Suppose that the tank in Fig. 11.3 empties through a hole of diameter d_o near its bottom, instead of draining through a long pipe. The opening is smooth and rounded on the inside.

Figure 11.3

(a) If viscous losses are negligible, the flow is turbulent, and the liquid level changes slowly, show that the outlet velocity is

This relationship between the velocity through a rounded opening and the liquid height above the opening is called Torricelli's law, after the Italian scientist Evangelista Torricelli (1608–1647).

(b) Determine H(t) and the time for the tank to become half-empty (t_1⁄2).

Transcribed Image Text:

H(0) Air P= Po Liquid V(0) |R | Q(1) L Air P= Po