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 :
From Bernoulli's equation, the sum of all forms of energy in a fluid flowing along an enclosed path (a streamline) is the same at any two points in the path. Therefore, \[p+\frac{1}{2}\rho v_{1}^{2}=p'+\frac{1}{2}\rho v_{2}^{2}\] Given, \[{{v}_{2}}=2v,\,\,\,\,\,\,\,{{v}_{1}}=v\] \[\therefore \] \[p+\frac{1}{2}\rho {{v}^{2}}=p'+\frac{1}{2}\rho {{(2v)}^{2}}\] \[\Rightarrow \] \[p'=p-\frac{3}{2}\rho {{v}^{2}}\].
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