First slide

Fluid dynamics

Question

A cylindrical vessel of height hand base area S is filled with water. An orifice of area s < < S is opened in the bottom of the vessel. Neglecting the viscosity of water determine how soon all the water will flow out of the vessel?

Difficult

A

Time = $\frac{S}{s} \sqrt{\frac{2 h}{g}}$
B

$Time = \frac{s}{S} \sqrt{\frac{g}{2 h}}$
C

$Time = Ss \sqrt{2 gh}$
D

$Time = \frac{2 h}{g} \sqrt{\frac{S}{s}}$

Solution

$W h e n t h e d e p t h o f l i q u i d i s y, a p p l y i n g e q u a t i o n o f c o n t i n u i t y w e c a n w r i t e, - S d y = s \sqrt{2 g y} d t \Rightarrow \int_{0}^{t} d t = - \frac{S}{s \sqrt{2 g}} \int_{0}^{h} y^{- \frac{1}{2}} d y \Rightarrow t = \frac{S}{s} \sqrt{\frac{2 h}{g}}$

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