Solving a Venturi Device for Height of Mercury Rise

AI Thread Summary
The discussion centers on calculating the height of mercury rise in a Venturi device with diameters of 4mm and 2cm, and air entering at a flow rate of 1200cm^3/m. Initial calculations yielded unreasonably high velocities of 954925m/s and 38197m/s, leading to an incorrect mercury height of around 400000m. The user identified a conversion error in changing cm^3 to m^3, which contributed to the inaccuracies in their results. The next steps involve correctly applying Bernoulli's equation with accurate values to determine the correct height of mercury rise.
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A Venturi device has a diameter of 4mm at one end and a diameter of 2cm at the other. Air enters at 1200cm^3/m. Mercury is in the botom of the device. Assuming mercury's density to be 13700kg/m^3, and air's density to be 1.2kg/m^3, find how high the mercury rises. Assume air to be an ideal fluid.

I got ridiculously large numbers for this.

Q=Av

12m^3/s=pi(0.002^2)v

v=954925m/s

This is outrageously fast, and I did the same calculation for the other end and got 38197m/s, using a 1cm radius.

I don't think this is quite right. Are these velocities correct? The next tep is to plug the velocities into Bernoulli's equation:

(Mercury's density)(g)(h)=(0.5)(density of air)(v2^2-v1^2)

And solve for v, but I got around 400000m for the answer. I know it is incorrect.

Am I doing something wrong here?
 
Physics news on Phys.org
I found out that I was converting the cm^3 to m^3 wrong. I calculated the height of the mercury in the tube to be 4.1, and it is wrong according to MasteringPhysics.
 
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