Chapter 25, Problem 20P

A spherical tank has a circular orifice in its bottom through which the liquid flows out (Fig. P25.20). The flow rate through the hole can be estimated as

$Q_{\text{out}}=CA\sqrt{2gH}$

where $Q_{\text{out}}=$ outflow (m3/s), $C=$ an empirically-derived coefficient, $A=$ the area of the orifice (m2), $g=$ the gravitational constant $\left(=9.81{\text{ m/s}}^2\right)$, and $H=$ the depth of liquid in the tank. Use one of the numerical methods described in this chapter to determine how long it will take for the water to flow out of a 3-m-diameter tank with an initial height of 2.75 m. Note that the orifice has a diameter of 3 cm and $C=0.55$.