Fluid Mechanics Viscosity Question 282
Question: A wide vessel with a small hole at the bottom is filled with water (density$ {\rho_{1}} $ , height$ h_{1} $ ) and kerosene (density$ {\rho_{2}} $ , height$ h_{2} $ ). Neglecting viscosity effects, the speed with which water flows out is :
Options:
A) $ [2g{{(h_{1}+h_{2})}^{1/2}} $
B) $ [2g{{(h_{1}{\rho_{1}}+h_{2}{\rho_{2}}]}^{1/2}} $
C) $ {{[2g(h_{1}+h_{2}({\rho_{2}}/{\rho_{1}}))]}^{1/2}} $
D) $ {{[2g(h_{1}+h_{2}({\rho_{1}}/{\rho_{2}}))]}^{1/2}} $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ P_{a}+\frac{1}{2}{\rho_{1}}v_{1}^{2}+0 $ $ =Pa+\frac{1}{2}{\rho_{2}}v_{2}^{2}+({\rho_{1}}gh_{1}+{\rho_{2}}gh_{2}) $ $ As,v_{2}«v_{1},,,,,,,,,\therefore ,v_{1}=\sqrt{2g(h_{1}+h_{2}\frac{{\rho_{2}}}{{\rho_{1}}}}) $
BETA
