Manometer tube – problems and solutions

Manometer tube – problems and solutions

1. A manometer tube is filled with two type of liquids. The density of liquid 1 is ρ₁ = 0.8 g.cm^-3, and the density of liquid 2 is ρ₂ = 1 g.cm^-3, and height h₁ = 10 cm, then what is the height of h₂.

Known :

Density of liquid 1 = 0.8 g.cm^-3

Density of liquid 2 = 1 g.cm^-3

Height 1 = 10 cm

Wanted: Height 2

Solution :

2. The height of the water is 50 cm, and the height of another liquid is 30 cm. What is the density of another liquid?

Known :

Acceleration due to gravity (g) = 10 m/s²

The height of water (h₁) = 50 cm

Density of water (ρ₁) = 1.00 x 10³ kg/m³ = 1000 kg/m³

Height of another liquid (h₂) = 30 cm

Wanted : The density of another liquid.

Solution :

pa + ρ₁ g h₁ = pa + ρ₂ g h₂

1. What is a manometer? Answer: A manometer is a device used to measure the pressure of gases and liquids. It typically measures the pressure difference between a fluid inside the manometer and the surrounding atmosphere or another fluid.
2. How does a simple U-tube manometer work? Answer: A U-tube manometer works based on balancing the pressure exerted by a column of liquid against the pressure of the fluid being measured. If there is a difference in pressure, the liquid column will move to a new position, and the height difference can be used to determine the pressure difference.
3. What are the common fluids used in manometers? Answer: Common manometric fluids include mercury, water, and oil. The choice of fluid depends on the application, desired sensitivity, and the range of pressures to be measured.
4. Why is mercury often used in manometers despite its toxicity? Answer: Mercury is dense and has a high specific weight, which allows for shorter column heights and smaller manometer designs for the same pressure difference. It also does not wet glass, making readings more accurate. However, its toxic nature requires careful handling and consideration for environmental safety.
5. What is the difference between an open manometer and a closed manometer? Answer: An open manometer has one end open to the atmosphere, and it measures the pressure difference between the fluid being tested and atmospheric pressure. A closed manometer, on the other hand, has one end sealed, often with a vacuum or a known reference pressure, and it measures the absolute pressure of the fluid.
6. How can a manometer be used to measure velocity? Answer: Using the principle of Bernoulli’s equation and the Pitot-static tube, the dynamic pressure (related to velocity) and static pressure can be measured. The height difference in the manometer corresponds to the dynamic pressure, which can be converted to velocity.
7. Why is it important for the manometer tube to be vertical during measurements? Answer: Keeping the manometer tube vertical ensures that the weight of the manometric fluid acts directly downward, and the height of the fluid column directly represents the pressure difference. Any tilt can introduce errors in the reading.
8. How does a differential manometer differ from a simple U-tube manometer? Answer: A differential manometer is designed to measure the difference in pressure between two points in a fluid system, whereas a simple U-tube manometer often measures the pressure difference between a fluid and the atmosphere.
9. What are the limitations of using a manometer? Answer: Manometers are gravity-dependent instruments, so they must remain vertical. They might not be suitable for very high-pressure measurements (depending on the manometric fluid used), and they can be sensitive to temperature changes which can affect fluid density.

10. What is a “well-type” manometer? Answer: A well-type manometer has one leg with a larger diameter called the “well.” The fluid in this well doesn’t rise or fall significantly with pressure changes, making the reading dependent only on the height change in the narrower leg. This design increases the sensitivity and readability of the manometer.