Double-Fluid Manometer for Pressure Difference Measurement

The double-fluid manometer is a device used to measure pressure differences between two points in a system. It consists of a U-shaped tube filled with two different fluids, each with a different specific gravity. The pressure difference between the two points is determined by measuring the difference in height of the two fluid columns.

Calculation of Pressure Difference

To calculate the pressure difference ΔP = PB – PA between the oil pipe and water pipe using the given fluid heights and specific gravities, follow the steps below:

1. Determine the pressure due to the weight of the oil column.

Pressure due to the weight of the oil column = ρoil × g × h1

Where,
ρoil = Specific gravity of oil = 0.85
g = Acceleration due to gravity = 9.81 m/s²
h1 = Height of the oil column = 100 mm

Substituting the given values, we get:

Pressure due to the weight of the oil column = 0.85 × 9.81 × 0.1 = 0.834 kPa

2. Determine the pressure due to the weight of the water column.

Pressure due to the weight of the water column = ρwater × g × h2

Where,
ρwater = Specific gravity of water = 1
h2 = Height of the water column = 150 mm

Substituting the given values, we get:

Pressure due to the weight of the water column = 1 × 9.81 × 0.15 = 1.4715 kPa

3. Calculate the pressure difference.

Pressure difference = PB – PA = (Pressure due to the weight of the water column) - (Pressure due to the weight of the oil column)

Substituting the calculated values, we get:

Pressure difference = 1.4715 - 0.834 = 0.6375 kPa

Therefore, the pressure difference between the oil pipe and water pipe is 0.6375 kPa.

Explanation

The double-fluid manometer works on the principle of Pascal’s law, which states that the pressure at any point in a fluid is transmitted equally in all directions. In this case, the pressure difference between the oil pipe and water pipe causes the fluid levels in the manometer to change. The difference in height of the fluid columns is proportional to the pressure difference between the two points. By measuring the heights of the fluid columns and knowing the specific gravities of the fluids, the pressure difference can be calculated using the above formulae.