Toricelli's principle and fluid flow

[Micko]

Hello to all,

I've been reading an article about modeling in which there is Toricelli's principle stated: rate of fluid flow through a hole in a tank is proportional to square root of its height. That is easy to understand and to derive this using Bernoulli formula. I have derived this to a simple case of cylindrical tank. I have found that for spherical tank there is some kind of constant that depends of the type of the fluid.
I cannot understand this. Can anyone explain why it is Cd = 0.6 for this particular case. How this Cd is determined? (Please look in the attachment).

Thank you

 

[tiny-tim]

Hello Micko!

From "[URL …

The actual speed of efflux differs somewhat from that given by Torricelli’s law and depends on the shape and size of the orifice; the viscosity of the liquid; and the flow rate, or discharge.

To take these factors into account, a correction coefficient is introduced, and the equation given above then takes on the form v = φ√(2gh).

The value of φ is less than unity. For small circular orifices and high Reynolds numbers φ is equal to 0.94–0.99. Values of φ for orifices of other shapes and sizes are given in hydraulics handbooks.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979).​