We were discussing the difference
between Notches and Weirs, discharge over a triangular notch or weir, expression
for discharge over a rectangular notch or weir and also the advantage of triangular notch or weir over rectangular notch or weir, in the subject of
fluid mechanics, in our recent posts.
Now we will go ahead to find out the discharge over
a trapezoidal notch or weir, in the subject of fluid mechanics, with the help
of this post.
As we can see here, in following figure, that a trapezoidal
notch or weir will be the combination of a rectangular and two triangular notches
or weirs. Therefore, discharge through a trapezoidal notch or weir will be
considered as the summation of the discharge through a rectangular notch or
weir and discharge through two triangular notches or weirs.
Discharge through a trapezoidal notch or weir =
Discharge through a rectangular notch or weir + Discharge through two triangular notches or weirs
Now, let us consider that we have channel
carrying water and let us think a trapezoidal notch or weir with this channel as displayed here in above figure.
We have following data from above figure
and these data are as mentioned here
H = Height of water above the notch
L = length of the crest of the notch
θ = Angle of notch
Cd1 = Co-efficient or
discharge for rectangular portion ABCD
Cd2 = Co-efficient or
discharge for triangular portion FAD and BCE
Discharge Q1 through rectangular portion ABCD
Discharge Q2 through two triangular notches portion FAD and BCE
Discharge through a trapezoidal notch or weir
Now we will go ahead to start a new
topic in the subject of fluid mechanics i.e. Discharge over a stepped notch.
Do you have any suggestions? Please
write in comment box.
Reference:
Fluid mechanics, By R. K. Bansal
Image Courtesy: Google
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