Fluid Mechanics
Fluid Mechanics
8th Edition
ISBN: 9780073398273
Author: Frank M. White
Publisher: McGraw-Hill Education
Question
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Chapter 10, Problem 10.77P
To determine

To estimate:

The flow rate in unit gal/min with y2 having the range 0.5ft<y2<5ft.

Expert Solution & Answer
Check Mark

Answer to Problem 10.77P

y2 Q
1.5 30173.6984
2.25 30173.6984
3 27526.92998
3.75 22233.2585
4.5 17469.0305

Explanation of Solution

The given figure is:

Fluid Mechanics, Chapter 10, Problem 10.77P

The discharge for sluice gate is having a free outflow have dissipation when the outflow is drowned. Q drops sharply, and given H=9 in.

Using the figure, the ratio is calculated as:

y1H=6(912)y1H=6(34)y1H=2438

The limits given for the tail water:

0.5ft<y2<5ft

0.5H<y2H<5H

0.5(912)<y2H<5(912)23<y2H<203

[H=912]

From the given figure with the intersection lines:

y2H=2,y1H=8,cd=0.57

Flow rate equation:

Q=cdHb2gy1

(1)

where,Q=cdHb2gy1Q=Flow rateb=gap widthg=acceleration

=0.57912×82×32.2×6=3.42386.467.227ft3/s

=67.227ft3/s×600.1336830173.6984gal/min

Height of the tail water is calculated:

y2H=2y2=2H

y2=2×91232=1.5ft

From equation (1):

Q=cdHb2gy1

=0.57912×82×32.2×6=3.42386.467.227ft3/s

=67.227ft3/s×600.1336830173.6984gal/min

Height of the tail water:

y2H=3y2=3Hy2=3×9122.25ft

At intersection lines the flow rate equation, y2H=4,y1H=8,cd=0.52 :

Q=cdHb2gy1

(1)

where,Q=cdHb2gy1Q=Flow rateb=gap widthg=acceleration

=0.52912×82×32.2×6=3.12386.461.33ft3/s=61.33×600.1336827526.92998gal/min

Height of the tail water,y2H=4y2=4Hy2=4×9123ft

From equation (1), with the intersection lines y2H=5,y1H=8,cd=0.42 :

Q=cdHb2gy1

=0.42912×82×32.2×6=2.52386.449.5357ft3/s=49.5357×600.1336822233.2585gal/min

Height of the tail water:

y2H=5y2=5Hy2=5×9123.75ft

At intersection lines the flow rate equation y2H=6,y1H=8,cd=0.33 :

Q=cdHb2gy1

(1)

where,Q=cdHb2gy1Q=Flow rateb=gap widthg=acceleration

=0.33912×82×32.2×6=1.98386.438.921ft3/s=38.921×600.1336817469.0305gal/min

Height of the tail water:y2H=6y2=6Hy2=6×9124.5ft Conclusion:

Thus, the flow rate in unit gal/min with y2 having the range 0.5ft<y2<5ft .is calculated.

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Chapter 10 Solutions

Fluid Mechanics

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