Chapter 2, Problem 2.23P

(a)

Interpretation Introduction

Interpretation:

To determine the velocity at location $2$ where an incompressible ( $\rho$ is constant) liquid flows steadily through a conduit of circular cross-section and increasing diameter.

Concept Introduction:

The equation of continuity is based on the concept that the mass that flows in is equal to the mass that flows out.

  $\rho A_1{V}_1=\rho A_2{V}_2$

The change in kinetic energy is:

  $\Delta KE=\frac{1}{2}{V}_2{}^2-\frac{1}{2}{V}_1{}^2$

Use the concept of continuity equation in order to find the velocity at location $2$ . And use the formula of Kinetic Energy as here mass and height is assumed to be constant at both the locations i.e. $1\text{and}2$ .

(b)

Interpretation Introduction

Interpretation:

To determine the kinetic energy change $\left(\text{J}\cdot k{\text{g}}^{\text{-1}}\right)$ of the fluid between location $1\text{ and }2$ .

Concept Introduction:

The equation of continuity is based on the concept that the mass that flows in is equal to the mass that flows out.

  $\rho A_1{V}_1=\rho A_2{V}_2$

The change in kinetic energy is:

  $\Delta KE=\frac{1}{2}{V}_2{}^2-\frac{1}{2}{V}_1{}^2$

Use the concept of continuity equation in order to find the velocity at location $2$ . And use the formula of Kinetic Energy as here mass and height is assumed to be constant at both the locations i.e. $1\text{and}2$ .