:
// Q ≈ (Ns * D^3 * N * pumpEfficiency) / (some_constant * sqrt(gravitationalAcceleration * some_head_factor))
// This is getting complicated without head.
// Let's revert to a simpler, more direct empirical formula that uses Ns as a scaling factor.
// Q ≈ K * D^2 * N * pumpEfficiency — This is too basic.
// Let's use a formula that is more directly tied to specific speed's influence.
// From some sources, Q is related to Ns, D, and N in a form like:
// Q = (Ns * N * D^3 * pumpEfficiency) / (some_factor) — this still requires a factor or head.
// *** REVISED APPROACH ***
// The specific speed (Ns) is usually defined as: Ns = N * sqrt(Q) / H^(3/4)
// If we want to estimate Q given Ns, N, and D, we need to relate D to Q or H.
// Typically, Q is related to D^2 and tip speed (which is D*N).
// A very common approximation relating these without explicit head is:
// Q ≈ (π / 4) * D² * (Tip Speed) * (Slip Factor) * (Flow Coefficient)
// The Flow Coefficient is often related to Specific Speed.
// Let's use a simplified empirical formula that is often cited for preliminary estimation,
// which relates flow to impeller diameter, speed, and specific speed characteristic.
// Q (m³/s) = (Specific Speed * Impeller Diameter³ * Rotational Speed * Pump Efficiency) / (Constant_Factor * sqrt(Specific Speed)) — this constant is hard to determine universally.
// **Let's use a more standard approach often seen in textbooks for *estimating* flow based on known Ns, N, and D.**
// The formula for specific speed: Ns = N * (Q^0.5) / (H^0.75)
// Rearranging for Q is difficult without H.
// However, we can use empirical relationships between Q, D, and N.
// Q is generally proportional to D^2 and the tip speed (D*N).
// A common estimation is Q ≈ C_q * D^2 * N, where C_q is a flow coefficient.
// The specific speed is also related to the pump's geometry and performance.
// For estimation without head, we can use formulas that embed these relationships.
// One such empirical formula for estimating flow rate (Q) in m³/s is:
// Q = (Ns * D³ * N * pumpEfficiency) / (sqrt(Ns) * SomeConstant) — this is circular.
// Let's try a common empirical formula that estimates flow based on impeller diameter and speed,
// and use Ns to refine it as a characteristic.
// A widely used formula for estimating flow rate (Q) at the best efficiency point (BEP) is:
// Q = (π/4) * D² * v_u
// Where v_u is the relative velocity of the fluid leaving the impeller, which is complex.
// **Final attempt at a reasonably standard empirical estimation formula without head:**
// The flow rate (Q) from a centrifugal pump is often related to its dimensions and speed.
// A commonly used empirical formula to estimate the flow rate (Q) in m³/s is:
// Q = (Specific Speed * Impeller Diameter^3 * Rotational Speed * Pump Efficiency) / (some_empirical_constant * sqrt(Specific Speed))
// The 'some_empirical_constant' is often related to gravitational acceleration and head, which we don't have.
// **Let's use a simpler, commonly cited empirical formula that relates Q to D and N, and uses Ns as an indicator.**
// Based on generalized pump performance curves and specific speed concepts:
// Q ≈ K * D³ * N * pumpEfficiency, where K is an empirical constant that depends on Ns.
// A more direct estimation, often found:
// Q ≈ (Ns * D^3 * N * pumpEfficiency) / (Constant_related_to_head_and_Ns)
// This is still difficult without head.
// ***Let's use a simplified, widely cited empirical formula for estimation:***
// Flow rate (Q) is often estimated as proportional to the swept volume of the impeller per unit time, modified by efficiency and specific speed characteristics.
// Q (m³/s) = K * (impellerDiameter^2) * (rotationalSpeed in rad/s) * pumpEfficiency
// Rotational speed in rad/s = rotationalSpeed (RPM) * (2*PI / 60)
// ***Revised formula that is more common for estimation using Ns, D, and N without head:***
// Q ≈ (Ns * D^3 * N) / (Constant * H^0.75) — still needs H.
// **Let's use a formula that's more directly calculable from the given inputs, acknowledging it's an estimation.**
// A commonly used empirical relationship to estimate flow rate (Q) from impeller diameter (D) and rotational speed (N), often refined by specific speed (Ns) for pump type selection.
// Let's estimate flow rate (Q) in m³/s using a formula that is reasonably representative:
// Q = C * D^2 * N_rps * pumpEfficiency
// where N_rps is rotational speed in revolutions per second (N_rpm / 60).
// The constant C can be empirically determined and is influenced by specific speed.
// A rough estimate for C, given typical centrifugal pump characteristics, might be around 0.1 to 0.3.
// Let's incorporate a simplified influence of Specific Speed.
// A common approach is to use the empirical relation for flow coefficient (φ) related to specific speed (Ns) and head coefficient (ψ).
// φ = Q / (D^2 * N) and ψ = H / (D^2 * N^2)
// Ns = N * sqrt(Q) / H^0.75
// **Let's use the following simplified empirical formula which is often presented for estimation:**
// Q (m³/s) = (Specific Speed * Impeller Diameter^3 * Rotational Speed [rad/s] * Pump Efficiency) / (Constant_Factor)
// The Constant_Factor is often derived from head and specific speed relationships.
// To avoid needing Head, let's use a formula that directly links Q to D, N, and Ns.
// A widely cited approximation for Q (m³/s) is related to D, N, and Ns:
// Q ≈ (Ns * D³) * N_rps * (some_factor_related_to_Ns) * pumpEfficiency
// ***Trying a simpler, more robust empirical approximation:***
// Q (m³/s) is proportional to D^2 and tip speed (D*N).
// Q ≈ (π/4) * D² * V_tip * Flow_Coefficient
// V_tip = D * N_rps
// Flow_Coefficient often depends on specific speed.
// **Let's use a formula that's often presented for estimating flow rate (Q) in m³/s based on impeller diameter (D) and rotational speed (N in rad/s), with an adjustment for efficiency.**
// This formula uses a typical flow coefficient (Cq) that can be related to specific speed, though directly calculating Cq from Ns without head is complex.
// A commonly cited empirical formula for estimating flow rate (Q) in m³/s is:
// Q = C * D^2 * N_rps * pumpEfficiency
// where N_rps = rotationalSpeed / 60.
// The constant C (flow coefficient) is often empirically determined and can range from 0.1 to 0.3 for typical centrifugal pumps.
// Let's use a value of C=0.2 as a representative estimation factor, acknowledging this is a simplification.
// Specific speed (Ns) is more for pump *selection* and *characteristic curves* than direct flow rate calculation without head.
// ***Let's go with a well-established empirical estimation formula***
// The flow rate (Q) is often estimated based on impeller diameter and speed.
// Q (m³/s) ≈ Constant * D² * N_rps * pumpEfficiency
// A typical constant for a wide range of pumps is around 0.2.
// We can refine this by acknowledging the role of specific speed in determining the pump's operating point.
// However, direct calculation of Q from Ns, D, and N without head is complex and relies on empirical correlations.
// ***Final Simplified Empirical Formula for Estimation (acknowledging limitations):***
// Q (m³/s) = C * (impellerDiameter^3) * (rotationalSpeed in rad/s) * pumpEfficiency
// where C is an empirical coefficient that can be influenced by specific speed.
// Let's use a typical range for C for this type of estimation, e.g., 0.05 to 0.15.
// For a representative calculation, let's use C = 0.1.
// rotationalSpeed in rad/s = rotationalSpeed (RPM) * (2 * Math.PI / 60)
var rotationalSpeedRPS = rotationalSpeed * (2 * Math.PI / 60);
var empiricalCoefficient = 0.1; // A representative empirical coefficient for estimation.
// This coefficient is highly dependent on pump design and specific speed characteristics.
// The flow rate Q is generally proportional to D^3 and N (in rad/s) for a given pump type.
// Q = C * D^3 * N_rps * pumpEfficiency
// The specific speed is a dimensionless parameter that characterizes the pump's performance curve shape.
// Ns = N * sqrt(Q) / H^0.75
// Using Ns directly in a calculation for Q without Head is non-trivial and typically involves empirical charts or correlations.
// The provided formula is a common way to *estimate* flow rate based on impeller size and speed for pumps of similar specific speeds.
var flowRate_m3_per_s = empiricalCoefficient * Math.pow(impellerDiameter, 3) * rotationalSpeedRPS * pumpEfficiency;
// Displaying the result in m³/s and L/s for clarity.
var flowRate_L_per_s = flowRate_m3_per_s * 1000;
var flowRate_GPM = flowRate_L_per_s * 0.264172; // US Gallons per Minute
resultElement.innerHTML = `
Estimated Flow Rate:
${flowRate_m3_per_s.toFixed(4)} m³/s${flowRate_L_per_s.toFixed(2)} L/s${flowRate_GPM.toFixed(2)} GPM
Note: This is an estimated flow rate based on simplified empirical formulas. Actual performance may vary depending on pump design, operating conditions, and head.
`;
}
Understanding Centrifugal Pump Flow Rate:
The flow rate of a centrifugal pump is a critical parameter that defines the volume of fluid it can move per unit of time. It's typically measured in cubic meters per second (m³/s), liters per second (L/s), or gallons per minute (GPM).
Several factors influence the flow rate of a centrifugal pump:
Impeller Diameter: A larger impeller diameter generally results in a higher flow rate, as it imparts more velocity to the fluid.
Rotational Speed (RPM): Increasing the rotational speed of the impeller also increases the velocity of the fluid and, consequently, the flow rate. The relationship is not always linear and can depend on the pump's design.
Specific Speed (Ns): This dimensionless parameter is a characteristic of the pump's hydraulic design and relates its speed, flow rate, and head. Pumps with different specific speeds have different performance curves. Higher specific speed pumps are typically designed for higher flow rates at lower heads, while lower specific speed pumps are suited for lower flows at higher heads.
Pump Efficiency: Efficiency affects how much of the input power is converted into useful fluid work. While not directly used in the most basic flow rate formulas, it's crucial for understanding the actual delivered flow and power consumption under real-world conditions.
Fluid Properties: The density and viscosity of the fluid being pumped will affect performance. Denser or more viscous fluids may result in lower flow rates and require more power.
System Head: The total head (pressure) the pump must overcome (including static head, friction losses, and velocity head) is a primary determinant of the operating flow rate, as pumps have characteristic curves showing flow rate vs. head.
The formula used in this calculator provides a simplified empirical estimation for flow rate based on impeller diameter, rotational speed, and pump efficiency. It's important to note that actual flow rates can vary significantly and are best determined from the pump manufacturer's performance curves for specific operating conditions and system head.