To determine the coefficient of discharge Cd, velocity Cv and contraction Cc of various types of orifices and mouth pieces.
Equipement Supply tank with overflow arrangement and provision of fitting of orifice or mouthpiece installed in the vertical plane of the tank side, Scale and sliding apparatus with hook gauge, a set of orifice.
Introduction and theory:An Orifice is an opening in the wall of tank, while a mouthpiece is a short pipe fitted in the same opening. A mouthpiece will be running full if its length does not exceed two to three times the diameter. Both orifice and mouthpiece are used for discharge measurement. The jet approaching the orifice continue to converge beyond the orifice till the streamlines becomes parallel. This section of the jet is then a section of in. area and is known as vena contracta.
If Vc is the true horizontal velocity at the vena contracta, then the properties of jet trajectory gives the following relationship:
y = g/2 ν2c.x 2
νc = {gx2/2y}1/2where x and y are the coordinates of the jet trajectory at any point
The theoretical velocity in the plane of the vena contracta V0 is given by
ν02/2g = h
i.e., ν0= (2gh)1/2
Now coefficient of velocity C ν = actual velocity/Theoritical velocity
C ν = x/2√yh
In which h is the constant head in the supply tank and x and y are coordinates of jet with respect to center of opening.
The actual discharge Q when divided by a √ 2gh yield the coefficient of discharge Cd. Here is the area of cross section of the orifice ( or the mouthpiece) and g is the acceleration due to gravity.
Once Cd and Cν are known the coeficient of contraction Cc can be obtained by dividing Cd with Cv
Cc = Cd / Cv
The coefficient of discharge can also be computed by falling head method in which the supply is kept closed after filling the tank to a suitable level and fall in the head from h1 to h2 in time T is noted. The coefficient of discharge is then obtained from Cd = 2A/T.a√2g[h1 1/2- h2 1/2]
Experimental Set Up:The experimental set up consist of a supply tank with over flow arrangement and glass tube with gauge for water level measurement in the tank. There is also provision for fixing the various orifices and mouthpieces (interchangeable) installed in the vertical plane of the tank side. Arrangement is made such that the water passes only through this attached opening. Water comes out of the opening in the form of jet.
A horizontal scale, on which is mounted a vertical scale with a hook gauge, is attached to the supply tank. Thus hook gauge can be moved horizontally as well as vertically in x and y direction and its corresponding movement can be read on horizontal and vertical scales respectively collecting tank used to find the actual discharge of water through the jet.
Note down the relevant dimensions as area of collecting tank and supply tank.
Attach a orifice/mouthpiece and note down its diameter. The apparatus is leveled.
The water supply was admitted to the supply tank and conditions allowed to steady to give a constant head. The lowest point of the orifice/mouthpiece used as the datum for the measurement of h and y.
The discharge flowing through the jet is recorded together with the water level in the supply tank.
A the orifice/mouthpiece used as the datum for the measurement of h and y.
The discharge flowing through the jet is recorded together with the water level in the supply tank.
A series of readings of dimensions x and y was taken along the trajectory of the jet.
The procedure is repeated by means of flow control value.
The procedure is repeated for other types of orfice/mouthpiece.
Observation and Computer Sheet:
Area of cross section of collecting tank =
Size and shape of the mouth piece/orifice =
Area of cross section of mouth piece/orifice. a =
Reading on the piezometer at the level on the centre of mouth piece/orifice ho =
Determination of Cd
| Sr. No. | Reading on the Piezometer, h1 (cm) | Value of h =(h1-h0) | Discharge Measurement/Initial(cm)/Final(cm)/Time (s)/Discharge, Q,(cm 3/s) | Cd = Q/a√2gh |
| Sr. No. | h (cm) | Reading on Scales/Horizontal, x'(cm)/Vertical, y'(cm) | x = x'- x0 (cm) | y = y'-y0 (cm) | Cν = X/2√yh |
Average Cν =
Therefore Cc = Cd/Cv =
Reading on the piezometer at the level on the center of mouth piece/orifice = h0 = k = 2A/a√2g
| Sr. No. | Piezometer Reading/Initial a1 (cm)/Final a2 (cm) | h1 = a1 - h0 | h2 = a2 - h0 | Time in lowering the water, T (s) | Cd= k/T (√h1-√h2) |
Get all latest content delivered to your email a few times a month.
