Pressure in tank pipe -- Bernoulli Equations

In summary: Just remember that when you're dealing with fluid mechanics problems, it's important to choose a consistent reference frame and datum. That will help you avoid getting confused and making mistakes. In summary, the conversation discusses a problem involving a pressurized cylindrical tank with water flowing through a pipe at various points. The goal is to find the pressure at point B. After some attempt at using the continuity and Bernoulli's equations, the conversation shifts to discussing the correct arrangement of the equations to reach the solution. The final solution involves using gauge pressure as the datum and setting the height datum at point B.
  • #1
AnotherParadox
35
3

Homework Statement


f4891dce2cb1bcdc52342eaa95a7df27.png
[/B]
A pressurized cylindrical tank, 5m in diameter, contains water which emerges from the pipe at point C with a velocity of 25 m/s. Point A is 10m above point B and point C is 3m above point B. The area of the pipe at point B is 0.07 m2 and the pipe narrows to an area of 0.02m2 at Point C. Assume the water is an ideal fluid in laminar flow. The density of water 1000kg/m3

Homework Equations


Continuity Equation:
VBAB=VCAC

Bernouli's equation:
Let D = density of water
PB + (1/2)DVB2+DghB = PC + (1/2)DVC2+DghC

The Attempt at a Solution


Let D = density of water
VBAB=VCAC
Therefore
VB=[VCAC]/AB=[25*0.02]/0.07=7.14m/s

PB + (1/2)DVB2+DghB = PC + (1/2)DVC2+DghC
Therefore
PB = PC + (1/2)DVC2+DghC -(1/2)DVB2-DghB

Except PC and PBis unknown so this approach shouldn't work. One of my peers claims it is the same as 1 ATM but I'm doubtful since this does not result in answer which is accurate. I don't see how The pressure at Point C could possibly be 1atm... 2 unknowns .. 1 equation.. not going to work :( correct me if wrong.

Upon searching the internet I came across the solution.. which does yield what I firmly believe is the correct answer .. however I don't not understand how this formula came about..

Let D = density of water

PB = [VC2/(2G) - VB2/(2G) + y)Dg
=(252/(2*9.8) - (7.142/(2*9.8) + 3)*1000*9.8
~=~ 316410 Pa ~=~ 320 kPa

It appears to be some variation of the Bernoulli formula but I need to demonstrate how to take those formulas and make them into this format... which I don't even know where to begin. I don't need to know how to derive the formulas that this one came from .. in other words.. I can just say here's the Bernoulli equation .. rearrange and combine like so and obtain this: (without having to derive the Bernoulli equation itself).

Please and thank you.
 
Physics news on Phys.org
  • #2
What are you trying to find? Pressure at B? Or Pressure at A? You don't need to consider what's going on at point B to do that.

AnotherParadox said:
Except PC and PBis unknown so this approach shouldn't work. One of my peers claims it is the same as 1 ATM but I'm doubtful since this does not result in answer which is accurate. I don't see how The pressure at Point C could possibly be 1atm...
.
Presumably the pipe vents to atmosphere, so point C must be at atmospheric pressure.

AnotherParadox said:
Let D = density of water

PB = [VC2/(2G) - VB2/(2G) + y)Dg
=(252/(2*9.8) - (7.142/(2*9.8) + 3)*1000*9.8
~=~ 316410 Pa ~=~ 320 kPa

It appears to be some variation of the Bernoulli formula but I need to demonstrate how to take those formulas and make them into this format... which I don't even know where to begin. I don't need to know how to derive the formulas that this one came from .. in other words.. I can just say here's the Bernoulli equation .. rearrange and combine like so and obtain this

That is just bernoulli's equation, you were actually very close to reaching that arrangement :
.
AnotherParadox said:
PB = PC + (1/2)DVC2+DghC -(1/2)DVB2-DghB

Use gauge pressure as your datum so PC = 0, and let your height datum be at point B so hB = 0. Plug all those in and collect like terms and you'll reach the solution you quoted, note that the answer is still guage, not absolute pressure.
 
  • Like
Likes Chestermiller and AnotherParadox
  • #3
billy_joule said:
What are you trying to find? Pressure at B? Or Pressure at A? You don't need to consider what's going on at point B to do that.Presumably the pipe vents to atmosphere, so point C must be at atmospheric pressure.
That is just bernoulli's equation, you were actually very close to reaching that arrangement :
.Use gauge pressure as your datum so PC = 0, and let your height datum be at point B so hB = 0. Plug all those in and collect like terms and you'll reach the solution you quoted, note that the answer is still guage, not absolute pressure.
Changed it to 0 and bam same kPa in for gauge pressure. Thanks a ton you have no idea how many countless hours I spent on this damn problem.
 
  • #4
AnotherParadox said:
Changed it to 0 and bam same kPa in for gauge pressure. Thanks a ton you have no idea how many countless hours I spent on this damn problem.
Great, you're welcome.
 

FAQ: Pressure in tank pipe -- Bernoulli Equations

1. What is the Bernoulli Equation and how does it relate to pressure in a tank pipe?

The Bernoulli Equation is a fundamental principle in fluid dynamics that describes the relationship between pressure, velocity, and elevation in a fluid flow. In the context of pressure in a tank pipe, the Bernoulli Equation states that as the fluid flows through the pipe, its pressure decreases along with an increase in velocity. This is due to the conservation of energy in a closed system, where the pressure energy is converted into kinetic energy as the fluid accelerates.

2. How does the shape and diameter of a tank pipe affect the pressure inside?

The shape and diameter of a tank pipe can significantly impact the pressure inside. A narrower pipe will result in a higher fluid velocity, which in turn leads to a lower pressure according to the Bernoulli Equation. Additionally, the shape of the pipe can cause changes in the flow pattern, leading to variations in pressure distribution along the pipe.

3. Can the pressure in a tank pipe be controlled?

Yes, the pressure in a tank pipe can be controlled through various means. One way is by adjusting the flow rate of the fluid entering the pipe. A higher flow rate will result in a lower pressure, and vice versa. Additionally, the use of valves, pumps, and regulators can also help regulate the pressure in a tank pipe.

4. How does the density of the fluid affect the pressure in a tank pipe?

The density of the fluid has a direct impact on the pressure in a tank pipe. According to the Bernoulli Equation, as the fluid density increases, the pressure also increases. This is because a denser fluid has more mass, resulting in a higher pressure needed to maintain the same flow rate and velocity.

5. Are there any external factors that can affect the pressure in a tank pipe?

Yes, there are several external factors that can affect the pressure in a tank pipe. These include changes in elevation, temperature, and atmospheric pressure. Additionally, any obstructions or changes in the pipe's cross-sectional area can also impact the pressure in a tank pipe.

Similar threads

What's the pressure long before the fluid exits a pipe?
Replies
13
Views
571
Hydrostatic pressure at a point inside a water tank that is accelerating
2
Replies
60
Views
4K
Pressure just before the exit hole in a draining tank
Replies
7
Views
2K
Bernoulli's Equation, Find gauge pressure at 2nd point
Replies
6
Views
4K
Bernoulli equation for calculation of water flow
Replies
30
Views
2K
How Does Bernoulli's Principle Apply to Varying Pipe Diameters and Water Flow?
Replies
3
Views
2K
Bernoulli Equation — Discharging water from a partially-filled sealed tank
Replies
6
Views
2K
Bernoulli equation / fluid flow / finding height
Replies
6
Views
2K
Bernoulli Equation and gauge pressure
Replies
5
Views
3K
Energy of a water tank with compressed air
Replies
5
Views
818

Hot Threads

Recent Insights

Back
Top