Chapter 8, Problem 8.8P

Interpretation Introduction

Interpretation: The flow rate and power consumption across a Venturi meter is to be calculated.

Concept introduction: A Venturi meter is a type of flow meter used to measure the flow rate of the fluid. It measures the flow rate by pressure drop in the cone of the meter. The pressure is recovered later due to decrease in the velocity of fluid.

The pressure drop in the Venturi meter 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,

  $\begin{array}{l}{\text{p}}_{\text{a}}\text{=}\text{Pressure}\text{at}\text{inlet}\text{of}\text{cone}\\ {\text{p}}_{\text{b}}\text{=}\text{Pressure}\text{at}\text{discharge}\text{end}\text{of}\text{cone}\\ \text{g}\text{=}\text{Acceleration}\text{due}\text{to}\text{gravity}\\ {\text{R}}_{\text{m}}\text{=}\text{Manometer}\text{Reading}\\ {\text{ρ}}_{\text{m}}\text{=}\text{Density}\text{of}\text{mercury}\\ \text{ρ}\text{=}\text{Density}\text{of}\text{water}\end{array}$

The flow rate of the fluid around venturi is,

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

The notations used here are,

  $\begin{array}{l}{\text{C}}_{\text{V}}\text{=}\text{0}\text{.98}\text{=}\text{Venturi}\text{coefficient}\\ {\text{S}}_{\text{b}}\text{=}\text{Area}\text{of}\text{throat}\text{=}\frac{\text{π}}{\text{4}}{\text{D}}_{\text{b}}{}^{\text{2}}\\ \text{β}\text{=}\frac{{\text{D}}_{\text{b}}}{{\text{D}}_{\text{a}}}\\ {\text{D}}_{\text{a}}\text{=}\text{Diameter}\text{of}\text{pipeline}\\ {\text{D}}_{\text{b}}\text{=}\text{Diameter}\text{of}\text{throat}\end{array}$

The power loss in Venturi is given as,

  $\text{P}\text{=}{\text{(p}}_{\text{a}}{\text{-p}}_{\text{b}}\text{)×Q}\mathrm{.......}\text{(3)}$

P is the power loss