The kinetic head of water flowing through a pipe of diameter 60 cm is 4 m, whereas the total head of the water at a cross-section, which is 6 m above the datum line, is 60 m. Determine the pressure head of water.
- A50 mCorrect
- B48 m
- C60 m
- D56 m
Solution
Concept
Total head = pressure head + kinetic (velocity) head + datum head.
Formula
H = p/(ρg) + V2/(2g) + z
Step-by-step solution
1. Total head H = 60 m. 2. Kinetic head V2/(2g) = 4 m. 3. Datum head z = 6 m. 4. Pressure head p/(ρg) = H − V2/(2g) − z = 60 − 4 − 6 = 50 m.
Explanation
Total head is the sum of pressure head, kinetic head and datum head. Subtract the kinetic head (4 m) and datum head (6 m) from the total head (60 m). The pressure head is 50 m. The pipe diameter is not needed.
Why the other options are wrong
B (48 m), C (60 m) and D (56 m) do not match 60 − 4 − 6. D subtracts only the kinetic head, and C takes the total head as the pressure head.
Shortcut
Pressure head = Total head − Kinetic head − Datum head.
Common mistake
Forgetting to subtract the datum head (giving 56 m) or trying to use the pipe diameter.
Correct answer: A) 50 m