Fundamentals of Momentum, Heat, and Mass Transfer
Fundamentals of Momentum, Heat, and Mass Transfer
6th Edition
ISBN: 9781118947463
Author: James Welty, Gregory L. Rorrer, David G. Foster
Publisher: WILEY
Question
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Chapter 4, Problem 4.14P

(a)

Interpretation Introduction

Interpretation:

For the uniform exit velocity, the value of mass flow rate and maximum velocity should be calculated.

Concept Introduction:

According to law of conservation of mass, energy can neither be created nor be destroyed.

The generalized form of equation is written as:

[Rate of mass in from control volume] - [Rate of mass out from control volume] + [Rate of accumulation]

Mass flow rate is defined as the ratio of the mass of fluid passing the point with respect to time.

m=ρ×v

Law of conservation of mass for control volume is given by,

Mt+dm=0

Where,

Mt is the rate of change of mass in control volume.

dm is the net mass outflow across the control surface

t is the time.

Mass flow rate in terms of average velocity is,

(ρv)averageA=AρvdA

Where,

A is the area.

v is the average velocity.

ρ is the density.

Maximum velocity is the velocity which exists at the center of circular passage. The relationship between average velocity and maximum velocity is,

vaverage=vmax2

(b)

Interpretation Introduction

Interpretation:

For the parabolic exit velocity,the value of mass flow rate and maximum velocity should be calculated

Concept Introduction:

According to law of conservation of mass, energy can neither be created nor be destroyed.

The generalized form of equation is written as:

[Rate of mass in from control volume] - [Rate of mass out from control volume] + [Rate of accumulation]

Mass flow rate is defined as the ratio of the mass of fluid passing the point with respect to time.

m=ρ×v

Law of conservation of mass for control volume is given by,

Mt+dm=0

Where,

Mt is the rate of change of mass in control volume.

dm is the net mass outflow across the control surface

t is the time.

Mass flow rate in terms of average velocity is,

(ρv)averageA=AρvdA

Where,

A is the area.

v is the average velocity.

ρ is the density.

The equation of parabolic velocity profile is given by,

v(y)=C1y+C2y2

Where,

C1 and C2 are constant.

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