# Determining Height of Mercury in U-tube: Air Flow Rate of 1200 cm^3/s

• asdifnlg
In summary, the conversation is discussing the calculation of the height of mercury in a U-tube using Bernoulli's equation and different densities for air and mercury. After realizing that the wrong densities were used, the correct answer was obtained. The conversation also mentions reliance on Google for constants due to not having a physics book at home.
asdifnlg
Ok, Air flows through this tube at a rate of 1200 cm^3/s. Assume that air is an ideal fluid.
What is the height h of mercury in the right side of the U-tube?
Here's a picture:
http://session.masteringphysics.com/problemAsset/1001181/6/knight_Figure_15_64.jpg

First, I found the velocity of the air in the 2 cm and 4 mm tube.
In m/s, for the 2cm, i came up with 1200/(1000000pi(.01^2))
and for the 4mm 1200/(1000000pi(.002^2))
Then, I plugged it into bernoulli's equation, with the density of air as 1.2 kg/m^3. This gave the 2cm tunnel to have 5462.5 less pascals than the other 4 mm tube.
Then, using 13540 for the kg/m^3 of Hg, and setting the pressures of the two sides equal, I came up with:
5462.5 = 13540 (9.8) (h), which gave me h= .0412 m, or 4.12 cm, which is wrong. Anybody know what I did wrong?

I'm not seeing a problem with what you did. Do you know the answer that is expected?

I wish I knew the answer that is expected :P Do you know if those are the right densities I used in kg/m^3?

Found out I was using the wrong densities ^^ I used 1.3 kg/m^3 for air and 13700 for Hg and got the right answer. My physics book is too big to bring home, so I rely on google for my constants :(

## 1. How is the height of mercury determined in a U-tube?

The height of mercury in a U-tube is determined by measuring the difference in levels between the two arms of the tube. This is known as the manometer reading.

## 2. What is the purpose of measuring the air flow rate in this experiment?

The air flow rate is measured in order to determine the pressure difference between the two arms of the U-tube. This pressure difference is directly related to the height of mercury in the tube.

## 3. Why is the air flow rate set at 1200 cm^3/s?

The air flow rate is set at 1200 cm^3/s in order to maintain a constant and consistent pressure difference between the two arms of the U-tube. This allows for accurate measurements of the height of mercury.

## 4. How does the height of mercury in the U-tube affect the air flow rate?

The height of mercury in the U-tube does not directly affect the air flow rate. However, the air flow rate will change depending on the pressure difference between the two arms of the tube, which is influenced by the height of mercury. A higher height of mercury will result in a higher pressure difference and therefore a higher air flow rate.

## 5. What are the potential sources of error in determining the height of mercury in a U-tube?

Potential sources of error in this experiment include air leaks in the apparatus, inaccurate measurement of the air flow rate, and variations in the density of the mercury. It is important to ensure the apparatus is properly sealed and calibrated for accurate results.

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