Fluids using Bernoullis principle

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The discussion revolves around calculating the velocity of water exiting a pipe in a dam using Bernoulli's principle, with specific conditions for summer and winter scenarios. For summer, the water level is at its maximum, while in winter, a 30cm thick ice layer affects the calculations. Participants emphasize the importance of assuming the ice is flush with the dam's top for winter calculations, although practical considerations may suggest otherwise. Additionally, the power output of the generator is noted as a crucial missing piece of information for solving the problem accurately. Overall, the thread highlights the application of fluid dynamics principles in varying seasonal conditions.
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.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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