Pump Impeller

What is modelled

The impeller gives the water angular momentum. At the rim the blade speed u2 is fixed by the rotation, the radial speed cm2 is the flow divided by the outlet area, and the blades guide the water so that the relative speed w2 follows the blade angle, with some slip. The tangential part of the absolute speed, cu2, then sets the ideal head. Hydraulic losses reduce it to the net head, the pipe sets a system curve, and the two curves meet at the operating point.

Equations

• Velocity triangle cu2 = σ (u2 − cm2 / tan β2), cm2 = Q / (π D2 b2 ψ), slip σ = 1 − √(sin β2) / z0.7.
• Euler head H = u2 cu2 / g, torque ρ Q r2 cu2.
• System Hsys = Hstatic + k Q2, affinity Q ∝ n, H ∝ n2, P ∝ n3.
• Suction NPSHa = (patm − pv)/(ρ g) − zs, vapour pressure from the Antoine equation.

Checks run in the page

• The cosine rule on the velocity triangle and the torque times speed against the Euler power.
• Affinity laws from two solved operating points.
• Energy balance: Euler power equals useful power plus the two loss powers.
• The Antoine vapour pressure at 20 C and the boiling point at atmospheric pressure.

Honest simplifications

Friction and shock losses are simple quadratic terms, the slip follows Wiesner's empirical formula, the blade angle is constant along the blade, the volute is not modelled and the NPSH required comes from a simple inlet-velocity rule. It teaches trends, not a pump selection.

• Close the valve (press Throttled valve) and watch the operating point slide to low flow and low efficiency.
• Press Hot water, high lift: the suction head available falls below the required value and the page marks cavitation.
• Press Steep blades and see how the Euler head curve flattens or rises with the blade angle.