Liquid Problem with Bernoulli's Equation

In summary, the problem involves a water pipe with a diameter of 2.6 cm and a speed of 0.90 m/s, carrying water into a basement at a pressure of 240 kPa. The pipe then tapers to 1.6 cm and rises to the second floor, 7.5 m above the input point. Using the continuity equation, we can determine the speed and water pressure at the second floor.
  • #1
sophzilla
20
0
A water pipe having a 2.6 cm inside diameter carries water into the basement of a house at a speed of 0.90 m/s and a pressure of 240 kPa. If the pipe tapers to 1.6 cm and rises to the second floor 7.5 m above the input point, what are the (a) speed and (b) water pressure at the second floor?

I tried to set it up as:

14kcu4i.jpg


But clearly it's wrong because I didn't take into consideration the area (given the diameter) etc.

I would appreciate any help. Thank you.
 
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  • #2
Oh, but to solve this problem you'll need to use your last topic equation (the continuity equation :wink: )
 
  • #3
All righty...

if it's A1V1 = A2V2...do we take into consideration the final height?
 

1. What is Bernoulli's Equation?

Bernoulli's Equation is a fundamental principle in fluid dynamics that describes the relationship between pressure, velocity, and elevation in a moving fluid. It states that as the velocity of a fluid increases, its pressure decreases, and vice versa.

2. What is the "liquid problem" with Bernoulli's Equation?

The "liquid problem" with Bernoulli's Equation arises when the fluid being analyzed is a liquid rather than a gas. This is because liquids are considered to be incompressible, meaning their density remains constant, while gases are compressible and their density can change.

3. How does the liquid problem affect the application of Bernoulli's Equation?

The liquid problem affects the application of Bernoulli's Equation by limiting its use to situations where the density of the fluid does not change significantly. This means it cannot be used to accurately analyze liquids where there are large changes in pressure or velocity.

4. Are there any solutions to the liquid problem with Bernoulli's Equation?

Yes, there are solutions to the liquid problem with Bernoulli's Equation. One solution is to use the more general form of the equation, which takes into account the compressibility of the fluid. Another solution is to use more advanced fluid dynamics equations that are specifically designed for incompressible fluids like liquids.

5. What are some real-world examples of the liquid problem with Bernoulli's Equation?

One real-world example of the liquid problem with Bernoulli's Equation is the flow of water through a pipe. As the water flows through the pipe, there are changes in pressure and velocity, but the density of the water remains relatively constant. Another example is the flow of blood through arteries and veins in the human body, where the density of blood remains constant, but there are changes in pressure and velocity.

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