Water is flowing through a pipe of 5 cm diameter under a pressure of 29·43 N/cm² (gauge) and with mean velocity of 2 m/s. What is the total head of the water at a cross-section, which is 5 m above the datum line? Take the density of water as 1000 kg/m³.
- A38·2 m
- B35·2 mCorrect
- C32·6 m
- D28·6 m
Solution
Concept
Total head
Formula
H = p/γ + V²/2g + z
Step-by-step solution
1. p = 29.43 N/cm² = 2.943 × 10⁵ N/m²; p/γ = 294 300 / 9810 = 30 m. 2. V²/2g = 4 / 19.62 = 0.204 m. 3. z = 5 m. 4. H = 30 + 0.204 + 5 = 35.2 m.
Explanation
The total head is the sum of pressure head, velocity head and elevation (datum) head.
Why the other options are wrong
The other values do not equal 30 + 0.2 + 5.
Shortcut
29.43 N/cm² = 30 m of water.
Common mistake
Forgetting the datum head.
Correct answer: B) 35·2 m