GOVERNMENT ENGINEERING COLLEGE - BHUJ FLUID MECHANICS NUMERICAL OF NOTCH APPERTUS• STUDENT NAME:- PARMAR UMANG R.• SUDENT ENROLLMENT NO.:-130150119076

EXAMPLE :- 1 A rectangular notch 0.5m wide has constant head of

400 mm. Find the discharge over the notch in liters per second, if the coefficient of discharge for the notch is 0.62.

Given , b = 0.5 m H = 400 mm = 0.4 m Cd = 0.62 We know that discharge over the rectangular notch,

sliters

sm

Q

smQ

smHgbCQ d

/231

/231.0

253.0915.0

/4.081.925.062.03

2

/23

2

3

32

3

32

3

Discharge over the notch = 231 liters/s

EXAMPLE :- 2 A rectangular notch has a discharge of 21.5 cubic

meter per minute , when the head of water is half the length of the notch. Find the length of the notch. Assume Cd = 0.6.

Given , Q = 21.5 m3 /min = 21.5 / 60 = 0.358 m3 /s H = b / 2 = 0.5 b Cd = 0.6 We know that the discharge over the rectangular

notch,

mb

b

bb

smHgbCQ d

8.0

572.0626.0

358.0

281.926.0

3

2358.0

/23

2

2

5

2

3

32

3

Length of the notch = 0.8 m

EXAMPLE :- 3 A right-angled V-notch was used to measure the

discharge of a centrifugal pump. If the depth of water at V-notch is 200mm, calculate the discharge over the notch in liters per minute. Assume coefficient of discharge as 0.62.

Given,

We know that the discharge over the triangular notch,

62.0

2.0200

90

dC

mmmH

25

32

5

2.045tan81.9262.015

8

/2

tan215

8

Q

smHgCQ d

min/1560

/26

/026.0018.0465.1 3

sliter

ssliterQ

smQ

Discharge over the notch = 1560 liters/s

EXAMPLE :- 4 A trapezoidal notch notch of 1.2m wide at the top and

450mm at the bottom is 300mm high. Find the discharge through the notch, if the head of water is 225mm. Take coefficient of discharge as 0.6.

Given, Width of the notch = 1.2m b = 450mm = 0.45m Height of the notch = 300mm = 0.3m H = 225mm = 0.225m Cd = 0.6

From the geometry of the notch, we get,

and the discharge over trapezoidal notch,

25.1600

750

300

1

2

4501200

2tan

ssliter

sm

Q

HgCHgbCQ dd

/128

/128.0

043.0085.0

225.025.181.926.015

8

225.081.9245.06.03

22

tan215

82

3

2

3

2

5

2

3

2

5

2

3

Discharge through the notch = 128 liters/s

EXAMPLE :- 5 Water flows over a rectangular notch of 1m length

over a depth of 150mm. Then the same quantity of water passes through a triangular right-angled notch. Find out the depth of water through the notch.

Take the coefficient of discharges for the rectangular and triangular notch as 0.62 and 0.59 respectively.

Given, For rectangular notch: 

For triangular notch:

62.0

15.0150

1

1

dC

mmmH

mb

?

59.0

90

2

H

Cd

First of all, consider the flow of water over the rectangular notch. We know that the discharge over the rectangular notch,

Now consider the flow of water over the triangular notch. We know that discharge over the triangular notch, (Q),

Depth of water through the triangular notch = 0.357 m

smQ

Q

HgbCQ d

/106.0058.0831.1

15.081.92162.03

2

23

2

2

2

5

2

5

mH

H

H

HgCd

357.0

076.0394.1

106.0

45tan81.92159.015

8106.0

2tan2

15

8106.0

2

2

5

2

2

5

2

2

5

Thank You…