Fluids using Bernoullis principle

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SUMMARY

The discussion focuses on calculating the velocity of water exiting a pipe through a dam using Bernoulli's principle. The scenario involves a reservoir with a width of 200m and a length of 2.4km, with a pipe located 8m below the water surface. In summer, the water exits the pipe at a higher velocity due to the absence of ice, while in winter, the presence of a 30cm thick ice layer affects the calculations. Key equations referenced include Bernoulli's Equation, which is essential for determining the flow rates in both seasonal conditions.

PREREQUISITES
  • Understanding of Bernoulli's Equation
  • Basic principles of fluid dynamics
  • Knowledge of density and pressure calculations
  • Familiarity with the concept of hydrostatic pressure
NEXT STEPS
  • Study the application of Bernoulli's Equation in various fluid flow scenarios
  • Learn about hydrostatic pressure calculations in fluid mechanics
  • Explore the effects of temperature on fluid density and viscosity
  • Investigate the design and operation of hydroelectric generators
USEFUL FOR

Students and professionals in engineering, particularly those specializing in fluid mechanics, civil engineering, and renewable energy systems, will benefit from this discussion.

clergy
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Homework Statement
1. A reservoir is held in a valley behind a dam. The valley is 200m wide, and the reservoir extends 2.4km upstream (with a constant width).
In winter, the entire surface of the reservoir is covered by a 30cm thick sheet of ice. The density of ice is 920kg/m3.
A pipe through the dam releases water to drive a generator. The pipe is 8m below the surface of the reservoir. (12)
i. How fast does the water leave the pipe in summer?
ii. How fast does the water leave the pipe in winter?
Relevant Equations
Bernoullis Equation
Please help!
 
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clergy said:
Problem Statement: 1. A reservoir is held in a valley behind a dam. The valley is 200m wide, and the reservoir extends 2.4km upstream (with a constant width).
In winter, the entire surface of the reservoir is covered by a 30cm thick sheet of ice. The density of ice is 920kg/m3.
A pipe through the dam releases water to drive a generator. The pipe is 8m below the surface of the reservoir. (12)
i. How fast does the water leave the pipe in summer?
ii. How fast does the water leave the pipe in winter?
Relevant Equations: Bernoullis Equation

Please help!
Please show some attempt at part i, per forum rules.
For part ii, you are probably supposed to assume that the top of the ice is flush with the top of the dam wall, i.e. at exactly the same height as the water surface in summer. However, I suspect that in practice the ice would rise above the top of the dam, leading to the same weight in both.
 
Do they tell you how much power the generator delivers? Without this, you won't be able to solve the problem.
 

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