A Simple Model for the Calculation of the Fluid Discharge from a Small Orifice

• Georgios M. Horsch ^[1]
  1. [1] University of Patras

     University of Patras

     Dimos Patras, Grecia

     
• Localización: The Physics Teacher, ISSN 0031-921X, Vol. 58, Nº. 2, 2020, págs. 113-115
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • One of the easily accessible results in elementary fluid mechanics is the so-called Torricelli’s theorem (or law), which states that the velocity Uth of the fluid exiting from an orifice at depth h from the free surface of a container filled with fluid, is the same as the velocity of a free-falling body from rest over a height h. This simple result can be verified experimentally by several methods, e.g., by measuring the parabolic path of the free jet exiting from the container and back-calculating its exit velocity. It turns out that the ratio of the experimental velocity, Uexp, to the theoretical velocity, Uth, called the velocity coefficient Cu, varies from 0.95 to 0.99. Yet, if one was to calculate the outflow volumetric flowrate (or discharge or rate of efflux) from the container by multiplying the Torricelli velocity by the cross-section area of the orifice, and compare it to the flowrate derived by dividing the volume of the bucket into which the jet flowed by the time it took to fill the bucket, one would get a large discrepancy, which, in view of the value of Cu, cannot be attributed to the deviation of the experimental velocity from the Torricelli value. This result seems paradoxical. It offers, therefore, an excellent opportunity to clarify important details in the application of simple fluid mechanics equations, and in addition to introduce at an early stage the concept of producing an approximate result through flow modeling, as we shall see below.