Bernoulli's Principle: How Does Water Flow in a Tower with Multiple Holes?

In summary: Atmospheric Pressure: 101,325 PaP1+101,325 Pa=P2+101,325 PaP1-101,325 Pa=P2-101,325 PaDelta P = (101,325/2)*g*Delta hDelta P= 50,625 Pa
  • #1
bmandrade
63
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Homework Statement



Examine the schematic of the tower. Water flows in at the top to balance the water flowing out through the holes, so the height of the water in the tower stays fixed.

Take state 1 at the top of the water in the tower and state 2 in the water just as it flows out of the hole.

for this part there is a picture that shows a water tower there are three holes one on the top one in the middle and one at the bottom.


a. What is the pressure at states 1 and 2?Explain.

c. If the holes are at heights of 3.0 cm, 13cm and 23 cm above the surface of the water in the lower basin and the top hole is 3.0 cm below the top of the water in the tower, predict which one you believe will go farthest (top, middle or bottom). Explain your reasoning.

Homework Equations



P1+1/2(m/V)v12+(m/V)gy1=P2+(m/V)v22+(m/V)gy2


density = m/V


The Attempt at a Solution



a) I would say that the pressure is the same as the atmospheric pressure because that is the only pressure that i found it could affect in this problem in this case then pressure at both states are the same

b) If P1 and P2 then somehow i can manipulate the bernoulli equation to get a velocity but i don't know how

please help me
 
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  • #2
You can get rid of the 1/2(m/V)v's in your Bernoulli's principle equation since that is irrelevant. You need to use the equation without 1/2(m/V)v's to figure out the pressure of the water at each height and then add the air pressure to get the absolute pressure at each height.
 
  • #3
So i would use this

P1 +m/V)gy1= P2 +(m/V)gy2

use water's density and g=10 and then for y1 would I use zero and for y2 I would use what height? what about P1?
 
  • #4
P1 +m/V)gy1= P2 +(m/V)gy2

Then move things around so it's

P1-P2=(m/V)gy2-(m/V)gy1

Then that changes to

Delta P = (m/V)g(y2-y1)

Delta P = (m/V)*g*Delta h

Delta P is the pressure of the water aka what you are looking for, and Delta h is the different heights of the holes 3cm,13cm,23cm or .03m, .13m, .23m (in SI units)

After you get the three different answers to Delta P add the pressure of the atmosphere to get the absolute pressures.
 
Last edited:

What is Bernoulli's principle?

Bernoulli's principle is a fundamental principle in fluid dynamics that states that as the speed of a fluid increases, its pressure decreases. This principle is based on the conservation of energy and is applicable to both liquids and gases.

How does Bernoulli's principle work?

Bernoulli's principle works by stating that as a fluid moves faster, it experiences a decrease in pressure. This is because the faster-moving particles create an area of low pressure, while the slower-moving particles create an area of high pressure. This difference in pressure causes the fluid to move from high pressure to low pressure, resulting in the observed decrease in pressure.

What are some applications of Bernoulli's principle?

Bernoulli's principle has many practical applications, including in airplane wings, where it helps to generate lift, and in carburetors, where it helps to mix air and fuel for combustion. It is also used in various sports, such as in the design of a golf ball to create lift and in the curve of a baseball pitch.

What are some common misconceptions about Bernoulli's principle?

One common misconception about Bernoulli's principle is that it only applies to moving fluids. In reality, it also applies to fluids at rest, where the pressure varies depending on the height of the fluid. Another misconception is that Bernoulli's principle is the only factor that determines lift in an airplane; while it is an important factor, there are other principles at play as well.

How can Bernoulli's principle be demonstrated?

Bernoulli's principle can be demonstrated through various experiments, such as the classic demonstration with a ping pong ball and a hair dryer. In this experiment, the fast-moving air from the hair dryer creates low pressure, causing the ping pong ball to be suspended in the air. Other demonstrations include blowing over a piece of paper to make it rise and using a Venturi tube to measure the change in pressure as a fluid speeds up.

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