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EXPERIMENT No.1

CORIOLLI’S COMPONENT APPARATUS

AIM :

To Measure the various parameters comprising the coriolli’s component of

acceleration.

THEORY : The apparatus has been designed to enable the student to measure the various

parameters comprising the coriolli’s component of acceleration. To maintain this

acceleration long enough for measurements to be taken the conventional slider

mechanism is replaced by two streams of water flowing radially outwards from an

inverted T shape tube which rotates about its vertical axis so that the water in

passing along the tube is subjected to coriolli’s component acceleration

Consider the motion of the slider B on the the crank OA . Let OA rotates with

constant angular velocity ω rad / sec. and slider B have the velocity v radially

outwards relative v outwards relative to the crank centre O . The velocity diagram

for the slider in two position separated by angular displacement dΘ

On the same diagram V1 represents the resultant choice of velocity of slider .

This velocity has two components vu and vu in radial and tangential directions

respectively.

Tangential Component = vu = vs + sµ

= r sin δ0 + w ( r + δ r )

= r δ0 + ω0 r ………….. ( 1 )

Rate of change of tangential velocity = r δ0 + ω δr

∆t δt

= ω r + ω r = 2 ω r …………( 2 )

Equation ( 2 ) represents the coriolli’s component of acceleration .This accelerationis made up of two component , one due to the increase of radius and other from

changing direction of the crank.

HYDRAULIC ANALOGY :

Consider the diagram , short column of fluid if length dr at a distance r from axisof rotation of the tube ,as shown in fig . then velocity of fluid relative to the tube rand the angular velocity of the tube is ω , the coriolli’s component of accelerationof the column is 2ωr in a direction perpendicular to , and in a place of rotation ofthe tube .The torque dT applied by the tube to produce this acceleration is then

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δ ω 2 ω rg

Where δ ω is the weight of the short column of fluidIf w is the specific weight of the fluid and a is the cross sectional area of the tube

oulet , thenδ ω = ω a δr

δT = 2r w ω a r δrg

and the complete torque applied to column of length 1 is given by

T = 2r w ω a r δrg

T = ω w r a I2

g

or coriolli’s component of acceleration

Ca = 2 g T ( Considering both tubes )

ω a I2

APPARATUS :

The apparatus consist of two brass tube , projected radialiy from centra Perspex

header tube , are rotated by direct D.C motor , mounted vertically in a ball

bearing housing . The torque supplied by the motor is measured by a voltmeter

and ammeter provided in the central panel. The speed of rotation of the motor ismeasured by RPM meter . Water from the pump flows to the header tube through

the flow control valve. A rotameter is provided to measure the water flow rate.

The water leaving the radial tubes returns to the via pump via sump . The splash

tank and all the accessories mounted on the fabricated frame

PROCEDURE :

1. Check the bypass valve is fully open

2. Check the position of dimmer stat . it must be zero position 3. After switching the main switch , with the help of dimmerstat increase the

speed of motor up to certain speed.

4. Now start the water pump and with the help of bypass valve adjust water

level constant ( any level ) in the vertical header tube.

5. Take the reading on the voltmeter , ammeter , rpm indicator , rotameter .

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6. Now switch off the pump and take reading of voltmeter and ammeter

7. Repeat the procedure by varying speed of the shaft and take the readings.

OBSERVATIONS :

1. Length of Rotating Arm : 0.3 m2. Dia of the tube outlet = 9mm3. Cross Sectional area of tube = 6.36 X 10

-6

4. N = No of Revolutions ( RPM Indicator )5. V = Velocity through the tube6. P = Power7. T= Torque

8. ρ = Density of water 9. L = Length of tube

10. v = Voltmeter reading

11. I = Ammeter reading

12. a = area of the tube 13. g = gravitational constant

14.1. OBSERVATION TABLE : PUMP ON POSITION

SR. NO. SPEED ( RPM ) FLOW RATELPH

VOLTMETER AMMETER

2. OBSERVATION TABLE : PUMP OFF POSITION

SR. NO. SPEED ( RPM ) FLOW RATELPH VOLTMETER AMMETER

CALCULATION :

Torque T1 ,

We have , P = 2 π N T Watts60

T1 = v X I X 60

2 π N

FRICTIONAL TORQUE ( T2 ) =

T2 = v X I X 60

2 π N

Net Torque T = ( T1 -- T2 )

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Now Coriolli’s Component of Acceleration

Ca = T m / sec2

2g ρ a L2

Now calculating coriolli’s component of Acceleration theoretically :

V = q / a m/secWhere

V = Velocity through the tubeq = Volumetric flow ratea = Cross Sectional area of tube

Ca theoretical = 2 X ω X Vω = 2 π N / 60 rad /sec

SAMPLE CALCULATION :

1. OBSERVATION TABLE : PUMP ON POSITION


VOLTMETER AMMETER

1. 120 1000 68.3 1.652. 200 800 87 1.95

3. 173 750 78 1.7

2. OBSERVATION TABLE : PUMP OFF POSITION


VOLTMETER AMMETER

1. 330 71.5 1.25

2. 92.5 1.333. 80 1.15

CALCULATION :Torque T1 ,

We have , P = 2 π N T watts60

T1 = v X I X 60

2 π N

T1 = 1.65 X 68.3 X 60

2 π x 120

= 2.57 N-m

FRICTIONAL TORQUE ( T2 ) =

T2 = v X I X 60

2 π N

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T2 = 1.25 X 71.5 X 60

2 π x 330

= 2.57 N-m

Net Torque T = ( T1 -- T2 )

= ( 8.97 – 2.57 )

= 6.4 N-m

Now Coriolli’s Component of Acceleration

Ca = T m / sec2

2g ρ a L2

Ca = 6.4 m / sec2

2 X 1000 X 6.36 X 10-5

X 0.32 X 9.81

= 56.98 m /sec2

Now calculating coriolli’s component of Acceleration theoretically :V = q / a m/secWhere

V = Velocity through the tubeq = Volumetric flow ratea = Cross Sectional area of tube

V = 1000 X 10-3

/ ( 3600 X 6.36 X 10-5

X 2 )

= 2.18 m /secCa theoretical = 2 Xω X V

ω = 2 π N / 60 rad /sec

ω = 2 π X 120 / 60 = 12.56 rad /secCa theoretical = 2 Xω X V

= 2 X 12.56 X 2.18

= 54.76 m /sec2

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E_01_FMHT