Coefficient of discharge of an orifice of a given shape by Mr. Aasif Baig (Asst. Professor, Civil Engineering Department, Tulsiramji Gaikwad-Patil College of Engineering and Technology)
To determine the coefficient of discharge of an orifice of a given shape. Also to determine the coefficient of velocity and the coefficient of contraction of the orifice and mouth piece.
An orifice is small geometrical opening provided in the side or at the bottom of a tank. It is used for the measurement of the discharge. Usually orifice has a sharp edge. A jet approaching the orifice continues to converage beyond the orifice till the streamlines are parallel. This section of the jet, which is at a distance of 0.5 times of the diameter of the orifice from the face of the tank, is a section of minimum area and is known as vena-contract. The ratio of the area of the jet at the vena-contract (ac), to the area of the orifice (a) is called the coefficient of contraction Cc.
Cc = ac/a
Because of the friction in fluid, the actual velocity is less than ideal velocity. The Coefficient of velocity (Cv) is the ratio of actual velocity (v) to ideal velocity or Theoretical velocity (Vth).
Cv = V / Vth
Experimentally, Cv can be determined from the equation.
Cv = (X2/ 4yh)
Where
X = horizontal coordinate of any point on the jet with respect to vena-contracta,
y = Vertical coordinate of the same point on the jet w.r.t. the axis of the opening and
h = height of water in the balancing tank above the center of the orifice.
The actual discharge from an orifice is less than the theoretical discharge because of the friction and also due to the contraction of the jet. The coefficient of discharge (Cd) of an orifice is given as:
Cd = Qact / Qth
Cd , Cv and Cc are related as :
Cd = Cv X Cc
For measuring x and y a pointer gauge mounted on a scale, which is attached to the balancing tank, is used. Pointer gauge can be moved horizontally as well as vertically and corresponding movements can be read on horizontal and vertical scales respectively.
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