A) \[5\,m\,{{s}^{-1}}\]
B) \[10\,m\,{{s}^{-1}}\]
C) \[25\,m\,{{s}^{-1}}\]
D) \[50\sqrt{10}\,m\,{{s}^{-1}}\]
Correct Answer: A
Solution :
According to Bernoulli's theorem \[{{P}_{1}}+\frac{1}{2}\rho v_{1}^{2}={{P}_{2}}+\frac{1}{2}\rho v_{2}^{2}\] (i) From question,\[{{P}_{1}}-{{P}_{2}}=3\times {{10}^{5}},\frac{{{A}_{1}}}{{{A}_{2}}}=5\] According to equation of continuity \[{{A}_{1}}{{v}_{1}}={{A}_{2}}{{v}_{2}}\]or,\[\frac{{{A}_{1}}}{{{A}_{2}}}=\frac{{{v}_{2}}}{{{v}_{1}}}=5\]\[\Rightarrow \]\[{{v}_{2}}=5{{v}_{1}}\] From equation (i)\[{{P}_{1}}-{{P}_{2}}=\frac{1}{2}\rho \left( v_{2}^{2}-v_{1}^{2} \right)\] or\[3\times {{10}^{5}}=\frac{1}{2}\times 1000\left( 5v_{1}^{2}-v_{1}^{2} \right)\] \[\Rightarrow \]\[600=6{{v}_{1}}\times 4{{v}_{1}}\]\[\Rightarrow \]\[v_{1}^{2}=25\] \[\therefore \]\[{{v}_{1}}=5m/s\]
You need to login to perform this action.
You will be redirected in
3 sec
