This document provides 5 examples of calculating discharge over notches of different shapes. Example 1 calculates discharge over a rectangular notch. Example 2 calculates the length of a rectangular notch given the discharge. Example 3 calculates discharge over a triangular notch. Example 4 calculates discharge over a trapezoidal notch. Example 5 calculates the depth of water required over a triangular notch to produce the same discharge as a rectangular notch. Formulas and step-by-step workings are shown for each example calculation.

1. GOVERNMENT ENGINEERING COLLEGE
- BHUJ
FLUID MECHANICS
NUMERICAL OF NOTCH
APPERTUS

2. 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
/4.081.925.062.0
3
2
/2
3
2
3
3
2
3
3
2
3





Discharge over the notch = 231 liters/s

3. 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
b
b
smHgbCQ d
8.0
572.0
626.0
358.0
2
81.926.0
3
2
358.0
/2
3
2
2
5
2
3
3
2
3










Length of the notch = 0.8 m

4. 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


 

 
 2
5
3
2
5
2.045tan81.9262.0
15
8
/
2
tan2
15
8



Q
smHgCQ d


5. min/1560
/26
/026.0018.0465.1 3
sliter
ssliterQ
smQ



Discharge over the notch = 1560 liters/s

6. 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

7.  From the geometry of the notch, we get,
 and the discharge over trapezoidal notch,
25.1
600
750
300
1
2
4501200
2
tan 



   
 
 
ssliter
sm
Q
HgCHgbCQ dd
/128
/128.0
043.0085.0
225.025.181.926.0
15
8
225.081.9245.06.0
3
2
2
tan2
15
8
2
3
2
3
2
5
2
3
2
5
2
3







Discharge through the notch = 128 liters/s

8. 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


 


9.  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
15.081.92162.0
3
2
2
3
2
2
2
5
2
5



 
mH
H
H
HgCd
357.0
076.0
394.1
106.0
45tan81.92159.0
15
8
106.0
2
tan2
15
8
106.0
2
2
5
2
2
5
2
2
5







10. Thank You…