Solving a Venturi Device for Height of Mercury Rise

[laminar]

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?

 

[laminar]

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.

 

[kyle8921]

I would first check my calculations to make sure I didn't make any mistakes in my conversions or equations. I would also double-check the given values for density and air flow rate to ensure they are accurate.

If my calculations still resulted in extremely high velocities, I would consider the possibility that the assumptions made in the problem may not be entirely accurate. For example, air may not behave as an ideal fluid in this scenario, and there could be other factors at play that affect the flow of air and mercury in the Venturi device.

I would also consider the limitations of the Venturi effect and how it may not accurately predict the height of the mercury rise in this specific device. There may be other variables at play that need to be taken into account, such as the shape and design of the device.

In conclusion, while the calculations may seem off, it is important to thoroughly examine all factors and assumptions before determining the accuracy of the results. Further experimentation and analysis may be needed to fully understand the behavior of the Venturi device and the height of the mercury rise.