# Fluid Mechanics and Venturi meter

• patep023
In summary, the conversation is discussing the calibration of a Venturi meter used to measure the flow rate of water in a 100 mm diameter water main. The meter has an inlet diameter of 100 mm and a throat diameter of 40 mm. The calibration involves determining the coefficient of discharge (Cd) for the meter at various flow rates, which is defined as the ratio of the actual flow rate to the theoretical flow rate. At a particular flow rate, 0.012 m^3 of water is collected in one second and the manometric levels differed by 375 mm. The conversation also includes discussion of Bernoulli's equation and the calculation of flow velocity at the inlet and throat in terms of the theoretical flow rate.
patep023

## Homework Statement

A Venturi meter is constructed with an inlet diameterof 100 mm and a throat
diameter of 40 mm. The meter must be calibrated prior to leaving the factory.
The meter is installed in a 100 mm diameter water main with a mercury
manometer connected across the inlet and throat of the device. Calibration comprises the determination of the coefficient of discharge (Cd) for the meter at
various flow rates. Cd is defined as the ratio of the actual flow rate to the theoretical flow rate. At one particular flow rate, 0.012 m^3 of water is collected in one second having passed through the meter. The manometric levels differed by 375mm at this flow rate.

## Homework Equations

p1/ρg +v1^2/2g+z1=p2/ρg +v2^2/2g+z2
Q=v1A1=v2A2
Cd=mass flow rate actual/mass flow rate theoretical.

## The Attempt at a Solution

So the theoretical solution for mass flow rate is 0.012 m^3s^-1
I haven't plugged in the numbers but I have played around with the equations a lot. An image of the question can be accessed from the link. I got as far as to putting a lot of equations together and getting z1-z2=(v2^2-v1^2)/2g - (p1/p2)/ρwg and z1-z2=(p2-p1 - ρwgh +ρmgh)/ρwg where ρw is density of water and ρm is density of mercury. p1 and p2 are pressure at point 1 and 2. The answer is 0.98 but I don't know all the variables to put into get the actual value for the mass flow.
http://i.imgur.com/PgCasr0.png

patep023 said:

## Homework Statement

A Venturi meter is constructed with an inlet diameterof 100 mm and a throat
diameter of 40 mm. The meter must be calibrated prior to leaving the factory.
The meter is installed in a 100 mm diameter water main with a mercury
manometer connected across the inlet and throat of the device. Calibration comprises the determination of the coefficient of discharge (Cd) for the meter at
various flow rates. Cd is defined as the ratio of the actual flow rate to the theoretical flow rate. At one particular flow rate, 0.012 m^3 of water is collected in one second having passed through the meter. The manometric levels differed by 375mm at this flow rate.

## Homework Equations

p1/ρg +v1^2/2g+z1=p2/ρg +v2^2/2g+z2
Q=v1A1=v2A2
Cd=mass flow rate actual/mass flow rate theoretical.

## The Attempt at a Solution

So the theoretical solution for mass flow rate is 0.012 m^3s^-1
I haven't plugged in the numbers but I have played around with the equations a lot. An image of the question can be accessed from the link. I got as far as to putting a lot of equations together and getting z1-z2=(v2^2-v1^2)/2g - (p1/p2)/ρwg and z1-z2=(p2-p1 - ρwgh +ρmgh)/ρwg where ρw is density of water and ρm is density of mercury. p1 and p2 are pressure at point 1 and 2. The answer is 0.98 but I don't know all the variables to put into get the actual value for the mass flow.
http://i.imgur.com/PgCasr0.png
Let Q be the theoretical flow rate. What would the mercury height difference in the manometer be if the volumetric flow rate was zero? In terms of Q, what is the flow velocity at the inlet? In terms of Q, what is the flow velocity at the throat? From Bernoulli's equation, what would the theoretical flow rate Q be if the height difference of mercury in the manometer were 375 mm? How does this compare with the observed value?

How does calculating the flow velocity at the inlet and throat help in terms of Q as Q is only theoretical and I am trying to work out practical?

patep023 said:
How does calculating the flow velocity at the inlet and throat help in terms of Q as Q is only theoretical and I am trying to work out practical?
You said the Cd is the ratio of the actual to the theoretical flow rate. So, you need to determine the theoretical flow rate at the measured 375 mm Hg in order to calculate the Cd.

Theoretical flow rate is already given 0.012 m^3s^-1. I need to calculate the actual flow rate

patep023 said:
Theoretical flow rate is already given 0.012 m^3s^-1. I need to calculate the actual flow rate
No. The problem statement says that 0.012 is the actual measured flow rate. You are trying to use this measurement to calibrate the venturi meter by determining the Cd. You can then use this Cd to determine the actual flow rates for other sets of flow conditions.

Chet

I am really confused now, my professor said that was the theoretical flow rate

patep023 said:
I am really confused now, my professor said that was the theoretical flow rate
What does the following mean to you: At one particular flow rate, 0.012 m^3 of water is collected in one second having passed through the meter.

This is the only piece of data you have to calibrate the flow meter (i.e., determine the Cd). With all due respect to your professor, it has to be the actual flow rate. Try it, and see if you get your 0.98 value.

Chet

Assuming I am only expected to calculate the flow rate and let's imagine that 0.012m^3 and Cd doesn't exist. How would I do it? I got as far as finding the equation so that I have the variables P2 and v2 which I don't know and am really stuck on that part. I did the following, equation 1=p2+Ro(w)g(z2-h)+Ro(m)gh=P1+Ro(w)g(z1) which I got by making Pa = Pb. My second equation was by using Bernoullies equation and making that equal to z1-z2 and then I put both equation together with 3 variables I didn't know. v1,v2,p2. I replaced v1 with v2A2/A1 using v1a1=v2A2.

patep023 said:
Assuming I am only expected to calculate the flow rate and let's imagine that 0.012m^3 and Cd doesn't exist. How would I do it? I got as far as finding the equation so that I have the variables P2 and v2 which I don't know and am really stuck on that part. I did the following, equation 1=p2+Ro(w)g(z2-h)+Ro(m)gh=P1+Ro(w)g(z1) which I got by making Pa = Pb. My second equation was by using Bernoullies equation and making that equal to z1-z2 and then I put both equation together with 3 variables I didn't know. v1,v2,p2. I replaced v1 with v2A2/A1 using v1a1=v2A2.

This is a really good start. Your first equation, when rearranged, gives:

(Ro(m)-Ro(w))gh=(p1-p2)-Ro(w)g(z1-z2)

What does your Bernoulli equation give for the right hand side of this equation?

Also, don't forget that v1a1=v2A2=Q. So, v1 = Q/a1, and v2 = Q/a2.

Chet

I got it. Thank you for the help and yes you were right, 0.012 is the actual value, turns out i just heard him wrong. sorry for the inconvenience

## 1. What is Fluid Mechanics?

Fluid mechanics is the branch of physics that deals with the study of fluids (liquids and gases) and the forces that act on them. It involves understanding the behavior of fluids under various conditions and how they interact with their surroundings.

## 2. What is a Venturi meter?

A Venturi meter is a type of flow meter that is used to measure the flow rate of a fluid in a pipeline. It consists of a tapered tube with a narrow throat section and pressure measuring devices at the inlet and outlet of the tube. The change in pressure between the two points is used to calculate the flow rate.

## 3. How does a Venturi meter work?

A Venturi meter works based on the principle of Bernoulli's equation, which states that as the speed of a fluid increases, its pressure decreases. The narrowing of the tube in a Venturi meter causes the fluid to speed up, resulting in a decrease in pressure. This pressure difference is measured and used to calculate the flow rate.

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

Some advantages of using a Venturi meter include its high accuracy, low maintenance requirements, and ability to measure a wide range of flow rates. It is also less prone to clogging compared to other types of flow meters.

## 5. What are some real-world applications of Fluid Mechanics and Venturi meters?

Fluid Mechanics and Venturi meters have various real-world applications, such as monitoring water flow in irrigation systems, measuring fuel flow in airplanes, and controlling air flow in HVAC systems. They are also used in industries such as oil and gas, chemical processing, and water treatment.

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