Calculating Air Speeds in a Venturi Tube Using Conservation of Fluid Mass

In summary, the problem involves determining the air speeds in the wider and narrower sections of a circular and horizontal Venturi tube. The height of the mercury column is given as 1.00 mm, and the density of mercury and air are also provided. The relevant equations are the continuity equation and the Bernoulli's equation. The areas of the entrance and exit of the venturi are calculated using the given diameters.
  • #1
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Homework Statement



Air is blown through a circular and horizontal Venturi tube, as shown in the figure below. The diameters of the narrow and wider sections of the tube are given, 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.)

http://www.webassign.net/hawkpse1/12-figure-058.gif

Homework Equations


P + 1/2pv^2 + pgh = constant

A1v1 = A2v2

The Attempt at a Solution



A1= pi*2.25e-4
A2= pi*2.5e-5
 
Last edited:
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  • #2
What's the matter? Is your calculator broken? At least calculate the areas of the entrance and the exit of the venturi.
 

FAQ: Calculating Air Speeds in a Venturi Tube Using Conservation of Fluid Mass

What is Conservation of Fluid Mass?

Conservation of fluid mass is a fundamental principle in fluid mechanics that states that the total mass of a closed system of fluid remains constant over time, regardless of any changes in pressure, temperature, or velocity.

Why is Conservation of Fluid Mass important?

Conservation of fluid mass is important because it helps us understand and predict the behavior of fluids, such as water and air, in various systems. It is also a key principle in many engineering and environmental applications, such as designing efficient pipelines and managing water resources.

How is Conservation of Fluid Mass calculated?

The conservation of fluid mass is calculated using the continuity equation, which states that the rate of change of mass within a closed system is equal to the net flow of fluid into or out of the system. This equation takes into account the density, velocity, and cross-sectional area of the fluid flow.

What factors can affect Conservation of Fluid Mass?

The conservation of fluid mass can be affected by changes in temperature, pressure, and velocity of the fluid. External forces, such as gravity and friction, can also impact the mass of fluid within a system.

How is Conservation of Fluid Mass applied in real-life situations?

Conservation of fluid mass is applied in various real-life situations, such as designing and operating pipelines, pumps, and turbines. It is also used in environmental management to understand and control the movement of pollutants in water and air. Additionally, conservation of fluid mass is essential in weather forecasting and studying the flow of blood and other bodily fluids in medical applications.

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