Venturi Meter Finding Pressure Difference

In summary, the conversation discusses the use of a manometer to measure pressure in a pipe and the derivation of the formula for a venturi meter. It also clarifies the misunderstanding about the pressure readings p1 and p2 and explains how they depend on the velocity of the liquid rather than gravitational force. The conversation concludes by discussing the importance of equal pressure at the same level in both arms of the manometer.
  • #1
Saladsamurai
3,020
7

Homework Statement



Picture1-36.png



I guess I am having a hard time seeing what that manometer is doing.

I assume that as fluid moves in at 1 it causes a displacement of the manometer fluid by some distance h.

Now, are we assuming that the pressure is uniform throughout the diameter of the pipe? I think we are, otherwise, I do not see how the manometer reading would be a reflection of the pipe pressure.

So, that being said, the pressure increase on the left side of the manometer is p1 and the pressure decrease on the right side of the manometer is p2.

Good?

So, if the pressure in the pipe=p1=the pressure at some depth h into the manometer and the same for p2, then we have:

[itex]p_1=\rho_mgh[/itex] and [tex]p_2=\rho_1gh[/itex]

thus, [itex]p_1-p_2=gh(\rho_m-\rho_1)[/itex]
 
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  • #3
Hey tiny-tim :smile:

I guess I still don't like what I have so far. I know that it is correct, but only because I already knew what formula for a venturi meter I supposed to arrive at.

That is, when I originally derived this, I had the densities reversed, i.e.,

[tex]p_1-p_2=gh(\rho_1-\rho_m)[/tex]

If you call the interface on the left hand side of the manometer (where the pipe fluid meets the manometer fluid) point A,

and the interface on the RHS of the manometer (where the manometer fluid meets the lower pressure fluid) point B:

then p1=pA and p2=pB right?

I am just trying to sort this out in my head.

Because it seems like then pA=h*g*rho_1 and errr...yeah I am lost now :redface:
 
  • #4
(have a rho: ρ :wink:)

I don't really understand what you're asking :confused:

The pressure difference is gh(ρM - ρ) …

now write out the two equations :smile:
 
  • #5
tiny-tim said:
(have a rho: ρ :wink:)

I don't really understand what you're asking :confused:

The pressure difference is gh(ρM - ρ) …

now write out the two equations :smile:

What I am asking, is why the pressure difference is

gh(ρM - ρ)

For some reason I am not seeing it as that. I am seeing it as

gh(ρ - ρM) :confused:

That's what this is all about

If you call the interface on the left hand side of the manometer (where the pipe fluid meets the manometer fluid) point A,

and the interface on the RHS of the manometer (where the manometer fluid meets the lower pressure fluid) point B:

then p1=pA and p2=pB right?
 
  • #6
Saladsamurai said:

Homework Statement


So, if the pressure in the pipe=p1=the pressure at some depth h into the manometer and the same for p2, then we have:

[itex]p_1=\rho_mgh[/itex] and [tex]p_2=\rho_1gh[/itex]

thus, [itex]p_1-p_2=gh(\rho_m-\rho_1)[/itex]
You have misunderstood about p1 and p2. Let p1 and p2 are the pressure along the common axis of the tubes. At any point on the axis it is same in all directions. When the liquid is not flowing, p1 = p2.. p1 and p2 does not depend on the gravitational force, but they depend on the velocity of the liquid.
Since liquid is moving from left to right, p1 > p2.
The mercury level at A in the left arm is at rest. That means at the same level in both arms, pressure must be the same.
Now proceed to calculate the pressure difference.
 
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1. What is a Venturi meter?

A Venturi meter is a device used to measure the pressure difference between two points in a fluid flow. It consists of a tapered tube with a narrow throat and wider inlet and outlet sections. As fluid flows through the meter, the change in cross-sectional area causes a decrease in pressure at the throat, which can be measured and used to calculate the pressure difference.

2. How does a Venturi meter work?

A Venturi meter works on the principle of Bernoulli's equation, which states that as the speed of a fluid increases, its pressure decreases. In a Venturi meter, the fluid is forced through a narrow throat, causing an increase in velocity and a decrease in pressure. The pressure difference can then be measured and used to calculate the flow rate of the fluid.

3. What is the equation used to calculate pressure difference in a Venturi meter?

The equation commonly used to calculate the pressure difference in a Venturi meter is ΔP = 0.5ρv2(1-(A1/A2)2), where ΔP is the pressure difference, ρ is the fluid density, v is the fluid velocity, and A1 and A2 are the cross-sectional areas at the inlet and throat of the meter, respectively.

4. What are the advantages of using a Venturi meter?

One of the main advantages of using a Venturi meter is its accuracy. The pressure difference measured by the meter is unaffected by changes in the fluid's density, viscosity, or temperature. Additionally, Venturi meters have a low pressure loss, making them suitable for use in systems where energy conservation is important.

5. What are some common applications of Venturi meters?

Venturi meters are commonly used in a variety of industries, including water supply and treatment, oil and gas, and chemical processing. They can be used to measure the flow rate of liquids, gases, and steam, making them useful for monitoring and controlling processes in these industries. They are also frequently used in HVAC systems to measure air flow.

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