notches and weir presentation by pritika

Vidhyadeep
Institute of Engineering and Technology
Address : Vidhyadeep Campus, Anita (Kim), Olpad, Surat.
NOTCHES AND WEIRS
Prepared By:-
 Baudh Komal S.
 Vasava Khushbu J.
 Rathod Mahesh h.
 Savita Ashish S.

Content
 Define of Notch & Weir
 Discharge over a Rectangular notch
 Discharge over a Triangular notch
 Cippoletti Weir
 Discharge over a Narrow crested weir
 Discharge over a Broad crested weir
 Discharge over a Sharp crested weir
 Time of emptying a tank with Rectangular &
Triangular notch & weir

Notch :-
A notch may be defined as an opening provided in one side of a
tank or a reservoir, with upstream liquid level below the top edge of the
opening.
Weirs :-
A weir may be defined as a structure constructed across a river or
canal to store water on the upstream side. Water flows over the crest of weir.

Notch
Discharge over a Rectangular notch
Consider a rectangular notch in one side of a tank over which water is flowing as
shown in figure.
Let,
H = Height of water above sill of notch
b = Width or length of the notch
Cd = Coefficient of discharge

Let us consider a horizontal strip of water of thickness dh at a depth of h from the
water level as shown in figure.
 Area of the strip = b.dh
We know know that the theoretical velocity of water through the strip.
V = 2.gh
Discharge through the strip.
dq = Cd X Area of strip X theoretical Velocity
= Cd X ( b X dh ) X 2.gh
 Equation of total discharge in Rectangular notch
 Q = 2/3 X Cd X b X 2g X H^(3/2)

 Discharge over a Triangular notch
A triangular notch is also called a V-notch. Consider a triangular notch, in one side
of the tank, over which water is flowing as shown in figure.
Let,
H = Height of the liquid above the apex of the notch
θ = Angle of the notch
Cd = Coefficient of discharge

From the geometry of the figure, we find that the width of the notch at the water
surface
= 2H tan/2
Area of the strip = 2 ( H  h ) tan/2
We know that the theoretical velocity of water through the strip = 2gh
and discharge over the notch,
dq = Cd X Area of strip X Theoretical velocity
dq = Cd X 2 ( H  h ) tan/2 . dh X 2gh
 Equation of total discharge in triangular notch
 Q = 8/15 Cd . 2g . tan/2 . H^(5/2)

Weirs
Cippoletti Weir
Cippoletti weir The Cippoletti weir is a trapezoidal weir, having side slopes 1
horizontal to 4 Vertical.
 The purpose of slope, on the sides. is to obtain an increased discharge through
the triangular portions of the weir, which, otherwise would have been decreased
due to end contractions in the case of rectangular weirs.

Thus, the advantage of a Cippoletti weir is that the factor of end . Francis formula
for Cippoletti weir is, General equation of discharge for Cippoletti weir, contractions
is not required, while using the Francis' formula.
Francis formula of Cippoletti weir.
Q = 1.84 L H^3/2
General equation of discharge for Cippoletti weir
Q = 2/3 . Cd . L . √2g . H^3/2
When velocity of approach considered
Q = 2/3 Cd. L . √2g [H1^3/2 - Ha^3/2]

 Discharge over a Narrow crested weir
If, 2b is less than H, the weir called a narrow crested weir.
b - width of the crest
H - Height of water above the crest.
A narrow crested weir is hydraulically similar to an ordinary weir or to a
rectangular weir. Hence, the formula for discharge over rectangular weir holds
good for discharge over a narrow crested weir.
Q = 2/3 . Cd . L. √2g . H^3/2

Discharge over a Broad crested weir
If,2b is more than II, the weir is called a broad-crested weir.
This is a weir having very broad crest (sill) so that the flow of water over crest
may be compared to the flow of water in a channel.
 Applying Bernoulli's equation at A and B,
Q = Cd . L . h . √2g(H-h)

Discharge over a Sharp crested weir
It is a special type of weir, having a sharp crest. The water flowing over the crest
comes in contact with the crest line and then springs up from the crest and falls as a
trajectory as shown in figure.
In a Sharp Crested weir, a sharp crested weir,
 i.e. the thickness (b) of the weir is kept less than H/2.
The equation of discharge for a sharp crested weir is same as for a rectangular
weir.
Q = 2/3 . Cd . L . √2g . H^3/2

 Time of emptying a tank with Rectangular notch & weir
Consider or a reservoir of uniform cross-sectional area A and B rectangular notch is
provided in one of its side, as shown in Fig. 8.15.
Let at any time, the height of liquid from crest of notch is h and let the liquid surface
fall by a small height dh in time dT.

Let
L = Length of crest of notch.
Cd = Co-efficient of discharge.
H1 = initial height of liquid above the crest of notch
H2 = Final notch of liquid above the crest of notch
T = Time required to fall from H to H2.
T = ( -3A /Cd . L . √2g) ( (1/√H2) - (1/√H1) )

 Time of emptying a tank with Tringular notch & weir
Consider a tank of uniform cross-sectional area 'A' and triangular notch is provided in
one of its side as shown in Fig. 8.16.

Let
0 = angle of the notch.
Cd = Co-efficient of discharge.
H1 = initial height of liquids above the apex of notch
H2 = Final height of liquid above the apex of notch
T = time required in seconds, to lower the height from H1 to H2 above
the apex of the notch.
Let at any instant, the height of liquid surface above the apex of notch or weir be
h and in a small time dT. let the liquid surface falls by dh'.
Then -ve sign indicates, as the time increases, height 'h' decreases. And
discharge for a triangular notch is given by
T = ( 5A /4Cd . Tan(/2) . √2g) ( (1/H2^(3/2)) - (1/H1^(3/2) )

notches and weir presentation by pritika

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