A) \[0.12\,m\,{{s}^{-1}}\]
B) \[0.62\,m\,{{s}^{-1}}\]
C) \[0.24\,m\,{{s}^{-1}}\]
D) \[0.42\,m\,{{s}^{-1}}\]
Correct Answer: A
Solution :
[a] Here, \[A=10m{{m}^{2}},a=5m{{m}^{2}},\rho =1.06\times {{10}^{2}}kg{{m}^{-3}}\] \[=1060kg{{m}^{-3}},{{p}_{1}}-{{p}_{2}}=22pa\] Speed of the fluid through the wide neck is \[v=\sqrt{\frac{2({{P}_{1}}-{{P}_{2}})}{\rho }}{{\left\{ {{\left( \frac{A}{a} \right)}^{2}}-1 \right\}}^{-1/2}}\] Or \[\frac{A}{a}=\frac{10}{5}=2\] \[\therefore v=\sqrt{\frac{2\times 22}{1060({{2}^{2}}-1)}}=0.12m{{s}^{-1}}\]
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