# Calculating Mercury Column Height in J-Shaped Tube: Manometry Homework Solution

• Queren Suriano
In summary, the problem involves a J-shaped tube filled with air and mercury, with a uniform cross section. The pressure at point 1 (the top of the air column in the left arm) is equal to the atmospheric pressure plus the product of air density, gravity, and the height of the air column (0.25 m). The pressure at point 2 (the top of the mercury column in the right arm) is equal to the atmospheric pressure plus the product of mercury density, gravity, and the height of the mercury column (2.25 m minus the height of the air column). The problem can be solved using the ideal gas law to relate the final pressure of the air to the initial (atmospheric) pressure in the

## Homework Statement

A J-shaped tube has an uniform cross section and it contains air to atmosphere pression of 75 cmo of Hg. It is pours mercury in the right arm, this Compress the closed air in the left arm. Which is the heigh of the mercury's column in left arm when the right arm is full of mercury? Consider that in every moment temperature is constant and that the air is an ideal gas. Consider h1 = 0.25m and h2 = 2.25m

2. Relevant equations

P= Patm + density*g*h
P1*V1 = P2*V2

## The Attempt at a Solution

I have equalized the pressure at point 1 with the pressure at point 2, and this looks like this:
Pressure at point 1 = Air density * gravity * (0.25-h)
Pressure at point 2 = Atmospheric pressure + mercury density * gravity* (2.25-h)

The atmospheric pressure I suppose is 75 cm Hg.

From previous equations I would solve for "h"

My question is if the approach is right? and how I could consider the density of the air?

Could I solve the problem by applying theory of ideal gases? thanks for your help

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Yes, you can use the ideal gas law, but you have to make some assumptions about how the mercury fills the tube. I suspect the amount of air trapped in the left arm originally occupied the entire left arm at atmospheric pressure. Your diagram does not show what h1 and h2 are. I assume they are the height of the mercury columns in the two arms. Correct?

Queren Suriano
kuruman said:
Yes, you can use the ideal gas law, but you have to make some assumptions about how the mercury fills the tube. I suspect the amount of air trapped in the left arm originally occupied the entire left arm at atmospheric pressure. Your diagram does not show what h1 and h2 are. I assume they are the height of the mercury columns in the two arms. Correct?
NEW
Kuruman thank you for your answer. h1 and h2 are the length of left and right arm respectively. So, how can I solve the problem with ideal gas law? thank you

Queren Suriano said:
NEW
Kuruman thank you for your answer. h1 and h2 are the length of left and right arm respectively. So, how can I solve the problem with ideal gas law? thank you
So you are saying that the left arm has length ##y## of air and length ##h_1-y## of mercury and the right arm has length ##h_2## of mercury. Correct?
You can use the ideal gas law to relate the final pressure of the air to the initial (atmospheric) pressure in the left arm. Note that the volume is proportional to the cross sectional area which does not change when the arm is partially filled with mercury.

So I can write Patm hinitial = P2 (0.25-h) where h is the heigh of compressed air. Me doubt is what is hinitial? Can I Convert the 75cm Hg to cm of air?

Queren Suriano said:
Me doubt is what is hinitial?
Did you not tell me in post #3 that hinitial is the length of the left arm, 0.25 m?

kuruman said:
Did you not tell me in post #3 that hinitial is the length of the left arm, 0.25 m?
Ok, thank you. So, am I saying something right if I said that P1 = Patm + air density * gravity* h1? Or could I assume that the P1 = Patm?

I think it is safe to assume that p1 = patm.

## 1. What is manometry?

Manometry is a diagnostic test used to measure muscle or organ function in the body, specifically in the digestive system. It involves inserting a small, flexible tube into the body and measuring pressure changes in different areas. This helps doctors diagnose conditions such as acid reflux, difficulty swallowing, and certain types of muscle disorders.

## 2. How is manometry performed?

During a manometry test, a thin tube with sensors is inserted through the nose or mouth and down into the esophagus or other area being tested. The patient will be asked to swallow, breathe, or perform other actions while the sensors measure the pressure. The test usually takes about 30 minutes to an hour and is generally painless.

## 3. What can manometry diagnose?

Manometry can diagnose a variety of conditions related to muscle or organ function in the digestive system. These include acid reflux, achalasia (difficulty swallowing), gastroparesis (delayed stomach emptying), and certain types of muscle disorders such as esophageal spasm or Hirschsprung's disease.

## 4. Are there any risks or side effects associated with manometry?

Manometry is generally considered a safe and low-risk procedure. However, some patients may experience mild discomfort or gagging during the insertion of the tube. In rare cases, the tube may cause a nosebleed or irritation in the throat. Infection is also a possible but uncommon risk.

## 5. How should I prepare for a manometry test?

Before a manometry test, your doctor will likely advise you to avoid eating or drinking for a certain amount of time to ensure accurate results. You may also need to stop taking certain medications that can affect muscle function. It's important to follow your doctor's instructions carefully to ensure the best possible results from the test.