Why is the pressure of two different liquids in a manometer the same?

In summary, the conversation discussed the use of a u-shaped tube or manometer to find the height of a substance, specifically oil, when added to one side. The formula used was P(water) = P(oil), or (ϱwater)gh = (ϱoil)gh. The speaker mentioned understanding how to solve the problem but not fully comprehending why the pressure of both substances is equal. They also asked for clarification on what happens at the bottom of the U-tube when there is a difference in pressure between the two sides.
  • #1
cherryrocket
19
0
I just finished a question in which a u-shaped tube (manometer) is filled with water to a certain height. Another substance, in this instance, oil, is added to one side of the manometer. I was asked to find the height of the new substance. I used the formula P(water) = P(oil), or
(ϱwater)gh = (ϱoil)gh. So, I know how to solve it, but I don't really understand it. Why is the pressure of both substances the same? Thanks for your replies.
 
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  • #2
Think about what happens at the bottom of the U-tube. What happens if the pressure on one side is greater than the pressure on the other at the bottom?
 
  • #3


The pressure of two different liquids in a manometer is the same because of the principle of hydrostatics, which states that the pressure at any point in a fluid is the same in all directions. In this case, the pressure at the bottom of the manometer is equal to the pressure at the top.

When the manometer is filled with water and oil, the two liquids will seek to reach the same level in each side of the tube. This is because the pressure at the bottom of the tube is determined by the weight of the liquid above it, which is the same for both liquids.

In other words, the pressure of each liquid is determined by its density and height, and since both liquids are at the same height, their pressures must be equal. This is why the formula (ϱwater)gh = (ϱoil)gh can be used to find the height of the new substance.

Overall, the pressure of two different liquids in a manometer is the same because of the principles of hydrostatics and the equal distribution of pressure in a fluid.
 

1. Why do we use a manometer to measure pressure?

A manometer is a device that measures the difference in pressure between two fluids. It is commonly used in scientific experiments and industrial processes to accurately measure pressure changes. By using a manometer, we can determine the pressure of a liquid or gas, which is important for understanding its behavior and properties.

2. How does a manometer work?

A manometer works by balancing the pressure of a known fluid against the pressure of an unknown fluid. The two fluids are connected through a U-shaped tube, with one side containing the unknown fluid and the other side containing the known fluid. As the pressure of the unknown fluid changes, it will cause the known fluid to move up or down the tube. By measuring the difference in height between the two fluids, we can calculate the pressure of the unknown fluid.

3. Why is the pressure of two different liquids in a manometer the same?

In a manometer, the pressure of the two different liquids will be the same because they are connected and in equilibrium. This means that the pressure exerted by one fluid on the other will be equal and opposite, resulting in a balanced system. Therefore, the pressure of the unknown fluid can be determined by measuring the pressure of the known fluid.

4. Can a manometer measure the pressure of any fluid?

Yes, a manometer can measure the pressure of any fluid, whether it is a liquid or a gas. However, the type of manometer used may vary depending on the properties of the fluid being measured. For example, a U-tube manometer is suitable for measuring low pressures, while an inclined manometer may be used for higher pressures.

5. How is the pressure read from a manometer?

The pressure is read from a manometer by measuring the height difference between the two fluids in the tube. This height difference is then used to calculate the pressure of the unknown fluid using the equation P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height difference between the two fluids.

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