EXPERIMENTAL DETERMINATION OF 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 experimental process to determine the hydraulic coefficients, in the subject of fluid mechanics, with the help of this post. 

Experimental process to determine the hydraulic coefficients 

Coefficient of discharge (C_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. 

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. 

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. 

Coefficient of discharge (C_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. 

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. 

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

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. 

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-contracta 

Coefficient of discharge (C_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. 

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. 

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

Reference:

Fluid mechanics, By R. K. Bansal

Image Courtesy: Google

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