Question

A rectangular trough, 1.9 m long, 0.60 m wide, and 0.35 m deep, is completely full of water. One end of the trough has a small drain plug right at the bottom edge. When you pull the plug, at what speed does water emerge from the hole? Please explain thoroughly.

Answer 1

$From\,\,Bernoulli's\,\,equation\,\, between\,\,point\,\,1\,\,and\,\,point\,\,2 \\\\ P_1+\frac{1}{2}\rho v_1^2+\rho gh_1=P_2+\frac{1}{2}\rho v_2^2+\rho gh_2 \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,......(1)$

$\\ Here,\\ P_1=P_2=P_{atm}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,[\because \,\,both\,\,points\,\,are\,\,opened\,\,to\,\,atmosphere]\\ v_1=0\\v_2=?\\ h_1= 0.35\,\,m\\h_2=0\\ \rho \,\,and\,\,g\,\,are\,\,density\,\,and\,\,acceleration\,\,due\,\,to\,\,gravity\,\,respectively.$

$Now\,\,from\,\,equation\,\,(1)\,\\\\ P_{atm}+\frac{1}{2}\rho \times 0^2+\rho gh_1=P_{atm}+\frac{1}{2}\rho v_2^2+\rho g\times0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,[\because \,\,v_1=0,\,\,\,\,h_2=0]\\\\ \Rightarrow \,\,\rho gh_1=\frac{1}{2}\rho v_2^2\\\\ \Rightarrow \,\,v_2=\sqrt{2gh_1}\\\\ \Rightarrow \,\,v_2=\sqrt{2\times9.81\times0.35}\,\,\,m/s \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,[\because \,\, g=9.81\,\,m/s^2] \\\\ \Rightarrow \,\,v_2=2.620\,\,m/s$

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