---
title: "Micro hydro net head, power and energy"
subject: "Energy Resources"
chapter: 5
key: "semester_6/energy_resources:micro-hydro-power-output-numerical"
source: https://www.bctengineer.com/q/semester_6/energy_resources/micro-hydro-power-output-numerical
site: BCT Engineering
---

# Micro hydro net head, power and energy

Energy Resources · Chapter 5: Micro and small hydro power systems

- Asked in: year not given, 6 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/energy_resources/micro-hydro-power-output-numerical
- Whole chapter: https://www.bctengineer.com/md/semester_6/energy_resources/chapter-5

## Question

A micro hydro site has a gross head of 60 m and a design flow of 0.15 m³/s. Penstock and other losses are 8 % of gross head. The turbine efficiency is 80 % and the generator efficiency is 92 %. Calculate (a) the net head, (b) the hydraulic power, (c) the electrical output, and (d) the annual energy if the plant factor is 0.6.

## Short answer

Net head = 60 - 0.08×60 = 55.2 m. Hydraulic power P_h = 1000×9.81×0.15×55.2 = 81.2 kW. Electrical output P_e = 0.80×0.92×81.2 = 59.8 kW. Annual energy = 59.8×0.6×8760 = 3.14×10⁵ kWh (314 MWh).

## Answer

#### (a) Net head
$$
H_n = H_g - h_L = 60 - 0.08(60) = 55.2\ \text{m}
$$

#### (b) Hydraulic power at turbine inlet
$$
P_h = \rho g Q H_n = 1000 \times 9.81 \times 0.15 \times 55.2 = 81\,227\ \text{W} = 81.2\ \text{kW}
$$

#### (c) Electrical output
$$
\eta_o = 0.80 \times 0.92 = 0.736
$$

$$
P_e = \eta_o P_h = 0.736 \times 81.2 = 59.8\ \text{kW}
$$

The scheme falls in the micro hydro range (5–100 kW). Gross hydraulic power was $\rho g Q H_g = 88.3$ kW, so overall efficiency from the gross head is $59.8/88.3 = 67.7\ \%$.

#### (d) Annual energy
$$
E = P_e \times 8760 \times PF = 59.8 \times 8760 \times 0.6 = 3.14\times10^{5}\ \text{kWh}
$$

**Answer:** $H_n = 55.2$ m; $P_h = 81.2$ kW; $P_e = 59.8$ kW; $E \approx 3.14 \times 10^5$ kWh (314 MWh) per year.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How is the net head found in the micro hydro numerical?
   A. Gross head plus the losses
   B. Gross head minus the losses (60 - 0.08 x 60 = 55.2 m)
   C. Gross head multiplied by 0.92 efficiency of the generator
   D. Gross head divided by the flow
   Answer: B. Penstock and other losses are subtracted from the gross head, giving 55.2 m. (Key point: Net head)

2. Which expression gives the hydraulic power at the turbine inlet?
   A. rho g Q Hg x turbine efficiency
   B. rho Q Hn
   C. rho g Q Hn = 1000 x 9.81 x 0.15 x 55.2
   D. g Q Hn / rho
   Answer: C. Hydraulic power is rho g Q times the net head, about 81.2 kW. (Key point: Hydraulic power formula)

3. How is the electrical output obtained from the hydraulic power?
   A. Multiply by the sum 0.80 + 0.92
   B. Multiply by the overall efficiency 0.80 x 0.92 = 0.736
   C. Multiply by 0.80 only
   D. Divide by 0.736
   Answer: B. Turbine and generator efficiencies act in series, so they multiply: Pe = 0.736 x 81.2 = 59.8 kW. (Key point: Overall efficiency)

4. Which calculation gives the annual energy with a plant factor of 0.6?
   A. 59.8 x 8760 x 0.6 kWh
   B. 59.8 x 365 x 0.6 kWh
   C. 81.2 x 8760 x 0.6 kWh
   D. 59.8 x 8760 / 0.6 kWh
   Answer: A. Annual energy is electrical output x 8760 hours x plant factor, about 3.14 x 10^5 kWh. (Key point: Annual energy)

## Related in Energy Resources

- [Site investigation for micro hydro plant](https://www.bctengineer.com/question.md?key=semester_6%2Fenergy_resources%3Amicro-hydro-site-investigation-head-measurement) — Energy Resources, chapter 5
- [Wind turbine power, tip speed ratio and energy](https://www.bctengineer.com/question.md?key=semester_6%2Fenergy_resources%3Awind-turbine-power-energy-numerical) — Energy Resources, chapter 4
- [Micro hydro scheme components and classification](https://www.bctengineer.com/question.md?key=semester_6%2Fenergy_resources%3Amicro-hydro-scheme-components-classification) — Energy Resources, chapter 5
- [Methods of stream flow measurement](https://www.bctengineer.com/question.md?key=semester_6%2Fenergy_resources%3Aflow-measurement-methods-micro-hydro) — Energy Resources, chapter 5

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