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

AI Thread Summary
To calculate the air speeds in a Venturi tube, the conservation of fluid mass and Bernoulli's principle are applied. Given the diameters of the tube's sections and the height of the mercury column, the areas of the entrance and exit are calculated using the formula A = πr². The relationship A1v1 = A2v2 is used to find the velocities in both sections, where A1 and A2 are the cross-sectional areas. The pressure difference created by the mercury column height is also factored into the calculations. Accurate area calculations are essential for determining the correct air speeds in the tube.
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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
 
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What's the matter? Is your calculator broken? At least calculate the areas of the entrance and the exit of the venturi.
 
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