RELATION BETWEEN HYDRAULIC COEFFICIENTS

We were discussing the basic difference between orifice and mouthpiece, classification 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, C_V

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 C_V 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, C_C

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 C_C 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, C_d

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 C_d 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

C_d = Q/Q_th

Where,

Q = Actual discharge from an orifice

Q_th = Theoretical discharge from an orifice

Q = Actual velocity x Actual area

Q_th = 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

C_d = C_V x C_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.

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