What are the air speeds in a Venturi meter with varying tube diameters?

In summary, the problem involves air being blown through a horizontal Venturi tube with diameters of 1.0 cm and 3.0 cm. The height of the mercury column is measured to be 1.00 mm. The question asks for the air speeds in the wider and narrower sections of the tube, assuming the density of mercury is 13,600 kg/m3 and the density of air is 1.29 kg/m3. Using equations for pressure, velocity, and area, the air speeds in the wider and narrower sections are calculated to be 14.46 m/s and 1.61 m/s, respectively.
  • #1
happysmiles36
54
2

Homework Statement



Air is blown through a horizontal Venturi tube. The diameters of the narrow and wider sections of the tube are 1.0 cm and 3.0 cm respectively, and the height h of the mercury column is measured to be 1.00 mm. What are the air speeds in the wider and the narrower sections of the tube? The density of mercury is 13,600 kg/m3. (Assume the density of air is 1.29 kg/m3.)

Air is blowing through the wider section to the smaller section.

Homework Equations


p=rho
P1 + (1/2)(p)(v1)^2 + pgy1 = P2 + (1/2)(p)(v2)^2 + pgy2
A1v1=A2v2
P1 = Po + pgh
A(circle)=pi(r)^2

The Attempt at a Solution


Formulas:
y1=y2 so the pgy1 and pgy2 can cancel and v2=A1v1/A2
We can rearrange the equation to give:
P1-P2 = (1/2)(p)(v1)^2((A1/A2)^2-1)
v1=((P1-P2)/((1/2)(p)((A1/A2)^2-1))^(1/2)

P1-P2
Po +pgh1 - Po - pgh2
Change in pressure: pg(h1-h2)

v2=A1v1/A2

What we have:
r1= 3.0cm/2/100= 0.015m
r2= 1.0cm/2/100= 0.005m
(P1-P2)= change in pressure
change in height = 1.00mm/1000= 0.001m
p(mercury)= 13600kg/m^3
p(air)= 1.29kg/m^3

------------------------------------------------------------------

Change in pressure:
pg(h1-h2)

(13600kg/m^3)(9.8m/s^2)(0.001m)= 133.28pa

A1= (0.015m)^2(pi)= 7.068583471x10^-4 m^2
A2= (0.005m)^2(pi)= 7.853981634x10^-5 m^2

v1=((P1-P2)/((1/2)(p)((A1/A2)^2-1))^(1/2)

(133.28pa/(1/2)(1.29kg/m^3)((7.068583471x10^-4 m^2/7.853981634x10^-5 m^2)^2-1))^(1/2)
v1= 1.607154546 m/s

v2=A1v1/A2
(7.068583471x10^-4 m^2)(1.607154546 m/s)/(7.853981634x10^-5 m^2)
v2=14.46439092 m/s

I am not sure if I am even doing this right. :(
Sorry if formatting is hard to follow/ugly, I am still getting used to the new changes, don't know where everything is yet.
 
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  • #2
I think this is the correct answer, I was plugging in everything at once on my calculator and I might have been doing something wrong so I was getting a lot of different answers. But I'd still like this to be checked. :)

Edit: If the change in height was 2.66mm, would v1 and v2 be:

v1: 2.621065424 m/s
v2: 23.58958882 m/s

?
(Used same equations as above)
 
  • #3
Nvm, I am right, I don't think I've made any mistakes.
 

FAQ: What are the air speeds in a Venturi meter with varying tube diameters?

1. What is a Venturi Meter and how does it work?

A Venturi Meter is a device used to measure the speed of air flow. It consists of a converging section, a throat, and a diverging section. As air flows through the meter, it speeds up at the throat due to the decrease in cross-sectional area. This increase in speed is directly related to the pressure drop across the meter, which can be measured and used to calculate air speed.

2. What is the principle behind a Venturi Meter?

The principle behind a Venturi Meter is Bernoulli's principle, which states that as the speed of a fluid increases, the pressure decreases. This is due to the conservation of energy in a fluid system. As air speeds up at the throat of the meter, the pressure decreases, and this pressure drop can be measured and used to determine air speed.

3. What are the advantages of using a Venturi Meter for air speed measurement?

One advantage of using a Venturi Meter is its accuracy. It is a highly precise method for measuring air speed compared to other devices such as pitot tubes. Additionally, Venturi Meters are simple in design and do not require any external power source, making them reliable and cost-effective.

4. What are the limitations of a Venturi Meter?

One limitation of a Venturi Meter is that it can only measure the average air speed at a given point in the meter. It cannot provide information on fluctuations or turbulence in the air flow. Additionally, Venturi Meters have a limited range of measurement and may not be suitable for high-speed air flow.

5. How is a Venturi Meter calibrated?

A Venturi Meter can be calibrated by comparing its readings to those of a more accurate device, such as a pitot tube, in a controlled air flow environment. Adjustments can be made to the meter's design or calculations to improve its accuracy. Regular calibration is important to ensure the reliability of the meter's measurements.

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