all chapter Munson , Young and Okiishi’s Fundamentals of Fluid Mechanics 8th edition solution manual PDF

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Authors: Philip M. Gerhart , Andrew L. Gerhart , John I. Hochstein
Published: Wiley 2016
Edition: 8th
Pages: 1855
Type: pdf
Size: 55MB
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FOLFNKHUHWRGRZQORDG Problem 1.1 The force, F , of the wind blowing against a building is given by F CD V 2A 2, where V is the wind speed, the density of the air, A the cross-sectional area of the building, and CD is a constant termed the drag coefficient. Determine the dimensions of the drag coefficient.

Solution 1.1 F

CD V 2

A 2

or

CD

2F V 2A

, where

F  MLT 2 ,  ML 3 , V  LT 1, A  L2 Thus, MLT CD 

ML 3

LT

2 1 2

M 0 L0T 0 L2

Hence, CD is dimensionless.

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FOLFNKHUHWRGRZQORDG

Problem 1.2

The Mach number is a dimensionless ratio of the velocity of an object in a fluid to the speed of sound in the fluid. For an airplane flying at velocity V in air at absolute temperature T , the Mach number M a is, Ma

V , kRT

where k is a dimensionless constant and R is the specific gas constant for air. Show that M a is dimensionless.

Solution 1.2

We denote the dimension of temperature by

and use Newton’s second law to get F

Then L T

Ma 1

FL M

L T ML T2 F

L2 T2

or

Ma

1.

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ML . T2

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FOLFNKHUHWRGRZQORDG

Problem 1.3

Verify the dimensions, in both the FLT and the M LT systems, of the following quantities, which appear in Table B.1 Physical Properties of Water (BG/EE Units). (a) Volume, (b) acceleration, (c) mass, (d) moment of inertia (area), and (e) work.

Solution 1.3 a) volume  L3 b) acceleration

time rate of change of velocity 

LT T

1

LT

2

c) mass  M

or with F  MLT

2

mass  FL 1T 2 d) m oment of inertia area e) work

second moment of area  L2

force distance  FL

or with F  MLT work  ML2 T

2

2

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L2  L4

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FOLFNKHUHWRGRZQORDG Problem 1.4

Verify the dimensions, in both the FLT and the M LT systems, of the following quantities, which appear in Table B.1 Physical Properties of Water (BG/EE Units). (a) Angular velocity, (b) energy, (c) moment of inertia (area), (d) power, and (e) pressure.

Solution 1.4 angular displacement T 1 time b) energy ~ capacity of body to do work single work force distance ➔ energy  FL

a) angular velocity

o r with F  MLT

2

➔ energy  MLT

c) moment of inertia area d) p ower e) pressure

2

2

2

L  ML T

second moment of area  L2

rate of doing work 

FL  FLT T

force F   FL 2  MLT area L2

2

1

 MLT

2

L 2  ML 1T

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L2  L4

L T 2

1

 ML2 T

3

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FOLFNKHUHWRGRZQORDG Problem 1.5

Verify the dimensions, in both the FLT system and the MLT system, of the following quantities, which appear in Table B.1 Physical Properties of Water (BG/EE Units). (a) Frequency, (b) stress, (c) strain, (d) torque, and (e) work. Solution 1.5 cycles T 1 time force F  2  FL b) stress = area L

a) frequency =

2

S ince F  MLT 2 , stress 

MLT 2

2

 ML 1T

2

L change in length L c) strain =   L0 dimensionless length L d) torque = force distance  FL  MLT 2 L  ML2 T

e) work = force distance  FL  MLT

2

L  ML2 T

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2

2

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FOLFNKHUHWRGRZQORDG Problem 1.6

If u is velocity, x is length, and t is time, what are the dimensions (in the M LT system) of (a) u / t, (b) 2 u / x t, and (c) ( u / t )dx ?

Solution 1.6

a)

u LT  t T

1

 LT

2

b)

c)

2

u LT 1  T x t ( L)( T)

LT u x t T

2

1

(L)  L2T

2

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FOLFNKHUHWRGRZQORDG Problem 1.7

Verify the dimensions, in both the FLT system and the MLT system, of the following quantities, which appear in Table B.1 Physical Properties of Water (BG/EE Units). (a) Acceleration, (b) stress, (c) moment of a force, (d) volume, and (e) work. Solution 1.7

velocity L  2  LT time T F force b) stress  2  FL 2 area L S ince F  MLT 2,

a) acceleration

MLT

2

2

 ML 1T 2 L2 c) m oment of a force force distance  FL  MLT stress 

2

d) v olume (length)3  L3 e) work

force distance  FL  MLT

2

L  ML2T

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2

L  ML2T

2

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FOLFNKHUHWRGRZQORDG Problem 1.8

If p is pressure, V is velocity, and is fluid density, what are the dimensions (in the MLT system) of (a) p / , (b) pV , and (c) p / V 2?

Solution 1.8

a)

p



FL 2 ML

MLT 2 L 2

3

b) pV  ML 1T c)

ML 2

ML 1T

3

ML 1

LT

p ML 1T 2  V2 ML 3 LT 1

2

ML

3

2

3

 L2T

2

 M 2L 3T

3

 M 0 L0T 0 dimensionless

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FOLFNKHUHWRGRZQORDG Problem 1.9

If P is force and x is length, what are the dimensions (in the FLT system) of (a) d P / dx , (b) d 3P / dx 3 , and (c) P dx ?

Solution 1.9 dP F   FL 1 a) dx L

b) c)

d3 P F  3  FL 3 dx3 L Pdx  FL

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FOLFNKHUHWRGRZQORDG Problem 1.10

If V is velocity, is length, and is a fluid property (the kinematic viscosity) having dimensions of L2 T 1 , which of the following combinations are dimensionless: (a) V (b) V , (c) V 2 , and (d) V ?

Solution 1.10

a) V

b)

V

LT 

d)

LT 1

LT 

2

2

1

LT

0

0

dimensionless

1

 L4T

L LT

1

2

c) V 2  LT V

1

 LT

L

L T

1

2

L2T

4

3

2

not dimensionless

not dimensionless

1

L LT

1

L

2

not dimensionless

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,

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FOLFNKHUHWRGRZQORDG Problem 1.11

The momentum flux is given by the product mV , where m is mass flow rate and V is velocity. If mass flow rate is given in units of mass per unit time, show that the momentum flux can be expressed in units of force.

Solution 1.11

M T

mV

where

1 gc

L T

M

L F T2 T2 M L

F

FT  2 comes from Newton’s Second Law. ML 

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FOLFNKHUHWRGRZQORDG

Problem 1.12

An equation for the frictional pressure loss p (inches H2O) in a circular duct of inside diameter d in. and length L ft for air flowing with velocity V ft/min is

p 0.027

L

V Vo

d1.22

1.82

,

where V0 is a reference velocity equal to 1000 ft/min. Find the units of the “constant” 0 .027.

Solution 1.12

Solving for the constant gives pL

0.027 L

V Vo

1.22

D

1.82

.

The units give

0.027

in. H 2O ft in.1.22

0.027

ft min ft min

1.82

in. H2O in.1.22 ft

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FOLFNKHUHWRGRZQORDG

Problem 1.13

The volume rate of flow, Q , through a pipe containing a slowly moving liquid is given by the equation R4 p Q 8 where R is the pipe radius, p the pressure drop along the pipe, is a fluid property called viscosity FL 2 T , and is the length of pipe. What are the dimensions of the constant Would you classify this equation as a general homogeneous equation? Explain.

Solution 1.13 3

LT L3T

1

1

L4 



8

8

FL

FL 2 T L3 T

2

L

1

The constantis

is dimensionless. 8 Yes. This is a general homogeneous equation because it is valid in any consistent units system.

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/8?

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FOLFNKHUHWRGRZQORDG Problem 1.14

Show that each term in the following equation has units of lb/ft3 . Consider u as velocity, y as length, x as length, p as pressure, and as absolute viscosity. 0

2

p x

u . y2

Solution 1.14

lb ft2 ft

p x

p x

or

lb , ft3

and 2

u

lb sec

2

2

y

ft

ft sec ft

2

2

or

u

lb

2

ft3

y

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