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Sunday, 12 August 2018

DISCHARGE THROUGH A TRAPEZOIDAL NOTCH

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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