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EXPERIMENT 7 : ORIFICE COEFFICIENT MEASUREMENT

INTRODUCTION

From application of Bernoulli’s equation (conservation of mechanical energy for a steady, incompressible, frictionless flow) : ideal orifice outflow velocity at the jet vena contracta (narrowest diameter) is:

vi= 2gh

Where h is the height of fluid above the orifice. The actual flow rate of the jet is defined as:

Qt= Acv

Where Ac is the cross-sectional area of the vena contracta, given by:

Ac= CcAo

Where Ao is the area of orifice and Cc is the coefficient of area contraction and, therefore, Cc<1, hence:

Qt = CcAoCv2gh

The product CcCv is called the discharge coefficient, Cd, so finally:

Qt = CdAo2gh

If Cd is assumed to ...view middle of the document...

The tank is filled to overflow level and the flow control valve is closed.

9. Start a stop watch when the level reaches the first convenient scale mark (noted as h1). Take a reading of the head (h2) at 20 seconds intervals.

Orifice apparatus

RESULT (Constant Head)

No. | Orifice diameter, d,(m) | Head, h(m) | Volume, V(m3) | Time, t(s) | Flow Rate, Qt(m3s) | h0.5(m0.5) | DischargeCoefficient,Cd(m3s) |

1 | 0.003 | 0.400 | 9.20 x 10-4 | 60 | 1.533 x 10-5 | 0.632 | 0.742 |

2 | 0.003 | 0.380 | 9.00 x 10-4 | 60 | 1.500 x 10-5 | 0.616 | 0.742 |

3 | 0.003 | 0.360 | 8.85 x 10-4 | 60 | 1.475 x 10-5 | 0.600 | 0.742 |

4 | 0.003 | 0.340 | 8.50 x 10-4 | 60 | 1.417 x 10-5 | 0.583 | 0.742 |

5 | 0.003 | 0.320 | 8.25 x 10-4 | 60 | 1.375 x 10-5 | 0.566 | 0.742 |

6 | 0.003 | 0.29 | 7.90 x 10-4 | 60 | 1.317 x 10-5 | 0.539 | 0.742 |

CALCULATION (constant head)

vi = 2gh Cc = AcAo

vi = 29.810.40 Cc = 5.473 ×10-67.07 ×10-6

vi = 2.801 Cc = 0.774 , Cc < 1

Qt = vt From the graph:

Qt = 9.2 ×10-460 S = 2.323 x 10-5

Qt = 1.533 × 10-5 m3s Cd = sAo2g

Qt = Acvi Cd = 2.323 × 10-5(7.07 ×10-6)(2(9.81)

Ac = 1.533 x 10-52.801 Cd = 0. 742

Ac = 5.473×10-6 m2

Ao = πd24

Ao = π(0.003)24

Ao = 7.07 × 10-6 m2

RESULT ( varying head)

No. | Bearing head, h(m) | Time, t(s) | h(m) | Cd |

1 | 0.400 | 0 | 0.632 | 0.119 |

2 | 0.384 | 5 | 0.620 | |

3 | 0.378 | 10 | 0.615 | |

4 | 0.365 | 15 | 0.604 | |

5 | 0.352 | 20 | 0.593 | |

6 | 0.340 | 25 | 0.583 | |

7 | 0.327 | 30 | 0.572 | |

8 | 0.314 | 35 | 0.560 | |

9 | 0.301 | 40 | 0.549 | |

10 | 0.289 | 45 | 0.538 | |

11 | 0.279 | 50 | 0.528 | |

12 | 0.266 | 55 | 0.516 | |

13 | 0.255 | 60...

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