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Tuesday, 10 July 2018

HYDRAULIC COEFFICIENTS

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

Now we will go ahead to find out the various hydraulic co-efficients, in the subject of fluid mechanics, with the help of this post. 

We will find out here following three types are hydraulic co-efficients as mentioned below 

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. 

Actual velocity of liquid jet at vena-contracta will be less than the theoretical velocity due to the friction of the orifice. 

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 

Value of co-efficient of velocity varies from 0.95 to 0.99 depending on the types of orifices, shape and size of orifice. 

For sharp edge orifice, value of co-efficient of velocity will be 0.98. Theoretical velocity of liquid jet could be understood by securing the post flow through an orifice

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 

Value co-efficient of contraction varies from 0.61 to 0.69 depending on shape and size of orifice and head of liquid under which liquid flow takes place. 

We will take usually 0.64 for Co-efficient of contraction. 

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 

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. 

Value co-efficient of discharge varies from 0.61 to 0.65 depending on shape and size of orifice. 
We will take usually 0.62 for Co-efficient of discharge. 

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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