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Sunday, 12 August 2018

August 12, 2018

DISCHARGE OVER A STEPPED NOTCH

We were discussing the difference between Notches and Weirsdischarge over a triangular notch or weirexpression for discharge over a rectangular notch or weiradvantage of triangular notch or weir over rectangular notch or weir and also the discharge over a trapezoidal notch, in the subject of fluid mechanics, in our recent posts. 

Now we will go ahead to find out the discharge over a stepped notch, in the subject of fluid mechanics, with the help of this post. 

As we can see here, in following figure, that a stepped notch will be the combination of rectangular notches. Therefore, discharge through a stepped notch will be considered as the summation of the discharge through different rectangular notches. 

Let us consider that we have a stepped notch as displayed here in following figure. 

H1, H2 and H3 = Height of water above the crest of notch 1, notch 2 and notch 3 respectively 
L1, L2 and L3 = Length of the notch 1, notch 2 and notch 3 respectively 
Cd = Coefficient of discharge of all notches 

Discharge through the stepped notch = Q1 + Q2 + Q3  

We have already discussed the discharge through the rectangular notch and therefore we will have following expression for the discharge through a stepped notch as displayed here. 

Now we will go ahead to start a new topic in the subject of fluid mechanics i.e. 

Do you have any suggestions? Please write in comment box. 

Reference: 

Fluid mechanics, By R. K. Bansal  
August 12, 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  

Also read

August 12, 2018

ADVANTAGE OF TRIANGULAR NOTCH OVER RECTANGULAR NOTCH

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

Triangular notch or weir is always preferred over a rectangular notch or weir due to the following reasons

The expression for discharge for a right angle V-notch or weir is very simple. 

Ventilation of triangular notch is not necessary. 

Triangular notch will provide more precise results during measuring low discharge as compare to result obtained from rectangular notch. 

Only one reading of H will be required for determination of discharge in case of triangular notch. 

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

Do you have any suggestions? Please write in comment box. 

Reference: 

Fluid mechanics, By R. K. Bansal 
Image Courtesy: Google 

Also read: 

Thursday, 9 August 2018

August 09, 2018

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
Cd = 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 = Cd 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. 

Do you have any suggestions? Please write in comment box. 

Reference: 

Fluid mechanics, By R. K. Bansal 
Image Courtesy: Google 

Also read: 

Friday, 3 August 2018

August 03, 2018

DISCHARGE OVER A RECTANGULAR NOTCH AND WEIR

We were discussing the various types of notches and weirs i.e. classifications of notches and weirs and also the difference between Notches and Weirs in the subject of fluid mechanics in our recent posts. 

Now we will go ahead to find out the discharge over a rectangular 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 rectangular notch or over a weir will be same. 

Now, let us consider that we have channel carrying water and let us think a rectangular 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 over the crest 
L = Length of the rectangular notch or weir 

Let us consider one elementary horizontal strip of water of thickness dh and length L as displayed in above figure. 
dh = Thickness of elementary horizontal strip of water flowing over the rectangular notch or weir 
h = Depth of elementary horizontal strip of water flowing over the rectangular notch or weir 
Cd = Co-efficient of discharge 

Area of elementary horizontal strip of water = L x dh 

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 a rectangular notch or weir. 

Now we will go ahead to start a new topic in the subject of fluid mechanics i.e. Discharge over triangular notch or weir with the help of our next post. 

Do you have any suggestions? Please write in comment box. 

Reference:
Fluid mechanics, By R. K. Bansal
Image Courtesy: Google 

Also read:

Sunday, 29 July 2018

July 29, 2018

CLASSIFICATION OF NOTCHES AND WEIRS

We were discussing the basic concepts and also difference between Notches and Weirs in the subject of fluid mechanics in our recent posts. 

Now we will go ahead to find out the various classifications of Notches and Weirs with the help of this post. 

Notch 

Notch is basically defined as a device which is used for determining the flow of liquid through a small channel or a tank. 

Notches might be defined as the opening provided in one side of a tank or reservoir or a small channel in such a way that the liquid surface in the tank or channel is below the top edge of opening. 

Classification of notches 

There are following types of notches on the basis of shape of opening and these are as mentioned here 
Rectangular Notch 

Triangular Notch or V- notch 
Trapezoidal Notch 
Stepped Notch 

There are following types of notches on the basis of the effect of sides on the nappe and these are as mentioned here 

  1. Notch with end contraction 
  2. Notch without end contraction or suppressed notch 

Weir 

A weir will be basically a concrete or masonary structure which will be located in an open channel over which flow will take place. 

We can also define as the structure constructed across the river or large canal for storing water on upstream side. 

Weir will be usually in the form of vertical wall, with a sharp edge at the top, running all the way across the open channel. 

Classification of weirs 

There are following types of weirs on the basis of shape of opening and these are as mentioned here 

  1. Rectangular weir 
  2. Triangular weir 
  3. Trapezoidal or Cippoletti weir 

There are following types of weirs on the basis of shape of the crest and these are as mentioned here 

  1. Sharp crested weir 
  2. Broad crested weir 
  3. Narrow crested weir 
  4. Ogee shaped weir  

There are following types of weirs on the basis of the effect of sides on the emerging nappe and these are as mentioned here 

  1. Weirs with end contraction 
  2. Weirs without end contraction or suppressed notch 

Now we will go ahead to find out the classifications of notches and weirs, in the subject of fluid mechanics, in our next post. 

Do you have any suggestions? Please write in comment box. 

Reference: 

Fluid mechanics, By R. K. Bansal 
Image Courtesy: Google