Solving a Venturi Device for Height of Mercury Rise

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SUMMARY

The discussion focuses 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 1200cm³/m. The user initially calculated velocities of 954925m/s and 38197m/s, which are unreasonably high. The correct approach involves applying Bernoulli's equation, where the user mistakenly converted volume units, leading to an incorrect mercury height calculation of 4.1m. The discussion highlights the importance of accurate unit conversion and proper application of fluid dynamics principles.

PREREQUISITES
  • Understanding of fluid dynamics principles, specifically Bernoulli's equation.
  • Familiarity with the Venturi effect and its applications.
  • Knowledge of unit conversion between cubic centimeters and cubic meters.
  • Basic grasp of density and its role in fluid calculations.
NEXT STEPS
  • Review Bernoulli's equation and its applications in fluid mechanics.
  • Learn about the Venturi effect and its implications in real-world scenarios.
  • Practice unit conversion techniques, particularly for fluid volume measurements.
  • Explore the concept of ideal fluids and their properties in fluid dynamics.
USEFUL FOR

Students and professionals in engineering, physics, and fluid mechanics who are working with fluid dynamics calculations and applications involving the Venturi effect.

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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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