question_answer

Water flows steadily through a horizontal pipe of variable cross section. If the pressure of water is P at a point where flow speed is v, the pressure at another point where the flow speed is 2v, is:

A) \[P-\frac{3\rho {{v}^{2}}}{2}\]            

B) \[P-\frac{\rho {{v}^{2}}}{2}\]

C) \[P-\frac{3\rho {{v}^{2}}}{4}\]            

D) \[P-\rho {{v}^{2}}\]

Correct Answer: A

Solution :

\[\operatorname{For} velocity\to  small v\] \[\operatorname{For} voltage \to capital V\] Apply bernoulli?s theorem \[\operatorname{P}+\frac{1}{2}\rho {{v}^{2}}+z={{P}_{1}}+\frac{1}{2}\rho {{(2v)}^{2}}+z\] \[\operatorname{P}+\frac{1}{2}\rho {{v}^{2}}={{P}_{1}}+2\rho {{\operatorname{v}}^{2}}\] \[{{P}_{1}}=P-\frac{3}{2}\rho {{\operatorname{v}}^{2}}\]