โ๏ธ Specific Speed & Cordier Diagram
Compute turbomachinery specific speed (Ns) and specific diameter (Ds). Locate placement on the Cordier diagram and estimate maximum achievable efficiency.
Tools
๐ Configuration
๐ Results
Configure and click Compute.
๐ Methodology
Specific Speed
Ns = ฯโQ/(gH)^0.75 is the dimensionless specific speed. It classifies machines: Ns < 0.2 โ positive displacement, 0.2-1 โ radial, 1-4 โ mixed flow, > 4 โ axial flow.
Specific Diameter
Ds = Dยท(gH)^0.25/โQ relates impeller size to operating conditions. The Cordier diagram plots Ds vs Ns and defines an optimal locus for each machine type.
Cordier Diagram
The Cordier line Ds = exp(1.25 โ 0.40ยทln Ns) predicts the optimal Ds for a given Ns. Deviation indicates suboptimal size. Peak efficiency typically occurs near the Cordier line.
๐ Calculation Methodology: Turbomachinery Specific Speed & Impeller Selection
Mathematical Model & Theory
Specific speed $N_s$ is a dimensionless or kinematic index that characterizes turbomachine impeller geometry (radial, mixed, or axial flow) regardless of physical size:
Assumptions
- Evaluated at Best Efficiency Point (BEP) at maximum impeller diameter.
- Head $H$ in meters, flow $Q$ in $ ext{m}^3/ ext{s}$ or GPM.
Academic References
- Stepanoff, A. J.: Centrifugal and Axial Flow Pumps, John Wiley & Sons.
- Hydraulic Institute Standards.
Worked Engineering Example
A pump operates at $N = 1450\text{ RPM}$ delivering $Q = 0.050\text{ m}^3/\text{s}$ ($180\text{ m}^3/\text{h}$) against head $H = 25\text{ m}$. Calculate metric specific speed and recommend impeller type.
Step-by-step Solution:
1. $H^{3/4} = (25)^{0.75} = (\sqrt{5})^3 = 5^{1.5} \approx 11.18$.
2. $N_s = 1450 \times \sqrt{0.050} / 11.18 = 1450 \times 0.2236 / 11.18 = 324.2 / 11.18 \approx 29.0\text{ (metric rpm, m}^3\text{/s, m)}$.
Final Result:
Specific speed is $N_s = \mathbf{29.0}$, indicating a **Radial Vane Centrifugal Impeller** with high efficiency.