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Tuesday, 10 July 2018

RELATION BETWEEN HYDRAULIC COEFFICIENTS

We were discussing the basic difference between orifice and mouthpiececlassification of orifices and mouthpieces, advantages and disadvantages of orifices and also hydraulic coefficients, in the subject of fluid mechanics, in our recent posts. 

Now we will go ahead to find out the relation between hydraulic coefficients, in the subject of fluid mechanics, with the help of this post. 

We will first briefly explain the various types of hydraulic coefficients and after that we will secure here the relation between hydraulic coefficients. 

Co-efficient of velocity, CV

Co-efficient of velocity is basically defined as the ratio of actual velocity of liquid jet at vena-contracta to the theoretical velocity of the liquid jet. 

Co-efficient of velocity is denoted by CV and will be given as mentioned here. 

Co-efficient of velocity = Actual velocity of liquid jet at vena-contracta / theoretical velocity 

Co-efficient of contraction, CC

Co-efficient of contraction is basically defined as the ratio of area of liquid jet at vena-contracta to the area of the orifice. 

Co-efficient of contraction is denoted by CC and will be given as mentioned here. 

Co-efficient of contraction = Area of liquid jet at vena-contracta / Area of the orifice 

Co-efficient of discharge, Cd

Co-efficient of discharge is basically defined as the ratio of actual discharge from an orifice to the theoretical discharge from the orifice. 

Co-efficient of discharge is denoted by Cd and will be given as mentioned here 

Co-efficient of discharge = Actual discharge from an orifice / Theoretical discharge from the orifice 

Relation between hydraulic coefficients

We can secure the relation between hydraulic coefficients by elaborating the formula of coefficient of discharge. 

As we have seen above that
Co-efficient of discharge = Actual discharge from an orifice / Theoretical discharge from the orifice 

Cd = Q/Qth
Where,
Q = Actual discharge from an orifice
Qth = Theoretical discharge from an orifice
Q = Actual velocity x Actual area
Qth = Theoretical velocity x Theoretical area 

Co-efficient of discharge = (Actual velocity x Actual area) / (Theoretical velocity x Theoretical area) 
Co-efficient of discharge = (Actual velocity / Theoretical velocity) X (Actual area / Theoretical area) 
Co-efficient of discharge = Co-efficient of velocity X Co-efficient of contraction 

Cd = CV x C

Therefore, we can also define the co-efficient of discharge as the product of Co-efficient of velocity and Co-efficient of contraction. 

Now we will go ahead to find out the method to determine the various types of hydraulic co-efficients, 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

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