Fluid Mechanics
Fluid Mechanics
8th Edition
ISBN: 9780073398273
Author: Frank M. White
Publisher: McGraw-Hill Education
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Chapter 10, Problem 10.91P

(a)

To determine

The oblique angle, β.

(a)

Expert Solution
Check Mark

Answer to Problem 10.91P

The value of wave angle β is, β=56.65

Explanation of Solution

Given information:

Average velocity, V = 0.94m/s

Depth of flat-water channel, y1=1cm

Wedge half angle,θ = 200

Calculation:

Fr1=V g y 1 ...............(1)Fr1=0.94 9.81×1× 10 2 Fr1=0.94 0.0981Fr1=0.940.3132Fr1=3.0013

As we know the following relation between y2 and y1

y2y1=121+8Fr11y21× 10 2=121+8×3.00131y21× 10 2=12.25.01041y21× 10 2=12×(5.001)1y21× 10 2=1.5005y2=1.5005×102y2=0.015m

As per the continuity equation we have following relation

V1y1=V2y2V1V2=y2y1V2=y2y1.V1V2=0.0150.01×0.94V2=1.41m/s

As we know the equation for oblique angle

tan( βθ)tanθ=V2V1 β=tan1( V 2 V 1 ×tanθ)+θ      β=tan1(1.410.94)+0.349β=tan1(1.5)+0.349β=56.301+0.349β=56.65             .

To determine

(b)

The Froud number Fr2 is, Fr2=0.343.

Expert Solution
Check Mark

Answer to Problem 10.91P

]

The Froud number Fr2

Explanation of Solution

Given information:

Average velocity, V = 0.94m/s

Depth of flat-water channel, y1=1cm

Wedge half angle,θ = 200

Solution:

Fr1=V g y 1 ...............(1)Fr1=0.94 9.81×1× 10 2 Fr1=0.94 0.0981Fr1=0.940.3132Fr1=3.0013

Fr2=Fr18 ( 1+8F r 1 2 1 ) 3 2 Fr2=3.00138 ( 1+8 (3.0013) 2 1 ) 3 2 Fr2=8.489 ( 1+8×9.00781 ) 3 2 Fr2=8.489 ( 72.062 ) 3 2 Fr2=8.489 ( 8.489 ) 3 2 =Fr2=(8.489)12Fr2=1 8.489Fr2=12.913Fr2=0.343(Asthisisasupercriticalflow,Fr2<1).

c

To determine

The value y2.

c

Expert Solution
Check Mark

Answer to Problem 10.91P

The value y2 is, y2=0.015m

Explanation of Solution

Given information:

Average velocity, V = 0.94m/s

Depth of flat-water channel, y1=1cm

Wedge half angle,θ = 200

Solution:

As we know the following relation between y2 and y1

y2y1=121+8Fr11y21× 10 2=121+8×3.00131y21× 10 2=12.25.01041y21× 10 2=12×(5.001)1y21× 10 2=1.5005y2=1.5005×102y2=0.015m

.

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Chapter 10 Solutions

Fluid Mechanics

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