Chapter 4, Problem 4.9P

(a)

Interpretation Introduction

Interpretation:

The variation between the total momentum and the product of mass flow rate and average velocity is to be determined.

Concept Introduction:

The volumetric flow rate of a fluid is given as,

  $\text{Q =}\text{u}\text{×}\text{S}$ ..... (1)

Q = Volumetric flow rate of the fluid

u = Fluid velocity

S = Total cross-section area

The mass flow rate is given as,

  $\text{<mover accent="true"><mo> m </mo><mo>˙</mo></mover>}\text{=}\text{ρ}\text{×}\text{Q}$ ..... (2)

  $\text{<mover accent="true"><mo> m </mo><mo>˙</mo></mover>}$ = Mass flow rate of the fluid

  $\text{ρ}$ = Density of fluid

The average velocity if the fluid is,

  $\text{<mover accent="true"><mo> u</mo> <mo>¯</mo></mover>}\text{=}\frac{\text{Q}}{\text{S}}$ ..... (3)

The momentum of the fluid is the product of the mass flow rate and the velocity of the fluid.

  $\text{M}\text{=}{\text{ρu}}^{\text{2}}\text{S}$ ..... (4)

M = Momentum of the fluid

(b)

Interpretation Introduction

Interpretation:

The situation at which momentum flow is equal to the product of mass flow and average velocity is to be determined.

Concept Introduction:

The volumetric flow rate of a fluid is given as,

  $\text{Q =}\text{u}\text{×}\text{S}$ ..... (1)

Q = Volumetric flow rate of the fluid

u = Fluid velocity

S = Total cross-section area

The mass flow rate is given as,

  $\text{<mover accent="true"><mo> m </mo><mo>˙</mo></mover>}\text{=}\text{ρ}\text{×}\text{Q}$ ..... (2)

  $\text{<mover accent="true"><mo> m </mo><mo>˙</mo></mover>}$ = Mass flow rate of the fluid

  $\text{ρ}$ = Density of fluid

The average velocity if the fluid is,

  $\text{<mover accent="true"><mo> u</mo> <mo>¯</mo></mover>}\text{=}\frac{\text{Q}}{\text{S}}$ ..... (3)

The momentum of the fluid is the product of the mass flow rate and the velocity of the fluid.

  $\text{M}\text{=}{\text{ρu}}^{\text{2}}\text{S}$ ..... (4)

M = Momentum of the fluid