We were discussing the basicÂ difference
between orifice and mouthpiece,Â classification
of orifices and mouthpieces,Â advantages
and disadvantages of orificesÂ and alsoÂ 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 experimental
process to determine the hydraulic coefficients, in the subject of fluid
mechanics, with the help of this post.Â

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**Experimental
process to determine the hydraulic coefficientsÂ **

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**Coefficient
of discharge (C**_{d})

_{d})

Let us consider a tank filled with water
and fitted with an orifice of area a as displayed here in following figure. Let
us think that water is flowing through the orifice under a constant head H.Â

Water flowing through the orifice will
be collected in a measuring tank for a time t and we will also measure the
height of water collected in the measuring tank in time t.Â

Image: Tank with orifice and measuring
tank

Actual discharge and theoretical discharge
through the orifice will be determined by the following formulas as mentioned
here.Â

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**Coefficient
of discharge (C**_{V})

_{V})

Let us think that water, flowing through the orifice, is developing a liquid
jet whose cross-sectional area is smaller than the cross-sectional area of the
circular orifice. Area of liquid jet is decreasing and area is minimum at
section CC.Â

Section CC will be
approximately at a distance of half of diameter of the circular orifice. At
section CC, the streamlines are straight and parallel with each other and
perpendicular to the plane of the orifice. This section CC will be termed as
Vena-contracta.Â

Beyond the section CC, liquid jet diverges and will be attracted towards the downward direction due to gravity.Â

Beyond the section CC, liquid jet diverges and will be attracted towards the downward direction due to gravity.Â

Let us consider that a
liquid particle which is at vena-contracta at any time and takes the position
at P along the jet in time t. Let us assume following data as mentioned here.Â

x = Horizontal distance
travelled by the particle in time t

y = Vertical distance
between P and section CC

V = Actual velocity of jet
at vena-contractaÂ

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**Coefficient
of discharge (C**_{V})

_{V})

Let us recall the relation
between hydraulic coefficient and we will secure the value of coefficient of contraction
by using the value of coefficient of discharge and coefficient of velocity.Â

Now we will go ahead to find out the
method to determine the flow through a large orifice, 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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