Chapter 2, Problem 2.8P

(a)

Interpretation Introduction

Interpretation:

The pressure drop in a U-tube manometer across an air-filter is to be calculated in appropriate units.

Concept Introduction:

The pressure drop across the two points A and B of the U-tube manometer is given as,

  ${\text{P}}_{\text{A}}\text{-}{\text{P}}_{\text{B}}\text{=}\frac{\text{g}}{{\text{g}}_{\text{c}}}{\text{R}}_{\text{m}}{\text{(ρ}}_{\text{A}}\text{-}{\text{ρ}}_{\text{B}}\text{)}\mathrm{.......}\text{(1)}$

The notations used in the above equation are,

  ${\text{P}}_{\text{A}}\text{-}{\text{P}}_{\text{B}}\text{=}\text{Pressure}\text{difference}\text{at}\text{points}\text{A}\text{and}\text{B}\text{or}\text{Pressure}\text{drop}$

  $\begin{array}{l}{\text{ρ}}_{\text{A}}\text{=}\text{Density}\text{of}\text{water}\\ {\text{ρ}}_{\text{B}}\text{=}\text{Density}\text{of}\text{air}\\ \frac{\text{g}}{{\text{g}}_{\text{c}}}\text{=}\text{1}\\ {\text{R}}_{\text{m}}\text{=}\text{Manometer}\text{Reading}\end{array}$

(b)

Interpretation Introduction

Interpretation:

The percentage error if air is not considered is to be determined.

Concept Introduction:

The error is the difference between the pressure drop at 2 different conditions and the percentage error is given as,

  $\text{\%}\text{Error}\text{=}\frac{\text{Difference}\text{in}\text{Pressure}\text{drop}\text{at}\text{2}\text{different}\text{conditions}}{\text{Initial}\text{Pressure}\text{drop}}\text{×100}\mathrm{.......}\text{(3)}$