Head Race Tunnel: Is the Head Loss Real, and When Do You Dewater?
A 330 MW station (3 × 110 MW) is fed by an 8.2 km concrete-lined D-shaped head race tunnel of 60 m² area, 25 m wetted perimeter and design Manning n = 0.014, designed for 250 m³/s at a gross head of 152 m with a design head loss of 9.0 m. After this year's floods, with all three units at 100 MW each (about 220 m³/s), the piezometric difference between the intake and the surge tank shows a head loss of 13.6 m instead of the expected value. There is no surge tank overflow. The trash-rack differential is 0.35 m against a 0.5 m alarm. The intake gate position indicator reads fully open, but the indicator was replaced last winter and has never been calibrated. The desilting chamber has been passing about 0.4 kg/m³ of silt against a design of 0.2 kg/m³ because two of four flushing cycles were skipped during the flood. The lean season begins in ten weeks and lasts about fourteen weeks, when inflows support about one unit at 90 MW; a 12-day unit maintenance outage is already planned for that period. Turbine efficiency is 92 % and generator efficiency 98.5 %.
1. Back-calculate the effective Manning n from the measurement and state what it implies at design discharge.
Read the worked answer
Velocity and slope at the measured point. V = Q/A = 220/60 = 3.67 m/s; R = A/P = 60/25 = 2.40 m; S = hf/L = 13.6/8200 = 0.001659.
Back-calculate n. From Manning, n = R^(2/3) S^(1/2)/V = (2.40^0.667 × 0.04073)/3.67 = (1.792 × 0.04073)/3.67 = 0.0199.
So the tunnel is behaving as if n ≈ 0.020 against a design 0.014 - a 42 % increase in the friction factor. That is far outside measurement noise and outside normal lining deterioration over one flood season; it is the signature of a surface that has been roughened (silt abrasion exposing aggregate) or of a local obstruction being wrongly lumped into friction.
What it means at design discharge. Loss scales roughly with Q²: hf(250) = 13.6 × (250/220)² = 13.6 × 1.291 = 17.6 m against a design 9.0 m, i.e. an excess of about 8.6 m at full discharge.
Sanity check on the measurement. Before believing the number, confirm the static reading: with the units shut down and no flow, the intake and surge tank piezometers should read equal water levels after correcting for instrument elevation and calibration. A discrepancy at zero flow proves it is an instrument or datum error, not a hydraulic loss - and this must be settled before any dewatering decision, because the whole case rests on one differential measurement.
2. Quantify the cost of the excess loss and decide whether to dewater now, dewater in the lean season, or defer.
Read the worked answer
Energy value of the excess loss. At 250 m³/s and combined efficiency 0.92 × 0.985 = 0.906: ΔP = 9.81 × 250 × 8.6 × 0.906/1000 ≈ 19.1 MW.
If the plant is spill-limited for about 2,000 hours a year, the annual loss is 19.1 × 2,000 = 38 GWh, roughly ₹17 crore a year at ₹4.5/kWh. That is recurring until the tunnel is restored.
Cost of dewatering. Lean-season output is about 90 MW. Each shutdown day costs 90 × 24 = 2,160 MWh ≈ ₹97 lakh, so a 20-day dewatering costs about ₹19 crore - more than one full year of the loss. A 12-day window costs about ₹11.7 crore.
The judgement.
- On pure energy arithmetic, a long dewatering is not justified this year unless the outage is short or partly overlaps the already-planned 12-day unit maintenance, when the station is largely down anyway and the incremental cost is much smaller.
- But the loss is recurring and the roughness may be progressing; a 12-day repair overlapping planned maintenance pays back in under a year if it restores n to near design.
- Free diagnostics come first: recalibrate the gate position indicator and confirm the gate is fully open; clean and re-read the trash rack; resume desilting. Any of these could account for part of the 8.6 m, and none costs generation.
Recommendation: spend two weeks on the free checks and a static-level verification; if the loss persists, tender a dewatering inspection targeted at the 12-day planned outage in the lean season, and in the meantime operate to the measured net head rather than to the design net head so that generation is declared honestly.
3. What alternative explanations would you test, and what measurements would separate them from friction?
Read the worked answer
Candidate explanations.
- Genuine roughness increase - silt abrasion of the lining, calcite or biological growth, a damaged invert. Consistent with the silt overload (0.4 against 0.2 kg/m³) and with skipped flushing.
- Partially closed or mis-rigged intake gate - the indicator was replaced and never calibrated, so 'fully open' is unverified. A throttled gate adds a local loss that would be wrongly attributed to n.
- Trash-rack or intake blockage - the 0.35 m differential is below alarm but the alarm setting itself may be too high for this flow; debris after a flood is common.
- A collapse or protrusion inside the tunnel - a dislodged lining panel, a construction adit cover, or aeration damage, giving a sudden local loss rather than distributed friction.
- Instrumentation - a drifted piezometer, a changed datum, or a level measured against a different reference after the flood.
Measurements that separate them.
- Zero-flow static test: intake versus surge tank level with units shut down. Equal levels confirm the instrumentation; a difference localises the error.
- Loss versus discharge at several points: friction, gate throttling and rack blockage all vary close to Q², so this alone does not discriminate - it only confirms the total.
- Intermediate piezometer or pressure tapping along the tunnel, if one exists, or a temporary one at the surge tank end, which will show whether the loss is distributed along the 8.2 km (friction) or concentrated near the intake (gate, rack).
- Gate position by direct mechanical indication - stem marking or a physical check during the next gate operation - not by the indicator panel.
- Trash-rack differential at known flow with a clean rack, to establish the true clean-rack baseline.
Only after these should the tunnel be drained for a physical inspection, because draining is the expensive step.