A centrifugal pump is required to lift 2.8 cum/s of water to a height of 7.5m. If the total loss of head in the pipe system is 0.25 m and the efficiency of the pump is 80%, then the brake horse power will be
- A(1000 × 2.8 × 7.5 × 0.8) / 75
- B(1000 × 2.8 × 7.75) / 0.8
- C(1000 × 2.8 × 7.75) / (0.8 × 75)Correct
- D(1000 × 2.8 × 7.75) / 75
Solution
Concept
Brake Horse Power of Centrifugal Pump
Formula
BHP = (γ × Q × H) / (75 × η)
Step-by-step solution
1. Calculate total head (H): H = 7.5 m + 0.25 m = 7.75 m 2. Identify values: γ = 1000 kg/m³, Q = 2.8 m³/s, η = 0.8 (80%) 3. Substitute into formula: BHP = (1000 × 2.8 × 7.75) / (0.8 × 75)
Explanation
To find the Brake Horse Power (BHP), total head is calculated by adding the lift height and head loss (7.5 m + 0.25 m = 7.75 m). Using the BHP formula (γ × Q × H) / (75 × efficiency), we substitute the density of water (1000 kg/m³), discharge rate (2.8 m³/s), total head (7.75 m), and efficiency (0.8) to get (1000 × 2.8 × 7.75) / (0.8 × 75).
Shortcut
To easily remember the formula structure for Brake Horse Power (BHP) in metric units:1. Numerator: Multiply water density (γ = 1000 kg/m³), discharge (Q), and total head (H = lift + head loss). 2. Denominator: Divide by pump efficiency (η) and the metric conversion factor (75) because efficiency and horse power conversion always belong in the denominator: BHP = (1000 × Q × H) / (η × 75).
Common mistake
Many students forget to add the head loss (0.25 m) to the static lift height (7.5 m) to get the total head (7.75 m), or they multiply by efficiency instead of dividing by it in the denominator.
Correct answer: C) (1000 × 2.8 × 7.75) / (0.8 × 75)