# Fluids using Bernoullis principle

• clergy
In summary, the problem involves a reservoir held in a valley behind a dam, with a width of 200m and extending 2.4km upstream. In winter, the reservoir is covered by a 30cm thick sheet of ice with a density of 920kg/m3. A pipe through the dam releases water to drive a generator, located 8m below the surface of the reservoir. The questions ask for the speed of water leaving the pipe in both summer and winter, and the relevant equation is Bernoulli's equation. However, the problem cannot be solved without knowing the power delivered by the generator and assuming that the top of the ice is flush with the top of the dam wall.
clergy
New poster has been reminded to always show their work on homework questions
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!

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.

## 1. What is Bernoulli's principle?

Bernoulli's principle states that as the speed of a fluid increases, the pressure within the fluid decreases. This principle is based on the law of conservation of energy, which states that energy cannot be created or destroyed, only transferred from one form to another.

## 2. How does Bernoulli's principle apply to fluids?

In the context of fluids, Bernoulli's principle explains the relationship between fluid speed and fluid pressure. As the speed of a fluid increases, the pressure within the fluid decreases. This can be seen in many everyday examples, such as the lift of an airplane wing or the flow of water through a pipe.

## 3. What are some real-world applications of Bernoulli's principle?

Bernoulli's principle has many practical applications, including in the design of airplane wings, car aerodynamics, and the functioning of carburetors and atomizers. It is also used in medical devices such as inhalers and nebulizers, as well as in water and wastewater treatment systems.

## 4. What are the limitations of Bernoulli's principle?

Bernoulli's principle assumes ideal conditions, such as a non-viscous fluid and steady, incompressible flow. In reality, fluids often have turbulence and viscosity, which can affect the accuracy of Bernoulli's principle. Additionally, it is important to consider other factors, such as the shape and size of the object, in order to fully understand the behavior of fluids.

## 5. How is Bernoulli's principle related to the conservation of mass?

Bernoulli's principle is related to the conservation of mass through the continuity equation, which states that the mass flow rate in a fluid must remain constant. As the fluid's speed increases, the area through which it flows must decrease in order to maintain a constant mass flow rate. This relationship is important in calculating the behavior of fluids using Bernoulli's principle.

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