DISCHARGE OVER A TRIANGULAR NOTCH OR WEIR

We were discussing the various types of notches and weirs i.e. classifications of notches and weirs, difference between Notches and Weirs and also the expression for discharge over a 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 triangular notch or weir, in the subject of fluid mechanics, with the help of this post.

We must note it here that the expression of the discharge over a triangular notch or over a weir will be same.

Now, let us consider that we have channel carrying water and let us think a triangular notch or weir with this channel as displayed here in following figure.

We have following data from above figure and these data are as mentioned here

H = Head of water above the V-notch

θ = Angle of notch

Let us consider one elementary horizontal strip of water of thickness dh and at a depth of h from free surface of water as displayed here in above figure.

dh = Thickness of elementary horizontal strip of water flowing over the triangular notch or weir

h = Depth of elementary horizontal strip of water from free surface of water

C_d = Co-efficient of discharge

We will determine the value of discharge dQ through the elementary horizontal strip of water. After securing the expression for discharge through the elementary horizontal strip, we will integrate the expression between the limit 0 to H and we will have the expression for the discharge over entire triangular notch or weir.

dQ = C_d x Area of strip x Theoretical velocity

Area of strip

First we will secure the value of area of horizontal elementary strip

Now we will secure here the expression for

Now we will go ahead to start a new topic in the subject of fluid mechanics i.e. Advantages of triangular notch or weir over rectangular notch or weir over.

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