Radial Force in Volute Pumps: Why volute pumps deflect at off-design and how to fix it

Radial force is one of the least understood but most damaging hydraulic phenomena in single-volute centrifugal pumps. When a pump operates away from its best efficiency point (BEP), the pressure distribution around the impeller circumference becomes non-uniform, generating a net radial force on the impeller and shaft. This force causes shaft deflection, which in turn causes seal face misalignment, bearing overload, shaft fatigue, and ultimately premature failure. For pumps operating at 50–70% of BEP flow — a common condition in throttled or oversized systems — radial force can be 2–3 times the BEP value, reducing seal and bearing life by 50–80%. Understanding radial force, how to calculate it, and how to mitigate it is essential for pump selection, system design, and reliability improvement.

What Causes Radial Force

The Volute Pressure Distribution

A single-volute pump casing is designed so that at BEP flow, the velocity of the fluid leaving the impeller matches the velocity in the volute. This match creates a uniform pressure distribution around the entire impeller circumference — the pressure is the same at every angle, so the net radial force is near zero (typically 1–3% of the force at shut-off).

When the pump operates at flows other than BEP, this velocity match is broken:

• Below BEP (part load): The impeller exit velocity is higher than the volute velocity. The fluid decelerates as it enters the volute, causing a pressure rise. The pressure rise is greatest at the cutwater (tongue) and decreases around the volute, creating a non-uniform pressure distribution. The net force points toward the cutwater.
• Above BEP (overload): The impeller exit velocity is lower than the volute velocity. The fluid accelerates in the volute, causing a pressure drop. The pressure is lowest at the cutwater and increases around the volute. The net force points away from the cutwater (opposite direction to part-load).
• At shut-off (zero flow): The pressure distribution is most non-uniform. The force is at its maximum, typically 5–10% of the total hydraulic force (impeller area × head).

Visualizing the Force Direction

Calculating Radial Force

Stepanoff's Method (Most Common)

The most widely used method for estimating radial force in single-volute pumps was developed by Stepanoff:

F = K × H × D₂ × b₂ × γ

Where:

• F = radial force (N or lbf)
• K = radial thrust coefficient (dimensionless, depends on flow ratio)
• H = pump head at operating point (m or ft)
• D₂ = impeller outer diameter (m or ft)
• b₂ = impeller outlet width (m or ft, including shrouds)
• γ = specific weight of fluid (N/m³ or lbf/ft³; 9810 N/m³ for water)

Radial Thrust Coefficient (K)

The K factor is the key variable — it depends on the ratio of actual flow to BEP flow (Q/Q_BEP):

Key observation: A double-volute casing reduces radial force by 70–90% compared to a single volute. This is why API 610 pumps and other high-reliability pumps use double-volute casings for medium-to-high head applications.

Worked Example

Pump: Single-volute chemical process pump

• Impeller diameter D₂ = 320 mm = 0.32 m
• Impeller width b₂ = 40 mm = 0.04 m
• BEP flow = 200 m³/h, BEP head = 50 m
• Operating flow = 100 m³/h (50% BEP, throttled)
• Head at 100 m³/h = 58 m (higher than BEP, typical rising curve)
• Fluid: water (γ = 9810 N/m³)

At BEP (Q/Q_BEP = 1.0):

• K = 0.01
• F = 0.01 × 50 × 0.32 × 0.04 × 9810 = 62.8 N (≈6.4 kgf)

At 50% BEP (Q/Q_BEP = 0.5):

• K = 0.18
• F = 0.18 × 58 × 0.32 × 0.04 × 9810 = 1,312 N (≈134 kgf)

Result: Operating at 50% BEP generates 21 times more radial force than at BEP. This 134 kgf force acts on the shaft, causing deflection, seal misalignment, and bearing overload.

If this pump had a double-volute casing:

• K = 0.03 (at 50% BEP)
• F = 0.03 × 58 × 0.32 × 0.04 × 9810 = 219 N (≈22 kgf)
• 83% reduction in radial force

Effects of Radial Force

Shaft Deflection

Radial force causes the shaft to bend (deflect) at the impeller. The deflection at the seal location is critical — excessive deflection causes:

• Seal face misalignment: Mechanical seal faces must remain parallel within 0.001–0.002 mm. Deflection at the seal of >0.05 mm causes face separation, leakage, and seal failure.
• Shaft fatigue: The radial force rotates with the shaft (the force direction is fixed in space, but the shaft rotates), creating a fully reversed bending stress. This can cause fatigue cracking at the impeller keyway or shaft step.
• Wear ring contact: Excessive deflection causes the impeller to contact the wear ring, increasing wear and potentially causing seizure.
• Bearing overload: Radial bearings see increased load, reducing L10 life. Bearing life is inversely proportional to the cube of load — doubling the load reduces life by 8x.

Calculating Shaft Deflection

Shaft deflection at the impeller can be estimated using the cantilever beam formula:

δ = F × L³ / (3 × E × I)

Where:

• δ = deflection (m)
• F = radial force (N)
• L = overhang length from bearing to impeller center (m)
• E = modulus of elasticity (Pa; 200×10⁹ for steel)
• I = area moment of inertia of shaft (m⁴; I = π × d⁴ / 64 for solid shaft)

Example (continued from above):

• F = 1,312 N (at 50% BEP, single volute)
• L = 200 mm = 0.2 m (typical overhang)
• Shaft diameter d = 45 mm = 0.045 m
• I = π × (0.045)⁴ / 64 = 2.02×10⁻⁷ m⁴
• δ = 1312 × (0.2)³ / (3 × 200×10⁹ × 2.02×10⁻⁷) = 0.000043 m = 0.043 mm

A deflection of 0.043 mm at the impeller is significant — at the seal location (closer to the bearing), deflection may be 0.02–0.03 mm, which is approaching the seal limit. For a pump operating continuously at 50% BEP, this will cause seal failures every 3–6 months.

Bearing Life Reduction

Bearing L10 life is calculated as:

L10 = (C / P)³ × 10⁶ / (60 × rpm) hours

Where C = basic dynamic load rating, P = equivalent dynamic load.

If radial force doubles the bearing load (P = 2× normal), L10 life is reduced to 1/8 of rated life. A bearing rated for 40,000 hours would last only 5,000 hours — about 7 months of continuous operation.

Mitigation Strategies

1. Double-Volute Casing (Most Effective)

A double-volute casing has two cutwaters (tongues) spaced 180° apart. The two volutes generate equal and opposite radial forces, canceling 70–90% of the net force. This is the standard solution for API 610 pumps and other high-reliability applications.

Advantages:

• Reduces radial force by 70–90% across the entire flow range
• Allows stable operation from shut-off to 120% BEP
• Standard on API 610 OH2, BB1, BB2 pumps

Disadvantages:

• More complex casing casting (higher cost)
• Slightly lower efficiency (1–2%) due to divider wall
• Not practical for very small pumps (<50 mm discharge)

2. Concentric (Circular) Casing

A concentric casing has a constant-area annular passage around the impeller, rather than a spiral volute. This creates a more uniform pressure distribution, reducing radial force at part load. However, it is less efficient than a volute at BEP.

Best for: Pumps that must operate at very low flows (e.g., boiler feedwater, high-pressure injection) where radial force is the primary concern.

3. Diffuser Vanes

Diffuser vanes (a ring of stationary vanes around the impeller) convert velocity to pressure more gradually and uniformly than a volute. Multi-stage pumps with diffusers have inherently low radial force. This is standard on BB3, BB4, BB5 multi-stage pumps.

4. Operate Near BEP (System Design)

The simplest mitigation is to ensure the pump operates near BEP (85–110% of BEP flow). This requires:

• Proper pump sizing (avoid excessive safety margins)
• Impeller trimming to match system requirements
• VFD for variable flow systems (adjust speed to maintain BEP operation)
• Minimum flow bypass for pumps that must operate at low flow

5. Minimum Flow Recirculation

For pumps that must operate below 50% BEP (e.g., standby pumps, batch processes), a minimum flow recirculation line ensures the pump always sees at least 25–30% of BEP flow. This prevents operation in the high-radial-force zone.

Components: Automatic recirculation valve (ARC valve) or orifice + check valve, sized for 25–30% of BEP flow.

6. Stiffer Shaft and Bearings

Increasing shaft diameter and using larger bearings reduces deflection and increases load capacity. API 610 requires a shaft stiffness that limits deflection at the seal to <0.05 mm (2 mils) at maximum radial force.

Key parameter: L³/d ratio (overhang length cubed / shaft diameter). Lower = stiffer. API 610 OH2 pumps typically have L³/d <60 (in inches), while general-purpose pumps may have L³/d >100.

7. Wear Ring Design

Proper wear ring clearance creates a hydrodynamic bearing effect at the impeller, providing additional support and reducing effective overhang. Too much clearance eliminates this effect; too little causes contact. API 610 specifies wear ring clearance based on diameter and material.

Selection Guidance for Buyers

When to Specify Double-Volute

Questions to Ask Your Pump Supplier

1. Is the casing single-volute or double-volute?
2. What is the radial force at my operating point (not just BEP)?
3. What is the calculated shaft deflection at the seal at minimum flow?
4. What is the L³/d ratio of the shaft?
5. What is the bearing L10 life at my actual operating point (not BEP)?
6. Can the pump operate continuously at my minimum flow without damage?
7. Is a minimum flow recirculation system required?
8. What is the wear ring clearance and material?
9. Can you provide a radial thrust curve (force vs. flow)?
10. What is the expected seal and bearing life at my operating conditions?

Our API 610 OH2 process pump range features double-volute casings as standard, with radial force reduced by 80–90% compared to single-volute designs. The stainless steel chemical pump range is available in both single-volute (standard) and double-volute (high-reliability option) configurations. For radial force analysis and pump selection, talk to our engineers with your operating conditions and system curve.

Case Study: Reducing Seal Failures with Double-Volute Retrofit

Initial Situation

• Pump: Single-volute chemical process pump, 200 m³/h at 50 m, 45 kW
• Service: Reactor feed, flow controlled by throttle valve
• Actual operation: 100–130 m³/h (50–65% BEP), throttled
• Seal MTBF: 4 months (failure mode: face misalignment, leakage, shaft scoring)
• Radial force at 50% BEP: 1,312 N (calculated)
• Shaft deflection at seal: 0.035 mm (exceeds seal limit of 0.025 mm)

Solution Options Evaluated

Solution: Double-Volute Casing Retrofit

• Replaced single-volute casing with double-volute casing from same pump frame
• New casing had two cutwaters 180° apart, matching impeller
• Reused existing impeller, shaft, bearings, and seal
• Installation during planned shutdown (2 days)

Results

Payback: $6,000 / ($3,000 - $400) = 2.3 years. Including reduced downtime and production loss, actual payback was under 12 months.

Common Problems and Solutions

Problem 1: Pump vibrates excessively at low flow. High radial force at part load causes shaft deflection and bearing overload. Solution: verify operating flow (should be >50% BEP). If below, install minimum flow recirculation or VFD. Check if casing is single-volute — consider double-volute replacement. Verify shaft and bearing condition (may be damaged from prolonged operation).

Problem 2: Mechanical seals fail repeatedly (every 3–6 months). Shaft deflection at seal exceeds seal face alignment limit. Solution: calculate radial force and deflection at actual operating point. If deflection >0.025 mm at seal, the pump is operating too far from BEP or needs double-volute. Check wear ring clearance (excessive clearance increases deflection). Consider upgrading to double-volute casing or installing VFD.

Problem 3: Bearing temperature runs high (>75°C). Radial force overloads the radial bearing, increasing friction and temperature. Solution: calculate bearing load at actual operating point. If load exceeds 50% of C (dynamic rating), bearing life is severely reduced. Check lubrication (oil level, oil quality). Consider larger bearing or double-volute casing. Verify bearing is correctly installed (no preload, proper clearance).

Problem 4: Shaft breaks at impeller keyway. Fatigue failure from cyclic radial force (force direction fixed in space, shaft rotates → fully reversed bending). Solution: inspect shaft for fatigue cracks (DPI/MPI). Calculate bending stress at keyway — should be <30% of yield strength for infinite life. If overstressed, increase shaft diameter or reduce radial force (double volute, operate near BEP). Use fillet radius at keyway (stress concentration factor).

Problem 5: Wear rings wear rapidly (less than 6 months). Shaft deflection causes impeller to contact wear ring, accelerating wear. Solution: check deflection at impeller (should be <0.1 mm). If excessive, reduce radial force or increase shaft stiffness. Replace wear rings with more wear-resistant material (silicon carbide, PTFE-filled carbon). Verify wear ring clearance is within specification (too much clearance = more deflection, too little = contact).

Problem 6: Pump performance drops over time (head and flow decrease). Wear ring clearance increases due to radial-force-induced contact, increasing internal recirculation and reducing performance. Solution: measure wear ring clearance (replace if >2x design). Check impeller for erosion or cavitation damage. Verify shaft is not bent (runout check). Address root cause of radial force (double volute, VFD, minimum flow).

Problem 7: Double-volute pump still has high vibration at low flow. Double-volute reduces but does not eliminate radial force — at very low flow (<30% BEP), residual force can still cause issues. Also, the two volutes may not be perfectly balanced due to casting tolerances. Solution: verify minimum flow is >30% BEP (install recirculation if needed). Check casing for casting defects or blockage in one volute. Verify impeller is centered in casing (no axial misalignment). Consider concentric casing for very low flow operation.

Selection Summary

1. Radial force is caused by non-uniform pressure distribution in single-volute casings at off-BEP operation
2. Force is maximum at shut-off, minimum at BEP, and reverses direction above BEP
3. Use Stepanoff's formula: F = K × H × D₂ × b₂ × γ, with K from flow ratio table
4. Single-volute K = 0.36 at shut-off, 0.01 at BEP; double-volute K is 70–90% lower
5. Radial force causes shaft deflection, seal misalignment, bearing overload, and shaft fatigue
6. Calculate shaft deflection: δ = F × L³ / (3 × E × I); seal deflection should be <0.025 mm
7. Bearing life is inversely proportional to load cubed — doubling load = 1/8 life
8. Best mitigation: double-volute casing (reduces force 70–90%), standard on API 610 pumps
9. Other mitigations: operate near BEP, VFD, minimum flow recirculation, stiffer shaft, proper wear rings
10. Specify double-volute for: variable flow, continuous critical duty, high head, API 610 service
11. Single-volute is acceptable for: fixed flow near BEP, standby duty, low head, small pumps
12. Ask suppliers for: radial thrust curve, shaft deflection at seal, bearing L10 life at your operating point
13. Our API 610 OH2 process pumps feature double-volute casings standard; stainless steel chemical pumps offer double-volute as an option