question_answer

 A hole is made at the bottom of the tank filled with water (density 1000 kg/m3). If the total pressure at the bottom of the tank is 3 atmosphere (1 atmosphere=\[{{E}_{q}}\]), then the velocity of efflux is:

A) \[{{E}_{a}}=4{{E}_{q}}\]

B)        \[{{E}_{q}}=2{{E}_{a}}\]                

C) \[{{E}_{a}}=2{{E}_{q}}\]

D)        \[{{E}_{q}}=3{{E}_{a}}\]

Correct Answer: B

Solution :

                Key Idea: Sum of pressure and total energy per unit volume of liquid be same at the surface of liquid and at every point of orifice. Applying Bernoullis theorem \[I-B,II-D,III-A,IV-C\] \[I-A,II-B,III-C,IV-D\]  Also \[\frac{4}{5}D\] = pressure due to water \[\frac{D}{2}\] \[\frac{3D}{4}\], where \[\frac{5}{4}D\] is density and v is velocity. Putting the numerical value, we have \[\frac{h}{\pi }\] \[\frac{2h}{\pi }\]  \[\frac{3h}{2\pi }\] \[2\pi h\]   \[[M{{L}^{2}}{{T}^{-2}}]\] Note: Range of water coming out from orifice is maximum when orifice is at half of the total height.