Experiment 2 Orifice Coefficients

Objective:

• To calculate the Coefficient of Discharge Cd, Coefficient of Velocity Cv, and Coefficient of Contraction Cc for various heads over orifice fitted in the side of a tank.

• To draw a relationship between these coefficients and the size of the orifice. Concepts to be learned: Principle of conservation of energy, continuity equation, Discharge, pressure, velocity, kinetic energy, pressure energy, potential energy and properties of fluids, loss due to entrance of flow in a pipe, contraction loss, related loss in pressure, velocity and mass flow rate. Theory: The coefficient of discharge is a ratio of the actual discharge and the theoretical discharge. The actual discharge is the discharge that occurs, affected by friction as the jet passes through the orifice. The theoretical discharge would be the discharge achieved without friction. The coefficient of discharge is related to the volumetric flow rate of the fluid and the cross sectional area of the orifice. It is also related to the gravitational constant and the head over the orifice.

Coefficient of Discharge theo

act

dQ

QC = , where

12gHaQth = and

t

HAQact

2⋅

=

where Qact = Volumetric Flow Rate (actual) a = Cross sectional area of the orifice A = Cross sectional area of the measuring tank g = the gravitational constant H1 = head over orifice H2 = Height of water collected in the tank t = Time of water collection in the tank The Coefficient of Velocity is the ratio of the actual velocity to the ideal velocity. The actual velocity is the velocity that is achieved affected by friction as the jet passes through the orifice. The ideal velocity would be the velocity achieved without friction. The Coefficient of Velocity is related to the horizontal (x) and vertical (y) distances spanned by the water jet. The trajectory of the jet from Vena-contracta of the orifice is that of the projectile under the action of the gravity.

tgHCvtVx a ⋅== 2 2

2

1gty =

yH

xCv

4

=

The Coefficient of Contraction is a ratio of the actual diameter of the jet divided by the ideal diameter of the jet. The actual diameter is the diameter of the water jet at the Vena-contracta. The ideal diameter would be the diameter of the orifice. The Coefficient of Contraction can be derived from a relationship with the Coefficients of Discharge and Velocity.

v

d

cC

CC =

Description of the Apparatus: The apparatus consist mainly of a cylindrical tank with a small orifice near the bottom of the tank. There is an inlet hose through which the tank is filled and supplied with water and there is an adjustable overflow pipe nearcan be perfectly maintained. The tank is mounted on a frame along with a recording system that is used to measure the jet of water produced from the orifice when in use. The recording systemconsists of a clipboard and adjustable needles. The needles can be adjusted in height to correspond with the arc of the water jet. Paper can be mounted against the clipboard and the position of the tops of the needles can be recorded on the paper. Experimental Procedure:

1. Set up the apparatus such that the orifice is facing the sink. Place the water drainer under the apparatus. Fill the water tank up to a level. Record the water level or head (H). Measure the diameter of the orifice fitted in the orificeshould be formed and protruding forcefully from the tank.

2. Place the paper in the clamp against the clipboard. Raise all the needles to their starting position.

3. Measure the flow rate Q of the water jet. Collect water frotime. Record the volume of water collected and the time for which it was collected.

4. Adjust the height of each needle such that the tip of the needle is just above the water jet as it passes underneath.

5. Once all the needles areagainst the clipboard. Venathe place where the water jet narrows from the diameter of the orifice to the diameter of the jet. The position of the venamarks are made, return the needles to their starting position.

6. Repeat steps 2 through 5 for 4 more heads. It is recommended that you simply increase the water level each time uthe input water flow.

7. Measure x-distance and y

Observations:

1. Cross sectional areas of orifice and measuring tank.2. For each jet, measure horizontal and vertical distances X and Y from vena

after locating a point on the falling jet.

S.No Water Head

The apparatus consist mainly of a cylindrical tank with a small orifice near the bottom of the tank. There is an inlet hose through which the tank is filled and supplied with water and there is an adjustable overflow pipe near the top of the tank through which the level of water in the tank can be perfectly maintained. The tank is mounted on a frame along with a recording system that is used to measure the jet of water produced from the orifice when in use. The recording systemconsists of a clipboard and adjustable needles. The needles can be adjusted in height to correspond with the arc of the water jet. Paper can be mounted against the clipboard and the position of the tops of the needles can be recorded on the paper.

Set up the apparatus such that the orifice is facing the sink. Place the water drainer under the apparatus. Fill the water tank up to a level. Record the water level or head (H). Measure the diameter of the orifice fitted in the orifice plate. At this time the water jet should be formed and protruding forcefully from the tank. Place the paper in the clamp against the clipboard. Raise all the needles to their starting

Measure the flow rate Q of the water jet. Collect water from the jet for a set amount of time. Record the volume of water collected and the time for which it was collected.Adjust the height of each needle such that the tip of the needle is just above the water jet

Once all the needles are set, mark the position of the top of each needle on the paper against the clipboard. Vena-contracta should serve as first mark. The venathe place where the water jet narrows from the diameter of the orifice to the diameter of

sition of the vena-contracta is usually very close to the orifice. Once all the marks are made, return the needles to their starting position. Repeat steps 2 through 5 for 4 more heads. It is recommended that you simply increase the water level each time until you near the top of tank. You need to increase the rate of

distance and y-distance for each jet of the orifice w.r.t. heads

(Available)

Cross sectional areas of orifice and measuring tank. each jet, measure horizontal and vertical distances X and Y from vena

after locating a point on the falling jet.

Water Head Height of water Location of a point in

The apparatus consist mainly of a cylindrical tank with a small orifice near the bottom of the tank. There is an inlet hose through which the tank is filled and supplied with water and there is

the top of the tank through which the level of water in the tank can be perfectly maintained. The tank is mounted on a frame along with a recording system that is used to measure the jet of water produced from the orifice when in use. The recording system consists of a clipboard and adjustable needles. The needles can be adjusted in height to correspond with the arc of the water jet. Paper can be mounted against the clipboard and the

Set up the apparatus such that the orifice is facing the sink. Place the water drainer under the apparatus. Fill the water tank up to a level. Record the water level or head (H).

plate. At this time the water jet

Place the paper in the clamp against the clipboard. Raise all the needles to their starting

m the jet for a set amount of time. Record the volume of water collected and the time for which it was collected. Adjust the height of each needle such that the tip of the needle is just above the water jet

set, mark the position of the top of each needle on the paper contracta should serve as first mark. The vena-contracta is

the place where the water jet narrows from the diameter of the orifice to the diameter of contracta is usually very close to the orifice. Once all the

Repeat steps 2 through 5 for 4 more heads. It is recommended that you simply increase ntil you near the top of tank. You need to increase the rate of

w.r.t. heads.

each jet, measure horizontal and vertical distances X and Y from vena-contracta,

in tank H1 collected in Measuring tank H2

the falling jet Horizontal distance X

Vertical distance Y

1 2 3 4 5 6

Specimen Calculations: Show calculation procedure at each stage of calculation for any one head over orifice. Show calculations for all head over orifice in the form of table.

1. Calculate theoretical discharge based on theoretical velocity of free falling jet from a tank.

2. Calculate actual discharge. 3. Obtain coefficient of discharge for each head over orifice. 4. Calculate Coefficient of velocity for each head using derived equation. 5. Obtain Coefficient of contraction from calculated Cd and Cv values.

S.No

12gHaQtheo = 60

2HA

Qact

⋅

= th

act

dQ

QC =

14YH

XCv =

v

d

cC

CC =

1

2 3

Report Requirements:

1. Calculate the Cd and Cv for all 5 readings. Then calculate the average of all readings. 2. From the average values for Cd and Cv, calculate Cc for the orifice. 3. Comment about the relationship between all three coefficients with respect to the

cross sectional area of the orifice and with respect to one another. Speculate on theory to explain these relationships.