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

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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.Â

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

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**Co-efficient of velocity, C**_{V}

_{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.Â

Co-efficient
of velocity is denoted by C

_{V}Â and will be given as mentioned here.Â

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

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**Co-efficient of contraction, C**_{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.Â

Co-efficient
of contraction is denoted by C

_{C}Â and will be given as mentioned here.Â

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

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**Co-efficient of discharge, C**_{d}

_{d}

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

Co-efficient
of discharge is denoted by C

_{d}Â and will be given as mentioned hereÂ

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

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**Relation between hydraulic coefficients**

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

As we have seen above that

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

C

_{d}Â = Q/Q_{th}
Where,

Q = Actual
discharge from an orifice

Q

_{th}Â = Theoretical discharge from an orifice
Q = Actual
velocity x Actual area

Q

_{th}Â = Theoretical velocity x Theoretical areaÂ
Co-efficient
of discharge = (Actual velocity x Actual area) / (Theoretical velocity x
Theoretical area)Â

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

Co-efficient
of discharge = Co-efficient of velocity X Co-efficient of contractionÂ

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**C**_{d}Â = C_{V}Â x
C_{CÂ }

_{d}Â = C

_{V}Â x C

_{CÂ }

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

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.Â

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

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**Reference:**

Fluid
mechanics, By R. K. Bansal

Image
Courtesy: Google

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