Manometer water and mercury problem

In summary, the problem involves a mercury manometer attached to a pipe carrying argon. Water is spilled into the manometer and has a height of 20 cm. The pressure drop across the manometer is 101.3 kPa, with the mercury on the left lower than on the right. The goal is to find the difference in height for the mercury levels on either side of the manometer tube. The general manometer equation will be used to solve the problem.
  • #1
keishuu
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Homework Statement


Water is spilled into a mercury manometer that was being attached to a pipe carrying argon. The water has a height of 20 cm in the manometer and the pressure drop across the manometer is 101.3 kPa (mercury on left lower than on the right) What is the difference in height for the mercury levels on either side of the manometer tube?


Homework Equations


General manometer eq: P1+rho1*g*d1=p2+rho2*g*d2+rho(fluid)*g*h


The Attempt at a Solution


I'm really stuck. Does it matter what kind of manometer it is? Can someone help me start this problem out. Thank you so much.
 
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  • #2
Could someone please help me start this? Please.
 
  • #3


As a scientist, my first step would be to gather all the necessary information and understand the problem at hand. From the given information, we know that the manometer is attached to a pipe carrying argon and that water has been spilled into it, resulting in a height of 20 cm and a pressure drop of 101.3 kPa. We also know that the mercury levels on the left side are lower than on the right side.

Using the general manometer equation, we can set up the following equation:

P1 + ρ1*g*d1 = P2 + ρ2*g*d2 + ρ(fluid)*g*h

Where P1 and P2 are the pressures on either side of the manometer, ρ1 and ρ2 are the densities of mercury and argon respectively, d1 and d2 are the distances from the surface of the mercury to the top of the manometer on either side, and h is the difference in height between the mercury levels.

Since we are looking for the difference in height between the mercury levels, we can rearrange the equation to solve for h:

h = (P1 - P2 + ρ1*g*d1 - ρ2*g*d2) / (ρ(fluid)*g)

Now, we need to plug in the values we know. The pressure on the left side is atmospheric pressure (101.3 kPa), the pressure on the right side is the pressure of the argon in the pipe, and the density of water is 1000 kg/m^3. We also know that the distance between the surface of the mercury and the top of the manometer is 20 cm (0.2 m) on both sides.

So, our equation becomes:

h = (101.3 kPa - P2 + 13600 kg/m^3 * 9.8 m/s^2 * 0.2 m - ρ2*g*0.2 m) / (1000 kg/m^3 * 9.8 m/s^2)

We can now solve for h by plugging in the value for P2, which we do not know. Depending on the pressure of the argon in the pipe, the difference in height between the mercury levels will vary. So, it does matter what kind of manometer it is and what the pressure of the argon is.

I hope this helps you get started on the problem. Remember
 

1. What is a manometer?

A manometer is a scientific instrument used to measure the pressure of a gas or liquid. It typically consists of a U-shaped tube filled with a liquid, such as water or mercury, and a scale to measure the height of the liquid.

2. How does a manometer work?

A manometer works by balancing the pressure of a gas or liquid with the weight of a column of liquid in one arm of the U-shaped tube. The height of the liquid in the tube is directly proportional to the pressure being measured.

3. What is the difference between a manometer using water and one using mercury?

The main difference between a manometer using water and one using mercury is the density of the liquid. Mercury is much denser than water, so it can measure higher pressures and is less affected by changes in atmospheric pressure.

4. How do you solve a manometer water and mercury problem?

To solve a manometer water and mercury problem, you must first determine the difference in density between water and mercury, as well as the height of the liquid in each arm of the manometer. From there, you can use the pressure equation (P = ρgh) to calculate the pressure difference between the two arms.

5. What are some common uses for manometers?

Manometers are commonly used in various industries, such as HVAC, automotive, and medical, to measure and monitor pressure in systems. They are also used in scientific experiments, such as measuring blood pressure in humans and animals.

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