A) \[\sqrt{2}\]
B) \[2\sqrt{2}\]
C) 4
D) \[4\sqrt{2}\]
Correct Answer: D
Solution :
Frictional head loss in a pipe \[{{h}_{f}}=\frac{4fl{{v}^{2}}}{2gd}\] \[Q=\frac{\pi }{4}\,{{d}^{2}}v\] or \[v=\frac{4Q}{\pi {{d}^{2}}}\] \[\therefore \] \[{{h}_{f}}=\frac{4fl}{2gd}\times \frac{16{{Q}^{2}}}{{{\pi }^{2}}{{d}^{4}}}=\left( \frac{32fl}{{{\pi }^{2}}g} \right)\times \frac{{{Q}^{2}}}{{{d}^{5}}}\propto \frac{{{Q}^{2}}}{{{d}^{5}}}\] For \[{{h}_{f1}}={{h}_{f2}}\] \[\frac{Q_{1}^{2}}{d_{1}^{5}}=\frac{Q_{2}^{2}}{d_{2}^{5}}\] \[\frac{{{Q}_{2}}}{{{d}_{1}}}={{\left( \frac{{{d}_{2}}}{{{d}_{1}}} \right)}^{5/2}}\] \[={{\left( \frac{20}{10} \right)}^{5/2}}\] \[{{2}^{5/2}}=\sqrt{32}=4\sqrt{2}\]
You need to login to perform this action.
You will be redirected in
3 sec
