Flow Through Orifice and Mouthpiece

Flow through orifice and mouthpiece Aim To study the flow of liquid through orifice and the mouthpiece and determine the coefficient of discharge and coefficient of velocity.

Apparatus     

Single phase power supply: 220 volts, 50 hz, 5 amp with earth. Measuring tank and sump tank. Adjustable overflow arrangements. Variable head tank. Control and by-pass valve.

Procedure         

Clean the apparatus and close the drain valves Close all flow control valves and open the by-pass valve Fix the test piece at testing section Switch on power supply and then the pump Adjust flow control valve to regulate water flow in variable head tank Adjust the water head in tank and record the head Fix the pointer at 3 different points of the stream and measure x and y coordinates so that you can plot the profile of flow After experiment is over close flow control valve Drain variable head tank in the sump tank

Theory  Orifice whenever liquid changes its direction abruptly it contracts until it becomes parallel to the flow. Contraction ends in vena-contracta.  Mouthpiece A short piece of length that is least 3 times diameter connected to face of orifice is called mouthpiece. Discharge rate through mouthpiece is higher that discharge rate of mouthpiece as fluid accelerates till vena-contracta.  Co-efficient of velocity It is the ratio between actual velocity of jet at vena contracta and theoretical velocity of jet. 𝒗 𝑪𝒗 = 𝟐 𝟐∗𝒈∗𝒉  Co-efficient of discharge It is the ratio of actual discharge from an orifice to theoretical discharge. 𝑸𝒂 𝑸𝒅 = 𝑸𝒕

ME-313, IIT Gandhinagar, Dept. of Mechanical Engineering

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Notations          

A = area of measuring tank. a = area of orifice and mouthpiece. v = actual velocity at vena contracta 2 2 ∗ 𝑔 ∗ ℎ= theoretical velocity (m/sec) R = rise of water level in measuring tank (cm) T = time taken to R (sec) h = Water head X = horizontal distance traveled by the liquid particle from Vena-contracta Y = vertical distance between vena-contracta and liquid particle

Formulae 

Co-Efficient of velocity 𝑪𝒗 =



𝒗 𝟐

Actual discharge 𝑸𝒂 =



𝟐∗𝒈∗𝒉

𝑨∗𝑹 𝒕 ∗ 𝟏𝟎𝟎

Theoretical discharge 𝑸𝒕 = 𝒂 ∗ 𝟐 𝟐 ∗ 𝒈 ∗ 𝒉



Coefficient of discharge 𝑸𝒅 =

𝑸𝒂 𝑸𝒕

Data       

No of Orifices: Material Acrylic (2 Nos.) Dia. 10mm and 15 mm Mouthpiece: Material Acrylic Constant Head tank : 35 Litres. Hook/Pointer Gauge: To measure X-Y co-ordinates of Jet. Flow Measurement: Using Measuring Tank with Piezometer, Capacity 25 Litres. Sump Tank: Capacity 70 Litres

ME-313, IIT Gandhinagar, Dept. of Mechanical Engineering

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Observation (Orifice) Origin= (0.1, 25.71)

water head 36.7

30

24

actual x 0 9.91 19.73 0 7.59 15.64 0 8.62 15.56

x 0.1 10.01 19.83 0.1 7.69 15.74 0.1 8.72 15.66

actual y 0 -1.35 -4.39 0 -1.13 -3.83 0 -1.77 -4.69

y 25.71 24.36 21.32 25.71 24.58 21.88 25.71 23.94 21.02

rise of water(R) 5.6 5.6 5.6 4.5 4.5 4.5 4.1 4.1 4.1

Time(t) 45 45 45 45 45 45 45 45 45

Cv

Qa

Qt

Cd

0.703953 0.777198

0.000124444 0.000124444

0.000210645 0.000210645

0.590777 0.590777

0.651796 0.729536

0.0001 0.0001

0.000190449 0.000190449

0.525074 0.525074

0.661279 0.73331

9.11111E-05 9.11111E-05

0.000170343 0.000170343

0.534868 0.534868

Observation(Mouthpiece) Origin= (0.42, 25.71)

water head 37

34

27

x 0.42 10.8 20.03 0.42 9.34 20.78 0.42 8.43 13.3

y 25.71 24.45 21.09 25.71 24.65 20.5 25.71 24.37 20.42

ME-313, IIT Gandhinagar, Dept. of Mechanical Engineering

rise of water(R) 5.1 5.1 5.1 4.9 4.9 4.9 4.2 4.2 4.2

Time(t) 45 45 45 45 45 45 45 45 45 Page 3

actual x 0 10.38 19.61 0 8.92 20.36 0 8.01

actual y 0 -1.26 -4.62 0 -1.06 -5.21 0 -1.34

Cv

Qa

Qt

Cd

0.760118 0.749939

0.000113333 0.000113333

0.000211505 0.000211505

0.535843 0.535843

0.742921 0.764873

0.000108889 0.000108889

0.000202749 0.000202749

0.537063 0.537063

0.665837

9.33333E-05

0.000180676

0.516578

Graphs For the flow through Orifice 0 0

5

10

15

20

25

-1 -2 Flow 1 -3

Flow 2 Flow 3

-4 -5 -6

ME-313, IIT Gandhinagar, Dept. of Mechanical Engineering

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For the flow throgh Mouthpiece 0 0

5

10

15

20

25

-1 -2 Flow 1 -3

Flow 2 Flow 3

-4 -5 -6

Precaution Never fully close the Delivery line and By-Pass line Valves simultaneously.

Errors  

Due to use of stop watch manual errors in timings are introduced. The gauge is not placed perfectly at centre so errors in coordinates are introduced.

Conclusion The coefficient of discharge is 0.57 and coefficient of velocity is 0.709 for an orifice. The coefficient of discharge is 0.53 and coefficient of velocity is 0.704 for a mouthpiece.

-Vrushiket Patil(09003044) Mechanical B’tech 2009

ME-313, IIT Gandhinagar, Dept. of Mechanical Engineering

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