A water supply pipe conveys 0.8 m³/s from a source (lowest water level RL = 92.00 m) to a reservoir (delivery RL = 108.00 m). Pipe length = 500 m, diameter = 0.5 m, friction factor = 0.03. Calculate the static head.
Correct Answer: C. 16 m
📚 Detailed Explanation: Static Head = Delivery RL − Source RL = 16 m
Why C (16 m) is correct: Static head is the pure vertical height difference a pump must overcome, independent of flow velocity, pipe friction, or diameter. It depends only on the difference in elevation between the water source and the delivery point.
Static head (H_st) formula:
H_st = RL of delivery reservoir – RL of source (lowest water level)
H_st = 108.00 m – 92.00 m = 16 m
H_st = RL of delivery reservoir – RL of source (lowest water level)
H_st = 108.00 m – 92.00 m = 16 m
Why Other Data Is Not Needed for Static Head
| Parameter Given | Used for Static Head? | What It Is Used For |
|---|---|---|
| Pipe diameter = 0.5 m | ✗ NO | Velocity head and friction losses |
| Flow rate = 0.8 m³/s | ✗ NO | Velocity = Q/A; friction head loss |
| Pipe length = 500 m | ✗ NO | Friction head loss (Darcy-Weisbach) |
| Friction factor = 0.03 | ✗ NO | Darcy-Weisbach friction losses |
| Source RL = 92 m | ✓ YES | Elevation of water source |
| Delivery RL = 108 m | ✓ YES | Elevation of delivery reservoir |
Total Dynamic Head (for context)
Total Dynamic Head = Static head + Friction losses + Velocity head
Static head = 16 m (only part asked)
Friction losses = calculated using Darcy-Weisbach (needs f, L, D, V)
Velocity head = V²/2g (needs flow rate and pipe area)
Static head = 16 m (only part asked)
Friction losses = calculated using Darcy-Weisbach (needs f, L, D, V)
Velocity head = V²/2g (needs flow rate and pipe area)
- Static head = delivery elevation − source elevation = 108 − 92 = 16 m.
- Pipe size, flow rate, and friction factor do NOT affect static head.
- Static head = purely the vertical lift requirement of the pump.