Chapter 6, Problem 6.11P

Interpretation Introduction

Interpretation: Diameter of throat of the Venturi meter is to be calculated with the given conditions of flow and inlet diameter.

Concept introduction: A Venturi meter is a device used to measure the flow of a fluid through the pipes and is based on the principle of Bernoulli’s equation in which the sum of Potential energy, Kinetic energy and Pressure energy is constant. The Bernoulli equation across 2 points of any system is given by:-

$\frac{{\text{P}}_{\text{1}}}{\text{ρ}}\text{+}\frac{{\text{v}}_{\text{1}}{}^{\text{2}}}{\text{2}}{\text{+ gZ}}_{\text{1}}\text{=}\frac{{\text{P}}_{\text{2}}}{\text{ρ}}\text{+}\frac{{\text{v}}_{\text{2}}{}^{\text{2}}}{\text{2}}{\text{+ gZ}}_{\text{2}}$ ........... (1)

P₁ and P₂ are pressure at 2 points of the system in Pascal.

v₁ and v₂ are velocities at 2 points of the system in m/s.

Z₁ and Z₂ are the locations of the inlet and outlet of the air.

$\begin{array}{l}\text{ρ}\text{=}\text{Density}\text{of}\text{air}\text{=}\text{1}\text{.22}{\text{kg/m}}^{\text{3}}\\ \text{g}\text{=}\text{Acceleration}\text{due}\text{to}\text{gravity}\text{= }\text{9}\text{.8}{\text{m/s}}^{\text{2}}\end{array}$

The volumetric flow rate in air is given as,

$\text{Q}\text{=}\text{A×v}$ ........... (2)

Here,

Q = Volumetric flow rate of air

A = Area of venturi

v = Velocity of air

$\begin{array}{l}{\text{P}}_{\text{1}}\text{-}{\text{P}}_{\text{2}}\text{=}{\text{ρ}}_{\text{a}}\text{gh}\\ \text{Here,}\\ \text{h}\text{=}\text{Reading of the differential manometer }\\ {\text{ρ}}_{\text{a}}\text{=}\text{Density}\text{of}\text{Alcohol}\end{array}$ ........... (3)

The continuity equation relates the Area and velocity at 2 points as,

$\begin{array}{l}{\text{A}}_{\text{1}}{\text{v}}_{\text{1}}\text{=}{\text{A}}_{\text{2}}{\text{v}}_{\text{2}}\end{array}$ ........... (4)

A₁ and A₂ are the area across 2 points of Venturi meter

v₁ and v₂ are the velocities across 2 points of Venturi meter