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) \[{{[2g({{h}_{1}}+{{h}_{2}}({{\rho }_{1}}/{{\rho }_{2}}))]}^{1/2}}\]
Correct Answer: C
Solution :
[c] \[{{P}_{a}}+\frac{1}{2}{{\rho }_{1}}{{v}_{1}}^{2}+0\] \[=Pa+\frac{1}{2}{{\rho }_{2}}{{v}_{2}}^{2}+({{\rho }_{1}}g{{h}_{1}}+{{\rho }_{2}}g{{h}_{2}})\] \[As\,{{v}_{2}}<<{{v}_{1}},\,\,\,\,\,\,\,\,\therefore \,{{v}_{1}}=\sqrt{2g({{h}_{1}}+{{h}_{2}}\frac{{{\rho }_{2}}}{{{\rho }_{1}}}})\]
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