Calculate the specific speed Ns from a pump's duty (flow, total head, speed and number of stages) and identify the optimum impeller shape. Move the sliders and the impeller cross-section morphs in real time from volute to axial, making clear what the specific speed — a "shape number" — really means.
Parameters
Flow rate Q
m³/min
Volume flow the pump delivers (per minute)
Total head H
m
Energy the pump adds, expressed as a height of fluid
Rotational speed N
rpm
Speed of the impeller (revolutions per minute)
Number of stages
st.
Impellers in series; they share the head
Results
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Specific speed Ns (total head)
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Head per stage (m)
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Per-stage Ns_stage
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Recommended impeller type
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Flow rate Q (m³/min)
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Specific-speed range
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Impeller cross-section — shape vs specific speed
The impeller cross-section changes with the per-stage specific speed. Low specific speed: a narrow, large-diameter volute shape; high specific speed: a wide, small-diameter axial (propeller) shape. Arrows show the flow path.
Specific speed Ns vs total head H
Per-stage specific speed Ns_stage vs stages
Theory & Key Formulas
$$N_s=\frac{N\sqrt{Q}}{H^{3/4}}$$
Specific speed Ns. N is the speed in rpm, Q the flow in m³/min, H the total head in m. For a multistage pump, H is the head PER STAGE when finding the per-stage specific speed.
Head per stage H_stage and per-stage specific speed Ns_stage. z is the number of stages. Sharing the head raises the specific speed of each stage.
Specific speed is a "shape number". Pumps with the same specific speed have geometrically similar impellers regardless of size: low specific speed corresponds to a narrow radial impeller, high specific speed to a wide axial impeller.
What is Pump Specific Speed?
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Is the "specific speed" of a pump just its rotational speed? There is a separate speed N slider, so I'm a bit confused.
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Good question. It has the word "speed" in it, but specific speed is not the rotational speed itself. Put simply, specific speed is a "shape number" for the pump. It rolls flow, head and speed into a single value, and any two pumps with the same specific speed have geometrically similar impellers — no matter how big or small. So from the specific speed alone you can immediately tell what kind of impeller suits that pump.
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I see, a shape number. When I raise the "total head H" on the left the specific speed keeps dropping. What does that mean?
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That's the key point. A low specific speed — a "high head, low flow" pump — wants a narrow, large-diameter radial volute impeller. Think of it flinging water outward with centrifugal force to build up high pressure. A high specific speed — a "low head, high flow" pump — wants a wide, small-diameter axial propeller, more like a fan that pushes a lot of water straight ahead. Move the head slider and watch the impeller in the canvas actually morph from volute to propeller.
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So if I need a really high head, can I just keep making the impeller narrower and narrower?
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It's not that simple. Push one impeller for too much head and the specific speed drops too far, so the impeller becomes extremely narrow. Efficiency falls and disk-friction losses climb. That is where "multistaging" comes in. Raise the number-of-stages slider — the head is shared among several impellers, so the head per stage drops and the per-stage specific speed moves back into the efficient range.
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It's true — adding stages raises the "per-stage specific speed". Does the same thing happen inside a real multistage pump?
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Exactly. Boiler feed pumps and tall-building water-supply pumps stack many impellers in series for precisely this reason. If a total head of 200 m is split over 5 stages, each stage only develops 40 m, and every stage can be designed as an efficient "mid specific speed Francis-type" impeller. Try to get 200 m from a single stage and the specific speed becomes absurdly low — you simply can't build a sensible pump. Think of multistaging as "a design technique for keeping every stage at a good specific speed".
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That makes sense. It's fascinating that the specific speed fixes the impeller shape. So in design you start from the specific speed?
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Yes — specific speed is the starting point of pump design. When a customer says "I need this flow and this head", you provisionally pick a speed and compute the specific speed. If it comes out too low, you multistage; too high, you reduce stages or move toward an axial design. You adjust speed, stages and type to land the specific speed in the "just-right" range. Use this tool to build a feel for that first-pass judgement.
Frequently Asked Questions
Specific speed Ns is a single index that, regardless of the pump's physical size, identifies the optimum impeller shape. In the metric form it is Ns = N·√Q / H^(3/4), where N is the speed in rpm, Q the flow in m³/min and H the total head in m. Two pumps with the same specific speed have geometrically similar impellers no matter how large or small they are. So once the duty (flow, head, speed) is fixed, the specific speed alone tells you what kind of impeller will be efficient.
A low specific speed (high head, low flow) calls for a narrow radial volute impeller, while a high specific speed (low head, high flow) calls for a wide axial propeller. This tool classifies from the per-stage specific speed: roughly below 200 a radial / volute impeller, 200-500 a Francis-type (toward mixed-flow) impeller, 500-1200 a mixed-flow impeller, and above 1200 an axial (propeller) impeller. Specific speed is a continuous quantity, so these boundaries are only guidelines.
A single impeller cannot develop a very high head efficiently. Pushing the head up drives the specific speed too low, the impeller becomes extremely narrow, efficiency drops and disk-friction losses rise. The answer is a multistage pump that splits the head among several impellers. Adding stages lowers the head per stage and brings the specific speed each stage works at back into a high-efficiency range. That is why boiler feed pumps and tall-building water-supply pumps are multistaged.
Because Ns = N·√Q / H^(3/4), raising the speed N or increasing the flow Q raises Ns, while raising the head H lowers it. The head enters as the 3/4 power, so it has a strong effect. For the same head and flow, a higher speed gives a higher specific speed and allows a smaller impeller. Multistaging to reduce the head per stage is another effective way to raise the per-stage specific speed.
Real-World Applications
Water-supply and transfer pumps: Pumps that move water through a city, or intake pumps, usually combine a large flow with a moderate head, so a mid specific-speed volute pump or Francis-type impeller is chosen. Designers compute the specific speed from the design flow and required head, then match the type and speed that give the highest efficiency. For low-head, high-flow duties such as bulk river intake, high specific-speed mixed-flow and axial pumps come into their own.
Boiler feed and high-pressure process pumps: A thermal power plant's boiler feed pump must develop heads of several hundred metres, sometimes over 1000 m. A single stage would push the specific speed far too low, so the pump is built with 5 to 10 or more stages to reduce the head per stage and keep every stage in an efficient specific-speed range. The stage slider in this tool lets you experience exactly this multistage design effect.
Agricultural irrigation and drainage pumps: Large pumps that supply water to paddy fields, or that drain low-lying land at pumping stations, handle enormous flows at low head. Their specific speed becomes very high, so axial (propeller) pumps are standard. The impeller looks like a fan and pushes water along the shaft axis. Such pumps protect critical infrastructure — for example draining inland water during a typhoon.
Pump selection and pre-CFD study: Before refining an impeller shape with detailed CFD, the specific speed gives a first read on "which type to design". If the specific speed falls outside the recommended range for a type, the speed or number of stages is revised before serious impeller design begins. Conversely, if the CFD efficiency differs greatly from what the specific speed predicts, it serves as a sanity check pointing to a setup or boundary-condition error.
Common Misconceptions and Pitfalls
The biggest source of confusion is the different unit systems for specific speed. Several definitions exist, and the numbers differ completely: the metric form (Q in m³/min, H in m), the SI dimensionless form (Q in m³/s, H in m, made non-dimensional), and the US customary form (Q in gpm, H in ft). For the very same pump, an Ns of about 350 in the metric form is around 0.1 as a dimensionless SI value and close to 2000 in US units. This tool uses the metric form (Q in m³/min, H in m) widely used in Japanese mechanical engineering. Always check which unit system a catalogue or paper value belongs to before comparing.
Next, treating the specific-speed boundaries as absolute. The transitions between volute, Francis, mixed-flow and axial are continuous; there is no sharp dividing line. The 200 / 500 / 1200 figures in this tool are guidelines only and differ slightly between manufacturers and references. In real design, when the specific speed sits near a boundary you study both types and decide on a balance of efficiency, cavitation behaviour and cost. Specific speed is a "starting indicator"; the final call is made with more detailed characteristic curves.
Finally, "the higher the specific speed, the better" is not true. A higher specific speed does let you shrink the impeller, but a high specific-speed pump has a steep head-flow characteristic, so efficiency and head swing a lot if the operating point shifts slightly. And raising the speed to gain specific speed increases the risk of cavitation — local vapour bubbles forming on the suction side and eroding the impeller. Specific speed is something to "land in the optimum range", not simply to maximise. It must also be balanced against the suction specific speed, which describes suction performance.
How to Use
Enter flow rate Q in m³/min (typical range 0.5–500 m³/min for industrial centrifugal pumps)
Input total head H in meters; for multistage pumps, the simulator divides by stage count automatically
Set rotational speed N in rpm (common values: 1450, 1750, 2900, 3600 rpm for electric motors)
Specify number of stages for multistage designs; single-stage defaults to 1
Read Ns (specific speed in SI units) and impeller type recommendation (centrifugal, mixed-flow, or axial)
Worked Example
A water supply station requires Q=50 m³/min, total head H=120 m at N=1450 rpm with 4 stages. Per-stage head = 120÷4 = 30 m. Per-stage Ns = 1450 × √50 ÷ (9.81 × 30)^0.75 ≈ 52 (SI), indicating centrifugal impellers. Total Ns ≈ 52 (dimensionless), confirming radial design for high-head applications. Compare against ISO 2548 envelope (Ns 10–350 typical range) to validate feasibility.
Practical Notes
Ns below 50 demands narrow, high-head centrifugal impellers; above 200 requires mixed-flow or axial designs with lower head rise per stage
Multistage pumps reduce per-stage Ns significantly; a 6-stage 1450 rpm pump handling 100 m head achieves Ns ~35–45 per impeller, avoiding cavitation and structural stress
Verify affinity law scaling: changing speed from 1450 to 2900 rpm increases Ns by factor √2, shifting impeller type toward axial characteristics