Pump sizing concept: If w is the weight of water per cubic metre, Q the discharge (m^3/s), and H the total head (m), what is the required water horsepower (output at water) of the pump?

Introduction / Context:
Water horsepower (WHP) is the hydraulic power imparted to the water by the pump. It excludes motor and pump efficiencies and is useful for preliminary power estimates before accounting for losses.

Given Data / Assumptions:

• w = weight of water per m^3 in kilogram-force per cubic metre (kgf/m^3), commonly ≈ 1000 kgf/m^3.
• Q in m^3/s; H in metres.
• 1 metric horsepower (HP) = 75 kgf·m/s.

Concept / Approach:
Hydraulic power P (kgf·m/s) equals w * Q * H. Converting to metric horsepower requires dividing by 75. If w were in newtons per m^3, division would be by 735.5 W per HP; but the variable here is in kgf units.

Step-by-Step Solution:

Verification / Alternative check:
Dimensional check: w (kgf/m^3) * Q (m^3/s) * H (m) gives kgf·m/s, then divide by 75 to get HP. Consistent.

Why Other Options Are Wrong:

• (a) missing conversion to horsepower.
• (c) uses 735.5 appropriate only if w is in N/m^3, not kgf/m^3.
• (d) is dimensionally incorrect.
• (e) is false because (b) is correct.

Common Pitfalls:
Mixing kilogram-force and newton systems; always confirm which specific weight unit the formula uses.

Final Answer:
(w * Q * H) / 75