Math Problem Statement

Kerosene flows in a pipe to which is connected a differential manometer as shown in the figure. Water is used as the indicating fluid and the water level below the centreline of the pipe is 570 mm at position 1 and 350 mm at position 2. Determine the pressure difference between position 1 and 2. Assume the relative density of kerosene is 0.78.

Solution

To determine the pressure difference between positions 1 and 2 in a pipe using a differential manometer filled with water, we need to apply the principles of fluid mechanics, specifically using the hydrostatic pressure difference.

Given Data:

  • Height difference at position 1: h1=570mm=0.570mh_1 = 570 \, \text{mm} = 0.570 \, \text{m}
  • Height difference at position 2: h2=350mm=0.350mh_2 = 350 \, \text{mm} = 0.350 \, \text{m}
  • Relative density of kerosene: ( \text{RD}_{\text{kerosene}} = 0.78 \

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Math Problem Analysis

Mathematical Concepts

Fluid Mechanics
Hydrostatics
Pressure Difference

Formulas

Pressure difference formula: ΔP = ρ_water * g * (h1 - h2) - ρ_kerosene * g * (h1 - h2)
ρ = RD * ρ_water (to calculate kerosene density)

Theorems

Hydrostatic Pressure Law
Relative Density Formula

Suitable Grade Level

Grades 11-12, College Level