question_answer

Water is moving with a speed of 5.0 m/s through a pipe with a cross area of 4.0 \[c{{m}^{2}}\]. The water gradually descends 10 m as the pipe increases to 8.0 \[c{{m}^{2}}\]. If the pressure at the upper level is \[1.5\times {{10}^{5}}\] Pa, the pressure lower level will be

A)  \[2.8\times {{10}^{5}}\] Pa         

B)  \[2.6\times {{10}^{5}}\] Pa

C)  \[2.4\times {{10}^{5}}\] Pa        

D)  \[2.1\times {{10}^{5}}\] Pa

Correct Answer: B

Solution :

                 From Bernaullis theorem                                 \[{{p}_{1}}+\rho gh+\frac{1}{2}pv_{1}^{2}={{p}_{2}}+\frac{1}{2}pv_{2}^{2}\]                                 \[15\times {{10}^{5}}+{{10}^{3}}\times 10\times 10+\frac{1}{2}\times {{10}^{3}}\times 25\]                                                 \[={{p}_{2}}+\frac{1}{2}\times {{10}^{3}}\times \frac{25}{4}\]                              \[15\times {{10}^{5}}+{{10}^{5}}+\frac{25}{2}\times {{10}^{3}}={{p}_{2}}+\frac{25}{8}\times {{10}^{3}}\]                                 \[{{p}_{2}}=\frac{25\times 83\times {{10}^{3}}}{8}\]                                 \[=259.375\times {{10}^{3}}=2.6\times {{10}^{5}}Pa\]