Bernoulli's Equation of water tower

In summary, the conversation discusses the pressure and volume flow rate at point 1 of a water tower that is drained by a nonviscous pipe. The absolute pressure at point 1 is determined by the water speed at point 2 and the effective cross-sectional area of the valve opening. The solution also mentions that point 1 is open to the atmosphere, indicating that the pressure at this point is the same as atmospheric pressure.
  • #1
keemosabi
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Homework Statement


The water tower in the drawing is drained by a pipe that extends to the ground. The flow is nonviscous.

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(b) What is the absolute pressure at point 1 when the valve is opened and the water is flowing? Assume that the water speed at point 2 is negligible.

(c) Assuming the effective cross-sectional area of the valve opening is 2.09 multiplied by 10-2 m2, find the volume flow rate at point 1.



Homework Equations





The Attempt at a Solution


For part b:

p1 +density(g)(y) + .5(density)(v)^2 = p2 +density(g)(y) + .5(density)(v)^2
p1 + 0 + .5(1000)v^2 = 101000 + 1000(9.8)(15)

I have two variables p1 and v, so how can I solve this?
 

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  • #2
Anyone?
 
  • #3
The fact that point 1 is essentially open to the atmosphere (hint, hint) dictates what the pressure is there.
 

What is Bernoulli's Equation of water tower?

Bernoulli's Equation is a fundamental equation in fluid dynamics that relates the pressure, velocity, and height of a fluid in a continuous flow system. It is often used to analyze the behavior of fluids in pipes, pumps, and other systems.

How does Bernoulli's Equation apply to a water tower?

In a water tower, the equation applies by relating the pressure at the bottom of the tower (due to the weight of the water above) to the velocity of the water exiting the tower through a pipe. This is why water can flow out of a water tower at a constant rate, even though the water level in the tower decreases.

What are the assumptions of Bernoulli's Equation?

Bernoulli's Equation assumes that the fluid is incompressible, non-viscous (no internal friction), and that there is no external work being done on the fluid. It also assumes that the flow is steady, meaning that the velocity and other properties of the fluid do not change over time.

Are there any limitations to using Bernoulli's Equation for water tower analysis?

While Bernoulli's Equation is a useful tool for analyzing fluid flow in water towers, it does have limitations. It does not take into account factors such as turbulence, surface tension, and energy losses due to friction. In some cases, these factors may need to be considered for a more accurate analysis.

How is Bernoulli's Equation derived?

Bernoulli's Equation is derived from the principle of conservation of energy, which states that energy cannot be created or destroyed, only transferred from one form to another. By applying this principle to a fluid in a steady flow system, Bernoulli's Equation can be derived through mathematical equations and simplifications.

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