The laboratory experiment procedure to determine hydraulic coefficients of an orifice is explained in this article. The coefficient of contraction, the coefficient of velocity and coefficient of discharge are hydraulic coefficients of an orifice.
Contents:
Theory
When flow takes place through an orifice from the supply tank, the water jet leaving the orifice gets contracted at the downstream of the orifice and the point where it gets the maximum contraction is called as vena-. Following are three hydraulic coefficients of orifice:
- Coefficient of Contraction (C_{c})
- Coefficient of Velocity (C_{v})
- Coefficient of discharge (C_{d})
1. Coefficient of Contraction (C_{c})
It is the ratio of area of water jet at vena-contracta to the area of the orifice.
Where,
a_{c} = Area of jet at vena-contracta
a = Area of the orifice
2. Coefficient of Velocity (C_{v})
It is the ratio of velocity of water jet at vena-contracta to the theoretical velocity.
Where,
x = Horizontal ordinate
y = Vertical ordinate
h = Head
3. Coefficient of discharge (C_{d})
It is the ratio of actual discharge to the theoretical discharge.
Where,
Q = Actual discharge
a = Area of the orifice
g = acceleration due to gravity
The relation between the of contraction, of velocity and coefficient of discharge can be expressed as :
Coefficient of discharge = coefficient of contraction X coefficient of velocity
Apparatus
- A supply tank with circular orifice, scales and sliding apparatus
- A Measuring tank
- A stopwatch
- Micrometer contraction gaug
Procedure
The Procedure to determine hydraulic coefficients of an orifice is as follows:
- Fill the supply tank with water and allow the water to flow through the orifice.
- Maintain a constant head in the supply tank by adjusting the water supply valve provided.
- After attaining constant head, now observe the water jet coming from the orifice and note the point where maximum contraction occurs which is nothing but vena-contracta.
- At vena-contracta, measure the diameter of using contraction gauge.
- Adjust the vertical scale to the position of vena-contracta such that the hook provided at the bottom of the vertical scale should touch the center of the water jet. Note down the initial coordinates (x_{1}, y_{1}) at this point.
- After recording initial coordinates, slide the vertical scale through the horizontal scale up to a certain distance and adjust the vertical scale with its hook touching the water jet and record the final coordinates (x_{2}, y_{2}).
- Take the stopwatch and note down the time taken for the rise of water up to a certain height in the measuring tank and calculate the discharge.
- Repeat the above procedure for various constant heads and calcite the average values of hydraulic coefficients of an orifice.
Observations
Diameter of the orifice, d =
Dimensions of the measuring tank =
S.No | Head (h) | Diameter of Jet at vena-contracta (d_{c}) | Area of Jet at vena-contracta (a_{c}) | Coefficient of Contraction (C_{c}) | x | y | Coefficient of Velocity (C_{v}) | Discharge in measuring tank (Q) | Coefficient of discharge (C_{d}) |
1 | |||||||||
2 | |||||||||
3 | |||||||||
4 | |||||||||
5 |
Calculations
Volume of water collected in tank in t seconds, V = area of tank X Rise of water level in t seconds
Discharge in measuring tank, Q = volume/time
Horizontal co-ordinate, x = x_{2} – x_{1}
Vertical co-ordinate, y = y_{2} – y_{1}
Result
Coefficient of contraction of orifice, C_{c} =
Coefficient of velocity of orifice, C_{v }=
Coefficient of discharge of orifice, C_{d }=