# Find out the correct pressure difference if the level of the liquid

• zorro
In summary, the question asks for the correct pressure difference in a manometer with uniform capillary tubes of different radii, given the density and surface tension of the liquid. The difference in liquid levels is due to the pressure difference caused by the liquid and surface tension. The correct pressure difference can be calculated using the equation ρ*g*h = 0.2 - 2*T/ρ*g*r, where ρ is the density, g is the acceleration due to gravity, h is the difference in liquid levels, T is the surface tension, and r is the radius of the narrower tube. The only error in the measurement is due to surface tension.
zorro

## Homework Statement

The limbs of a manometer consist of uniform capillary tubes of radii 1.4 x 10^-3 m and 7.2 x 10^-4 m. Find out the correct pressure difference if the level of the liquid (density 10^3 kg/m^3 and surface tension 72 x 10^-3 N/m) in narrower tube stands 0.2 m above that in the broader tube.

## The Attempt at a Solution

Please explain me the meaning of this question. Why is there a false pressure difference?
The manometer measures the pressure of a gas. So it ought to show the correct pressure.

The difference between the liquid levels is due to pressure difference due to the liquid and surface tension.
So 0.2 m = ρ*g*h + 2*T/ρ*g*r.

Hence correct pressure difference = ρ*g*h = 0.2 - 2*T/ρ*g*r.

so the only error is due to surface tension?

so the only error is due to surface tension?

Yes.

What is the significance of the liquid level in this scenario?The question is asking for the correct pressure difference between the two tubes of the manometer, given the specific dimensions and properties of the tubes and the liquid being used. The significance of the liquid level is that it is used to measure the pressure difference between the two tubes. The manometer works by balancing the pressure of the gas being measured with the pressure of the liquid in the tubes. The difference in the level of the liquid in the two tubes indicates the pressure difference between them.

As for the false pressure difference, it is possible that the measurements or calculations used to determine the pressure difference may not be accurate, leading to an incorrect value. This could be due to errors in measurement, assumptions made in the equations used, or other factors. It is important for scientists to carefully consider and verify their results to ensure accuracy and avoid false conclusions.

## 1. What is the formula for calculating pressure difference in a liquid?

The formula for pressure difference in a liquid is ΔP = ρgh, where ΔP is the pressure difference, ρ is the density of the liquid, g is the gravitational acceleration, and h is the height or depth of the liquid.

## 2. How do you measure the level of a liquid in a container?

The level of a liquid in a container can be measured using a ruler, measuring tape, or a graduated cylinder. Alternatively, you can use a pressure sensor to measure the pressure at the bottom of the container and calculate the liquid level using the formula ΔP = ρgh.

## 3. What is the unit of measurement for pressure difference in a liquid?

The unit of measurement for pressure difference in a liquid is usually expressed in Pascals (Pa) or Newtons per square meter (N/m^2). However, it can also be measured in other units such as pounds per square inch (psi) or millimeters of mercury (mmHg).

## 4. How does the level of a liquid affect the pressure difference?

The pressure difference in a liquid is directly proportional to the height or depth of the liquid. This means that as the level of the liquid increases, the pressure difference also increases. Similarly, as the level of the liquid decreases, the pressure difference decreases.

## 5. Are there any factors that can affect the accuracy of calculating pressure difference in a liquid?

Yes, there are several factors that can affect the accuracy of calculating pressure difference in a liquid. These include temperature, density of the liquid, atmospheric pressure, and the presence of any impurities or air bubbles in the liquid. It is important to control these factors in order to obtain accurate pressure difference measurements.

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