Flow measurement in venturi meter

In summary, the conversation discusses the process of finding the theoretical flow rate using a venturi-meter installed in a pipe with a 30mm diameter. The individual is having trouble finding the answer due to confusion about the diameter of the pipe and the use of A1 and A2 in the formula. They also discuss finding the pressure difference (P1-P2) and the use of a U-tube manometer. The conversation then shifts to finding the pressure at a depth in a liquid and determining the appropriate reference points for this calculation. They also mention the importance of having the same liquid at the reference points.
  • #1
freshbox
290
0
First I am trying to find the theoretical flow rate but I am not able to get the answer because since diameter of the pipe is 0.03m throughout, when I sub into the formula:

My A1/A2 will be 1, and 1-1 = 0. And I will get maths error whatever is divided by 0.

Am I going in the wrong direction?

Please advice, thanks.
 

Attachments

  • ques1.jpg
    ques1.jpg
    28.8 KB · Views: 1,069
  • formula.jpg
    formula.jpg
    14.1 KB · Views: 599
Last edited:
Physics news on Phys.org
  • #2
freshbox said:
First I am trying to find the theoretical flow rate but I am not able to get the answer because since diameter of the pipe is 0.03m throughout, when I sub into the formula:

My A1/A2 will be 1, and 1-1 = 0. And I will get maths error whatever is divided by 0.

Am I going in the wrong direction?

Please advice, thanks.

No, the diameter is not 0.03 m throughout. Read the problem statement again.
 
  • #3
I mean the 2 pipes at point 1 & 2 connecting to the venturi meter
 
  • #4
freshbox said:
I mean the 2 pipes at point 1 & 2 connecting to the venturi meter

As per the given question, at point 1 it is 0.03 m and at point 2 (throat), its 0.012 m.
 
  • #5
I am confused. Is A1= Area of Left hand side pipe, A2= Area of Right hand side pipe in the theoretical flow rate formula?

"A venturi-meter is installed in a pipe of 30mm diameter" the pipe the question is talking about is it the 2 vertical pipes or the horizontal pipe?
Thanks.
 
  • #6
freshbox said:
I am confused. Is A1= Area of Left hand side pipe, A2= Area of Right hand side pipe in the theoretical flow rate formula?

No. Your book defines A1 and A2, maybe on the previous page, no?

Do you know about Bernoulli theorem?

"A venturi-meter is installed in a pipe of 30mm diameter" the pipe the question is talking about is it the 2 vertical pipes or the horizontal pipe?

The 30 mm diameter pipe is the horizontal pipe (isn't that obvious? :biggrin: ).

The vertical pipes are used for calculating pressures at point 1 and 2.
 
  • #7
Ok I think I got it for the pipes. I am having problem finding P1-P2

Can I ask Since P1=P2

P1=pg(0.045)
P2=pg(0.027)

P1=P2
1000x9.81(0.045)=1000x9.81(0.027)
441.45=264.87 -> Stuck...

There is a note in my book saying "The pressure difference, (P1-P2) is obtained from a U-tube manometer."
Since this is not a u-tube manometer, how do I go about finding P1-P2?Thanks.
 
  • #8
freshbox said:
Ok I think I got it for the pipes. I am having problem finding P1-P2

Can I ask Since P1=P2

P1=pg(0.045)
P2=pg(0.027)

P1=P2
1000x9.81(0.045)=1000x9.81(0.027)
441.45=264.87 -> Stuck...

There is a note in my book saying "The pressure difference, (P1-P2) is obtained from a U-tube manometer."
Since this is not a u-tube manometer, how do I go about finding P1-P2?


Thanks.

How P1=P2? :confused:

What is the pressure at a depth in a liquid?
 
  • #9
I take the reference point at P1 and P2. Like how I did for Px and Py in the attached screenshot.What is the pressure at a depth in a liquid? I don't know sorry.
 

Attachments

  • w.jpg
    w.jpg
    29.4 KB · Views: 754
  • #10
freshbox said:
I take the reference point at P1 and P2. Like how I did for Px and Py in the attached screenshot.

Looks good to me. Can't you find P1 and P2 in the problem you have posted?

P1=P_(atm)+(density)*g*(h1).

Similarly find P2.
 
  • #11
What is P_(atm)? Why do I need to take in account into my equation?

So can I still take my reference point at point 1 & 2 like how I did for Px & Py (Px=Py) so P1=P2?Thanks.
 
Last edited:
  • #12
freshbox said:
What is P_(atm)? Why do I need to take in account into my equation?Thanks.

Sorry, I should have defined it. P_(atm) is the atmospheric pressure. I can't help you further until you learn how to calculate pressure at a depth. Pressure at depth, which is taught in hydro statics should be in your notes or you haven't yet started with it? But its unlikely that you begin with hydrodynamics before studying hydro statics.

For this problem, P1-P2=(density)*g*(difference in heights of liquid in vertical tube).
 
  • #13
Is P1=P2?
 
  • #14
freshbox said:
Is P1=P2?

You should refer your textbook or search online for pressure at depth.
 
  • #15
I have search and don't understand the information online. My teacher said that I should find a reference point and the reference point should have the same liquid.

So I tried to apply post #9 method on my post #1 question which is by taking a reference point. Post #9 I can find the pressure difference between 1 & 2. But for post #1, I am unable to form the equation to "P1-P2=xxxx"

Can you tell me where I go wrong?Thanks.
 
  • #16
freshbox said:
I have search and don't understand the information online. My teacher said that I should find a reference point and the reference point should have the same liquid.

So I tried to apply post #9 method on my post #1 question which is by taking a reference point. Post #9 I can find the pressure difference between 1 & 2. But for post #1, I am unable to form the equation to "P1-P2=xxxx"

Can you tell me where I go wrong?


Thanks.

What you do in post #9 is same as calculating pressure at a depth.

In post #9, you go down, in this problem you go up. :wink:

Think where you should mark X and Y in this case.
 
  • #17
Ok. I have labeled my new Px and Py. But I think it's abit wrong because what do I do for the "?" part of water in Px.

But if it is wrong I thought my reference point should have the same liquid:confused:
 

Attachments

  • ad.jpg
    ad.jpg
    30.2 KB · Views: 529
  • #18
freshbox said:
Ok. I have labeled my new Px and Py. But I think it's abit wrong because what do I for the "?" part of water in Px.

But if it is wrong I thought my reference point should have the same liquid:confused:

It would much easier if you place Px at the top most point on the liquid inside the vertical tube on the left.
 
  • #19
Ok. How about my Py? I thought they should be on the same level with each other and with the same liquid too?

Because my post #9 referencing points are at the same level and having the same liquid.Please explain, I'm abit confused. thank you sir.
 
  • #20
freshbox said:
Ok. How about my Py? I thought they should be on the same level with each other and with the same liquid too?Thanks.

Yes, take them on the same level.

EDIT: And don't call me sir, I am a student myself. :D
 
  • #21
Ok same referencing point but Py is not having the same liquid as Px.

My lecturer said that referencing point must be at the same level and is having the same liquid.

I'm confused over this part.It's ok, it's a form of respect, if you don't like I won't call you that haha.. Thanks anyway for your help :)
 

Attachments

  • g.jpg
    g.jpg
    26.1 KB · Views: 458
Last edited:
  • #22
Px=9810(0.045)+P1
Py=9810(0.027)+P2+Patm

Since Px=Py

9810(0.045)+P1=9810(0.027)+P2+Patm
P1-P2=264.87-441.45
P1-P2=-176.58 -> Is the answer wrong?
 
  • #23
freshbox said:
Px=9810(0.045)+P1
Py=9810(0.027)+P2+Patm

Since Px=Py

9810(0.045)+P1=9810(0.027)+P2+Patm
P1-P2=264.87-441.45
P1-P2=-176.58 -> Is the answer wrong?

Py is actually the atmospheric pressure. Going up from P1,
P1-9810(0.045)=Px

If we go up from P2,
P2-9810(0.027)=Py.

Pressure above the liquid in the vertical tubes is same everywhere so Px=Py. Solve to find P1-P2.
 
  • #24
Don't understand at all. The questions that I did I will add the pressure together. :cry:
 
  • #25
freshbox said:
Don't understand at all. The questions that I did I will add the pressure together. :cry:

The value you calculated for P1-P2 is correct but the sign is wrong. You can substitute that value if you wish and obtain the answer but the way you calculated is wrong. I don't know how can I explain it to you in simpler terms. We should wait for the experts to join.
 
  • #26
Answer wrong :cry:
 

Attachments

  • az.jpg
    az.jpg
    6 KB · Views: 343
  • #27
freshbox said:
Answer wrong :cry:

I can't read what's written in front of the root symbol. Also, you need not plug in the value of g, look at the formula, g cancels out so omit it.
 
  • #28
0.03 is written in front of the root symbol. With or without the g I will still can the same answer right?
 
  • #29
freshbox said:
0.03 is written in front of the root symbol.
Why 0.03? The formula shows that its area in front of root symbol so it should ##\pi(0.015)^2##.
With or without the g I will still can the same answer right?
Yes.
 
  • #30
Yea sorry missed out on that one..hehe.. I calculated as 0.27L/s. Did you get the answer?
 
  • #31
freshbox said:
Yea sorry missed out on that one..hehe.. I calculated as 0.27L/s. Did you get the answer?

I haven't calculated it but isn't that correct?
 
  • #32
No answer is 0.064L/s :cry:

I still don't understand :cry:
 
  • #33
freshbox said:
No answer is 0.064L/s :cry:

Hmm...are you sure it is L/s, not mL/s?
 
  • #34
The answer from post #1 0.064 L/s is written by my lecturer.
 
  • #35
The problem I am having right now is how do I go about finding P1-P2.

Can someone please explain to me, thanks!
 
<h2>1. What is a venturi meter and how does it work?</h2><p>A venturi meter is a type of flow measurement device that uses the principle of Bernoulli's equation to measure the flow rate of a fluid. It consists of a converging section, a throat, and a diverging section. As the fluid flows through the converging section, its velocity increases and the pressure decreases. The throat is the narrowest part of the meter where the velocity is the highest. The fluid then passes through the diverging section, where its velocity decreases and the pressure increases. The difference in pressure between the converging and diverging sections is used to calculate the flow rate.</p><h2>2. What are the advantages of using a venturi meter?</h2><p>One of the main advantages of using a venturi meter is its accuracy. It is highly accurate in measuring the flow rate of both liquids and gases. It also has a wide range of flow rates that it can measure, making it suitable for a variety of applications. Additionally, venturi meters have no moving parts, which makes them low maintenance and less prone to wear and tear.</p><h2>3. How do you calculate the flow rate using a venturi meter?</h2><p>The flow rate through a venturi meter can be calculated using the Bernoulli's equation, which states that the pressure drop across the meter is proportional to the square of the flow rate. The equation is Q = (A1/A2) * √(2gΔP/ρ), where Q is the flow rate, A1 and A2 are the cross-sectional areas of the converging and diverging sections, g is the acceleration due to gravity, ΔP is the pressure difference between the two sections, and ρ is the density of the fluid.</p><h2>4. What are the limitations of using a venturi meter?</h2><p>One of the limitations of using a venturi meter is that it can only be used for fluids that are clean and free from any particles or impurities. The presence of particles can affect the accuracy of the measurement. Additionally, the installation of a venturi meter can be complex and requires a certain length of straight pipe before and after the meter to ensure accurate readings.</p><h2>5. How can the accuracy of a venturi meter be improved?</h2><p>The accuracy of a venturi meter can be improved by calibrating it regularly and ensuring that it is installed correctly. The use of a flow straightener before the meter can also improve accuracy by reducing turbulence in the flow. Additionally, selecting the appropriate meter size for the flow rate and ensuring that the fluid is within the specified temperature and pressure range can also improve accuracy.</p>

1. What is a venturi meter and how does it work?

A venturi meter is a type of flow measurement device that uses the principle of Bernoulli's equation to measure the flow rate of a fluid. It consists of a converging section, a throat, and a diverging section. As the fluid flows through the converging section, its velocity increases and the pressure decreases. The throat is the narrowest part of the meter where the velocity is the highest. The fluid then passes through the diverging section, where its velocity decreases and the pressure increases. The difference in pressure between the converging and diverging sections is used to calculate the flow rate.

2. What are the advantages of using a venturi meter?

One of the main advantages of using a venturi meter is its accuracy. It is highly accurate in measuring the flow rate of both liquids and gases. It also has a wide range of flow rates that it can measure, making it suitable for a variety of applications. Additionally, venturi meters have no moving parts, which makes them low maintenance and less prone to wear and tear.

3. How do you calculate the flow rate using a venturi meter?

The flow rate through a venturi meter can be calculated using the Bernoulli's equation, which states that the pressure drop across the meter is proportional to the square of the flow rate. The equation is Q = (A1/A2) * √(2gΔP/ρ), where Q is the flow rate, A1 and A2 are the cross-sectional areas of the converging and diverging sections, g is the acceleration due to gravity, ΔP is the pressure difference between the two sections, and ρ is the density of the fluid.

4. What are the limitations of using a venturi meter?

One of the limitations of using a venturi meter is that it can only be used for fluids that are clean and free from any particles or impurities. The presence of particles can affect the accuracy of the measurement. Additionally, the installation of a venturi meter can be complex and requires a certain length of straight pipe before and after the meter to ensure accurate readings.

5. How can the accuracy of a venturi meter be improved?

The accuracy of a venturi meter can be improved by calibrating it regularly and ensuring that it is installed correctly. The use of a flow straightener before the meter can also improve accuracy by reducing turbulence in the flow. Additionally, selecting the appropriate meter size for the flow rate and ensuring that the fluid is within the specified temperature and pressure range can also improve accuracy.

Similar threads

  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Mechanical Engineering
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
9
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
3K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
16
Views
1K
Replies
2
Views
953
  • Introductory Physics Homework Help
Replies
3
Views
5K
  • Aerospace Engineering
Replies
10
Views
603
  • Introductory Physics Homework Help
Replies
2
Views
2K
Back
Top