Chapter 9, Problem 9.13P

(a)

Interpretation Introduction

Interpretation:

The fluid acceleration, pressure force, and viscous force all lie in the same plane are to be proved.

Concept Introduction :

The fluid acceleration, pressure force, and viscous force all lie in the same plane are to be proved by using the Navier-Stokes equation in the vector form and the law of the vector addition.

The Navier-Stokes equation in vector form is,

  $\rho \frac{D\overrightarrow{V}}{Dt}=\rho \overrightarrow{g}-\nabla P+\mu {\nabla }^2\overrightarrow{V}$

(b)

Interpretation Introduction

Interpretation:

The fluid accelerates in the direction of the decreasing pressure in the absence of the viscous forces is to be proved.

Concept Introduction :

The fluid accelerates in the direction of the decreasing pressure in the absence of the viscous forces is proved by suing the Navier-Stokes equation in vector form.

The Navier-Stokes equation in vector form is,

  $\rho \frac{D\overrightarrow{V}}{Dt}=\rho \overrightarrow{g}-\nabla P+\mu {\nabla }^2\overrightarrow{V}$

(c)

Interpretation Introduction

Interpretation:

A static fluid will always start to move in the direction of the decreasing pressure is to be proved.

Concept Introduction :

The Bernoulli’sprinciple is used to prove the flow condition of a static fluid.

The Bernoulli’sequation is,

  $\frac{P_1}{\rho }+\frac{V_1^2}{2}+g{Z}_1=\frac{P_2}{\rho }+\frac{V_2^2}{2}+g{Z}_2$