Q.94 A 0.3 m diameter pipe carries oil of specific gravity 0.8 at flow velocity of 1.5 m/s and the pressure at a point A is 20 kN/m² (gauge). If the point A is 3 m above the datum line, calculate the approximate total energy at point A in meters of oil.
- A6.31 m
- B5.25 m
- C5.95 m
- D5.65 mCorrect
Solution
Concept
Total energy head = pressure head + velocity head + datum head.
Formula
H = p/(ρg) + V2/(2g) + z
Step-by-step solution
1. Density of oil: ρ = 0.8 × 1000 = 800 kg/m³. 2. Pressure head = 20000/(800 × 9.81) = 2.548 m of oil. 3. Velocity head = 1.52/(2 × 9.81) = 2.25/19.62 = 0.115 m. 4. Datum head z = 3 m. 5. Total head H = 2.548 + 0.115 + 3 = 5.663 m ≈ 5.65 m of oil.
Explanation
Total energy per unit weight at a point is the sum of pressure head, velocity head and datum head. The pressure head must be found using the oil density, not the water density. The sum is about 5.66 m of oil, so option D is closest.
Why the other options are wrong
A: 6.31 m does not match any correct combination of heads. B: 5.25 m is too low; it may come from a calculation error such as missing the velocity head and using water density. C: 5.95 m is too high; it may come from wrong unit conversion or arithmetic.
Shortcut
p/(ρg) = 20/(0.8 × 9.81) ≈ 2.55 m; add 3 m and about 0.11 m to get about 5.66 m.
Common mistake
Using the density of water (1000) instead of oil (800) for the pressure head gives 2.04 m and a wrong total.
Correct answer: D) 5.65 m