Chapter 8, Problem 8.6P

Interpretation Introduction

Interpretation: The flow rate through anOrifice meter for a particular manometer reading is to be calculated.

Concept introduction:AnOrifice meter is a type of flow meter used to measure the flow rate of the fluid. It measures the flow rate by decreasing the cross-section of the flowing stream as it passes through the orifice and thus increases the velocity head at the expense of pressure head and this reduction in pressure is measured by the manometer attached to the orifice. It is given as,

  ${\text{p}}_{\text{a}}\text{-}{\text{p}}_{\text{b}}\text{=}{\text{gR}}_{\text{m}}{\text{(ρ}}_{\text{m}}\text{-ρ)}\mathrm{.......}\text{(1)}$

The notations used here are,

  $\begin{array}{l}{\text{p}}_{\text{a}}\text{-}{\text{p}}_{\text{b}}\text{=}\text{Pressure drop across the manometer in the orifice}\\ \text{g}\text{=}\text{Acceleration}\text{due}\text{to}\text{gravity}\\ {\text{R}}_{\text{m}}\text{=}\text{Manometer}\text{Reading}\\ {\text{ρ}}_{\text{m}}\text{=}\text{Density}\text{of}\text{mercury}\\ \text{ρ}\text{=}\text{Density}\text{of}\text{water}\end{array}$

The flow rate of the fluid around the Orifice meter is,

  $\text{Q}\text{=}\frac{{\text{C}}_{\text{0}}{\text{S}}_{\text{b}}}{\sqrt{{\text{1-β}}^{\text{4}}}}\sqrt{\frac{{\text{2(p}}_{\text{a}}{\text{-p}}_{\text{b}}\text{)}}{\text{ρ}}}\mathrm{.......}\text{(2)}$

The notations used here are,

  $\begin{array}{l}{\text{C}}_{\text{0}}\text{=}\text{0}\text{.61}\text{=}\text{Venturi}\text{coefficient}\\ {\text{S}}_{\text{b}}\text{=}\text{Area}\text{of}\text{throat}\text{=}\frac{\text{π}}{\text{4}}{\text{D}}_{\text{b}}{}^{\text{2}}\\ \text{β}\text{=}\frac{{\text{D}}_{\text{b}}}{{\text{D}}_{\text{a}}}\\ {\text{D}}_{\text{a}}\text{=}\text{Diameter}\text{of Orifice}\\ {\text{D}}_{\text{b}}\text{=}\text{Diameter}\text{of}\text{throat}\end{array}$