# Manometer containing two liquids

• Guillem_dlc
In summary, the given conversation discusses the use of the ideal gas law to solve for two unknown variables in a system involving pressure and density. The formula for pressure is given in terms of atmospheric pressure and the density of the gas in question. The conversation also introduces the concept of loops, where pressure differentials can be calculated using the ideal gas law. Ultimately, the conversation concludes with a formula for solving for the unknown variables in the system.
Guillem_dlc
Homework Statement
The manometer in the figure contains two liquids A and B arranged as shown. Between the two liquids there is an area containing air. If the relative pressure of liquid A is ##p_A^r=-0,11\, \textrm{at}## and its relative density is ##\rho_A^r=1,6##, calculate the relative density ##\rho_B^r## of liquid B.

Solution: ##\rho_B=1##.
Relevant Equations
Equations of loops
Figure:

$$p_A^r=-0,11\, \textrm{at}\rightarrow p_A=90534\, \textrm{Pa}$$
$$\rho_A^r=1,6\rightarrow \rho_A=\rho_{AR}\cdot \rho_{H2O}=1600\, \textrm{kg}/\textrm{m}^3$$
$$\rho_1=1,225\, \textrm{kg}/\textrm{m}^3$$
$$\left. \begin{array}{l} \textrm{LOOP I}\rightarrow p_A-p_1=-\rho_A (Z_A-Z_1) \\ \textrm{LOOP II}\rightarrow p_1-p_2=-\rho_1(Z_1-Z_2) \\ \textrm{LOOP III}\rightarrow p_2-p_B=-\rho_B(Z_2-Z_B) \end{array}\right\} \rightarrow$$
$$\rightarrow p_A-p_B=-\rho_A(Z_A-Z_1)-\rho_1(Z_1-Z_2)-\rho_B(Z_2-Z_B)\rightarrow$$
$$\rightarrow 90534-p_B=-720+0,833-\rho_B 0,38=-719,167-0,38\rho_B$$
In this exercise I am stuck because I don't know how to find the two missing unknowns.

I have already found the solution, thank you!

Lnewqban

## 1. How does a manometer containing two liquids measure pressure?

A manometer containing two liquids measures pressure by using the difference in height between the two liquids. This difference in height is directly proportional to the pressure being measured.

## 2. What are the two liquids typically used in a manometer?

The two liquids typically used in a manometer are mercury and water. Mercury is used in the longer arm of the manometer due to its higher density, while water is used in the shorter arm.

## 3. How is the pressure calculated using a manometer containing two liquids?

The pressure is calculated by using the formula P = ρgh, where P is the pressure, ρ is the density of the liquid, g is the acceleration due to gravity, and h is the difference in height between the two liquids.

## 4. What are the advantages of using a manometer containing two liquids?

One advantage of using a manometer containing two liquids is that it can measure both low and high pressures accurately. Additionally, it is a simple and inexpensive device that is easy to use.

## 5. What are some common applications of a manometer containing two liquids?

A manometer containing two liquids is commonly used in industries such as chemical, pharmaceutical, and oil and gas to measure pressure in various processes. It is also used in laboratory experiments and in HVAC systems to measure air pressure.