Specific speed calculation for a centrifugal pump (metric SI): Compute N_s (dimensionless-in-rpm form). Data: Discharge Q = 750 L/s, Head H = 15 m, Rotational speed N = 725 rpm. Use N_s = N × √Q / H^(3/4), with Q in m³/s. Choose the correct numerical value.

Given data

• Q = 750 L/s = 0.75 m³/s
• H = 15 m
• N = 725 rpm

FormulaN_s = N × √Q / H^(3/4)

Step-by-step calculation√Q = √0.75 ≈ 0.8660H^(3/4) = 15^(0.75) ≈ 6.652N_s = 725 × 0.8660 / 6.652 ≈ 628.85 / 6.652 ≈ 94.6? Recheck precisely.Accurate computation: N_s ≈ 82.4 r.p.m. (using precise evaluation: 725×0.8660 ≈ 628.85; 15^(0.75) ≈ 7.628 → then 628.85/7.628 ≈ 82.4)

VerificationMagnitude (~80) corresponds to radial/Francis-type pump specific speed, reasonable for H = 15 m and Q = 0.75 m³/s.

Final Answer82.4 r.p.m.