Chapter 8, Problem 8.4P

Interpretation Introduction

Interpretation: The kinematic viscosity of the fluid through the viscometer is to be determined by using the energy balance equation.

Concept introduction: The Energy balance across the pipe is given by the Bernoulli’s equation in which the sum of Potential head, Kinetic head and Pressure head is constant. The Bernoulli equation across 2 points of any system is given by:-

  $\frac{{\text{P}}_{\text{1}}}{\text{ρg}}\text{+}\frac{{\text{v}}_{\text{1}}{}^{\text{2}}}{\text{2g}}{\text{+ Z}}_{\text{1}}\text{+}\text{H}\text{=}\frac{{\text{P}}_{\text{2}}}{\text{ρg}}\text{+}\frac{{\text{v}}_{\text{2}}{}^{\text{2}}}{\text{2g}}{\text{+ Z}}_{\text{2}}$  ........ (1)

The notations used in equation (1) are:-

P₁and P₂are pressure at the 2 points on viscometer

v₁ and v₂ are velocity at 2 points on the viscometer

Z₁ and Z₂ are the locations of the liquid.

  $\text{ρ}$ = Density of the fluid

H = Head developed by the fluid

g = Acceleration due to gravity

The kinematic viscosity of the fluid is given as,

  $\text{ν}\text{=}\frac{\text{μ}}{\text{ρ}}$  ........ (2)

  $\text{ν}$ = Kinematic viscosity of the fluid

  $\text{μ}$ = Dynamic viscosity of the fluid

The head developed by the fluid is given as,

  $\text{H}\text{=}\frac{\text{32vνL}}{{\text{gD}}^{\text{2}}}$  ........ (3)

D = Diameter of the tube

L = Length of the tube