Finding the Power Produced by a Hydroelectric Generator

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SUMMARY

The discussion focuses on calculating the power produced by a hydroelectric generator using specific parameters: a volumetric flow rate of 10 m³/min and a height of 75 m. The conversion of flow rate to mass flow rate is performed using the density of water (1000 kg/m³), resulting in a mass flow rate of 166.67 kg/s. The potential gravitational energy formula, P = ṁgh, is applied, yielding a power output of 122,627.45 Watts. The calculations are confirmed as accurate by participants in the discussion.

PREREQUISITES
  • Understanding of fluid dynamics principles
  • Knowledge of gravitational potential energy calculations
  • Familiarity with unit conversions (m³/min to m³/s)
  • Basic understanding of hydroelectric power generation
NEXT STEPS
  • Research the efficiency of hydroelectric generators
  • Learn about the impact of head height on power output
  • Explore advanced fluid dynamics concepts relevant to hydroelectric systems
  • Investigate methods for optimizing flow rates in hydroelectric plants
USEFUL FOR

Engineers, hydrologists, and students studying renewable energy systems, particularly those focusing on hydroelectric power generation and fluid mechanics.

bieon
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Homework Statement
A hydroelectrical power plant receives 10 m³/min water from a dam, where the water level is 75 m above the turbine discharge water level. Determine the electric power generated.
Relevant Equations
Refer Below
My Attempt So Far:

1. Write down all information:
Q=10m³ /min
h=75m

2. Change 10m³ /min to m³ /s

10m³ /min × min/60s =1/6 m³ /s
​
3. Change Volumetric Flow Rate to Mass Flow Rate

ṁ=ρQ
ṁ=1000kg/m³ × 1/6 m³ /s
ṁ=166.67 kg/s
​
4. Apply Potential Gravitational energy but replacing the Mass with Mass Flow Rate

P=ṁgh
P=166.67kg/s × 9.81m/s² × 75m
P=122627.45WattThese are my attempt but I am unsure if my answers are correct?​
 
Last edited:
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Looks good.
 
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Likes   Reactions: bieon
gleem said:
Looks good.
Thank you!
 

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